Guest contributors Darioosh Naderi and Mark Marshall of Silicon Sensing look at how far the technology has come and why it’s poised to disrupt the market.

For years, manufacturers have focused on the consumer and industrial grade performance that MEMS inertial technology provides, with many in the industry assuming that’s as far as MEMS capabilities can take them. That perception is beginning to shift, though, with several companies proving their MEMS inertial sensors are capable of achieving tactical performance levels—and that’s changing the game.

When users switch to high-performance MEMS sensors, they’re often surprised with the results, Silicon Sensing’s Head of Business Development Darioosh Naderi said. The level of performance provided goes well beyond their expectations, with the solutions displacing fiber optics and other technologies, while demonstrating they can perform exceptionally well over a wide range of environments. 

As strong as it is today, MEMS certainly hasn’t reached its limits. The technology has so much potential in terms of the capabilities and performance it can provide in the future, helping to solve many of the challenges the industry faces. Companies like Silicon Sensing are working to advance MEMS technology and unlock its full potential.

“There’s a state of flux right now, and companies are starting to go further with the technology,” Silicon Sensing Chief Engineer Mark Marshall said. “The accepted benefits of MEMS really are their lower size, weight and power consumption—as well as their potential for mass manufacturing, which keeps the cost lower than traditional inertial technology. Alongside these, two lesser-known benefits are their robustness and reliability—a consequence of the lack of moving parts in each unit. This means MEMS products will maintain performance in very harsh environments.” 

Marshall continues: “There is no doubt there remains huge, untapped potential in MEMS-based technology, which has been limited to date by its ability to deliver market-disruptive performance.”

That disruption, however, is on the horizon as technological advances mean a number of inertial sensors are now demonstrating navigation grade performance. 

How MEMS Compares

There are various technologies that can be leveraged in inertial systems, all with pros and cons. “Mechanical gyros, for example, have been around for years and are a well understood, mature technology,” Marshall said. “But because they have moving parts, they need more maintenance, cost more, and aren’t as robust as MEMS alternatives.”

“Mechanical systems typically need to be recalibrated and must go through a certification period,” Naderi explained. “They may also require extensive maintenance, such as work to replace complex, well-balanced bearings.”

“Ring laser gyros (RLG) have advantages over mechanical systems,” Marshall continued, “with the biggest being their precision performance. RLG unit size can be an issue, but they are becoming smaller as manufacturing processes improve. However, they are not the most affordable solution. The cost of these devices is much higher than both mechanical systems and MEMS.”

“Fiber optic gyros (FOG), another option, have an inherently high bandwidth that addresses noise issues and delivers excellent performance. But, again, size can be an issue because it is necessary to wind a longer coil to achieve higher performance levels. They also have a higher price point.”

As the performance of MEMS inertial sensors continues to advance, this technology is now starting to offer the capability and performance levels needed by applications with much stricter stability and precision requirements. This is beginning to render them a viable and affordable inertial option, even for applications that call for tactical grade performance, and beyond. 

Getting to Navigation Grade 

“Over the last 20 years, MEMS inertial sensors have continued to improve,” Marshall explained, “with improvements made in a variety of areas including bias, drift, noise, scale factors and angle random walk.” MEMS inertial sensors that have traditionally been used for industrial grade applications are finding their way into more tactical and navigation-grade applications that demand higher precision and lower drift rates.

“There are incremental improvements available today,” Marshall continued. “But we’re also focusing on that stepwise improvement, that order of magnitude improvement, that will see MEMS inertial sensors truly disrupt the market for higher-end technologies. Silicon Sensing is just one of many companies with a focus on working toward navigation grade inertial sensors at reduced cost, size weight and power (CSWaP) with encouraging levels of success.” 

“For companies like Silicon Sensing, the real goal is to enable our partners to solve their guidance or navigation challenges, whilst recognizing the need to work with increased levels of signal disruption, an increased need for prolonged autonomy, and a requirement to operate in more extreme environments across land, air, sea and space.”

It basically comes down to solving two problems: Enabling users to gyrocompass in an often intense, dynamic environment, and providing aided navigation in a frequently GNSS denied environment.

“Today, you can take a Silicon Sensing MEMS sensor and rotate it around a step motor to find true north,” Naderi explained. “This is ideal for users, such as the downhole drilling market, who need to know where true north is quickly and unaided.” 

“Right now, companies are paying tens of thousands of dollars for complex and costly systems that allow them to gyrocompass when in reality they might not need all the performance their chosen solution provides,” he said. “Similarly, they may not be able to use a magnetometer because, while the performance may be sufficient, it may be too susceptible to local magnetic fields. The ability to provide a device that is capable of true north seeking without external aiding, doesn’t suffer from local interference, and has the size and price of a MEMS unit will significantly disrupt the market.” 

“To solve the gyro-compassing problem, solutions need to offer sub-one degree an hour for residual bias,” Naderi explained. “But for navigation-grade performance, you have to get much lower, again with different markets and applications having different requirements in terms of performance.” 

“The main goal is to get bias and associated parameters as low as possible. This will give us that order of magnitude ‘stepwise’ improvement Mark talks about needing to achieve,” Naderi explained. “Improving noise and scale factor are also priorities.” 

“And that’s where you say: What problems are you trying to solve and what are your key parameters. Most will say they are scale factor, bias and angle random walk,” Marshall said. “If you look at our gyro technology as standalone sensors with their own electronics, we are closing the gap to navigation grade in many parameters today. Some of our customers are virtually there without any aiding sources and without any mechanical rotation or gyrocompass. They are about to cross that threshold. But that’s just the gyros. There are also accelerometers to consider.”

Extremes of temperature is another key consideration. 

“It’s not just sitting on the bridge of a vessel at 25 degrees Celsius forever,” Marshall said. “Getting the sensors to work in any environment, from minus 55 degrees all the way up to plus 85 degrees, is a real challenge. We have customers operating at all temperature brackets—and in even more extreme situations.” 

A Look at the Market

Today, the main customers relying on tactical MEMS for an IMU are the surveying and mapping markets, 
marine gyro-compassing customers, and defense applications for guided munitions, Naderi explained. “One of the biggest markets primed for disruption is avionics. The performance parameters that must be met are clear, and while this won’t be easy, it is within reach for MEMS manufacturers.” 

The aerospace market is an obvious candidate for MEMS, Naderi believes, along with broader defense applications such as tactical wheeled vehicles and any theater of conflict where GNSS jamming and spoofing are concerns. In fact, MEMS would have application almost anywhere a ring laser gyro is currently in use. 

And because MEMS technology is a fraction of the price and size of other options, “it opens doors to applications tomorrow that we don’t even know exist today,” Naderi believes. 

“We could be creating new applications. Just one area with huge potential would be in the growing unmanned markets,” Naderi said. “Longer endurance and beyond visual line of sight is becoming more feasible. And when you have a navigation system that doesn’t rely on a constant external input, it presents so many new opportunities. It disrupts by definition.” 

Advancing the Technology

Silicon Sensing already has a patented high-performance gyro that has gone through multiple design iterations. Just one area the company is focused on today is material use, Marshall explained. “A key avenue we’re looking at is new novel materials in the MEMS structure itself. That’s something we believe there’s quite a bit of mileage in. There’s really some exciting work going on.” 

This includes looking at the detailed construction of the gyro and how the layers are made up, exploring re-positioning the MEMS within another structure with the ASICs to control them, and working on complex discreet electronics to drive the gyros optimally such as improving how information outputs are delivered. The company is also making advances in the way sensors are calibrated. 

“So, we are looking at a whole system on every front and we’re seeing many innovations we can introduce,” Marshall said. 

Critically, the company is also exploring improvements for more efficient volume production. 

Silicon Sensing has three different modes of operation for its gyros, Naderi explained. Some are driven with magnets, some are capacitive and others use a thin film PZT material. 

“If we look at the inductive gyro, we can improve the magnetic circuitry in it and gain benefits in the scale factor almost immediately,” Naderi said. “If we look at the design of the gyro, which is on a base, and if we change the base without changing the fundamental design, that gives us benefits in terms of bias. So, we can take the exact existing design, existing manufacturing process, make a minor tweak, and that can give, in some cases, a three-fold improvement. And we can do that today.”

“MEMS feature layers of material, including silicon, metal and glass,” Naderi said. “The thermal characteristics of these different layers is a key area of consideration. Manufacturers can look at different techniques to try to improve on existing designs without going back to the drawing board.” 

“You look at the improvements we can make to an existing drive type, with the magnet and with the structure it’s on, then you look at the material mismatching, so already you’ve got some ground,” Naderi said. “Then you look at the capacitive type gyros that are three millimeters or four millimeters, we can make them larger, and possibly apply some very clever real-time balancing techniques. And we can get a sense of a performance improvement that could be four times better than we have today. Versions of these sensors have been built and tested. Our focus now is on bringing that product to market with a set of electronics that will get the best out of the sensor, whilst maintaining the attractive size and cost of a typical silicon MEMS inertial product.”

Steering the Development

Silicon Sensing has its own MEMS foundry, enabling the company to produce parts at a much lower cost and at higher volumes. It also allows them to be far more involved in the design and manufacturing than those who outsource production. 

“We have the flexibility to be able to tweak the designs and we work very closely with the foundry processing, calibration and engineering teams. We have ultimate control,” Marshall explained, “so we can do all the finite element modeling and we can steer the development.” 

The foundry’s sole purpose is to turn out MEMS inertial sensors, Naderi explained, so the team has acquired a wealth of knowledge about the products that a third-party foundry just wouldn’t have. 

“It could take years to get a prototype that ticks all the boxes out of a third-party foundry,” Naderi said. “Our foundry has a very quick turnaround, speeding up product development and time to market. And it is a powerful asset, having decades of knowledge and foundry expertise.”

Looking Ahead

In the next three to five years, Naderi expects to see more companies pushing toward navigation grade MEMS offerings, with those small, iterative steps making revolution possible. The disruption these sensors will cause is closer to five years out. It comes down to putting everything together in a package that delivers what’s required and costs significantly less than alternative technologies. Accelerometers are also advancing. Silicon Sensing is working on offerings that have the required performance, with some promising initial results. However, formal qualification programs take time, as do the vital updates to production lines that will allow reliable production of these much higher performing sensors. 

“In some respects, the design of a navigation grade MEMS gyro exists today. Bringing it all together in terms of the drive electronics and reliable, full-scale production is our main challenge,” Naderi concluded. 

Authors

Dr. Mark Marshall was appointed Chief Engineer of Silicon Sensing Systems in February 2023 having joined Silicon Sensing in 2017 as the lead engineer on numerous inertial programs. Previously, Dr. Marshall worked as a senior research engineer in the field of laparoscopic electro-surgical instruments, with many patents and refereed papers. He has a first class honors degree in Computer Aided Engineering, an MSc in Advanced Manufacturing Systems and a PhD from the University of Cambridge.

Darioosh Naderi is the sales, marketing and business development lead for Silicon Sensing Systems Ltd (SSS). SSS is a leading provider of silicon micro electro-mechanical systems (MEMS)-based inertial sensors and systems, including gyros, inertial measurement units (IMU) and accelerometers. Mr. Naderi has worked in business development and product strategy within Silicon Sensing, and within one of its parent companies, for some five years.

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This is the most efficient way to combine INS with aiding data. Here’s a look at the key principles and benefits.

Inertial navigation enables self-contained navigation in any environment. To reduce drift in INS outputs, sensor-fusion mechanizations use data from various aiding sources (such as GNSS, maps, electro-optical sensors, etc.). A complementary fusion methodology represents the most efficient way to combine INS with aiding data. This column discusses its key principles and main benefits.

Navigation Architecture

Figure 1 shows a high-level diagram of complementary sensor-fusion with inertial navigation.

The algorithm uses differences between aiding measurements and their INS-based predictions as inputs to the complementary estimator. An Extended Kalman Filter (EKF) is the most common form of the complementary estimation, however, other estimation methods (such as particle filters and factor graphs) have been applied as well. 

Example Implementation

To provide insights into complementary filter design aspects, this section considers an example case of loose GNSS/INS integration with the EKF-based fusion. The Kalman filter mechanization is completely defined by (i) state vector X, (ii) state transition matrix F, (iii) process noise covariance Q, (iv) measurement (or observation) vector z, (v) observation matrix H, and (iv) measurement error covariance R. Once these six terms are defined, recursive Kalman filter updates are applied using standard filter equations. The INS error propagation defines the first three terms. The propagation mechanism was considered in a previous Inertialist column (see May/June 2022 issue of Inside GNSS). To complete the integrated system mechanization, we need to define the remaining three terms. 

For loose integration, complementary position observables are formulated as differences between INS and GNSS position solutions (rˆ_INS and rˆ_GNSS):

where δr is the INS position error and ε_r is the GNSS position measurement error vectors, respectively. Note the update rate of INS solution is generally higher than that of GNSS. Hence, the observation update at t_n is applied only if GNSS position is available at that time. Otherwise, the complementary filter relies on prediction with state estimates being assigned their predicted values. 

Additionally, the formulation makes two other simplifications. First, INS and GNSS solutions are assumed to arrive at the exact same time (i.e., stay completely synchronized). Generally, this is not the case and timing adjustments must be made. The adjustment can be performed by propagating INS navigation states to the time of validity of GNSS measurements. Second, the inertial measurement unit (IMU) and GNSS antennas are assumed to be collocated with each other (i.e., their relative lever arm vector is zero). Equation 1 needs to be updated to include a lever-arm term for non-zero lever-arm cases.

The observation matrix H defines how elements of the state vector project into measurement observables. This matrix has a size of K×P, where K is the number of scalar measurements and P is the number of elements in the state vector. For position updates (three position components) and a 15-state INS error model (including position, velocity and attitude errors, and gyro and accelerometer biases), H has a size of 3×15. Position error states directly project into the observation vector, while the contribution of other error states is zero. Hence, the H matrix is formulated as:

where I_(3×3) and 0_(3×3) are the 3×3 unit matrix and zero matrix, respectively. 

Formally, the observation matrix is derived by taking partial derivatives:

where: 

H_k,p is the element of the observation matrix that corresponds to its k^th row and p^th column; 

z_k is the k^th element of the observation vector; and, 

X_p is the pth element of the state vector. 

It can be readily verified that when partial derivatives of the observation vector in Equation 1 are computed with regard to the elements of the state vector, this results in the observation matrix in Equation 2.

By definition, the measurement error covariance R is:

where E[ ] denotes the mean value and ^T is the matrix transpose operator.

The Kalman filter assumes that measurement errors are zero-mean Gaussian. R is a diagonal matrix when errors in different GNSS position components are not correlated with each other:

where σ_x , σ_y and σ_z are standard deviations of x, y and z position errors, respectively. 

This example of loosely coupled GNSS/INS can be extended to other complementary sensor fusion mechanizations such as tightly coupled GNSS/INS and fusion with other aiding data sources (e.g., bearing angles to visual landmarks at known or unknown locations). The INS system propagation remains the same, but the state vector may have to be augmented by error states associated with the aiding sensor (such as GNSS receiver clock error states and misorientation between the IMU and video camera). The complementary observations are formulated in a similar manner, i.e., as differences between actual aiding measurements and their INS predicted values, for example, between measured and predicted GNSS pseudoranges. The observation matrix H is derived by taking partial derivatives of the measurement observables similarly to Equations 2 and 3. Finally, the measurement noise matrix R is formulated based on measurement noise covariances. 

Main Benefits

As compared to the full-state formulation (i.e., direct estimation of the navigation states), the main benefit of a complementary filter for GNSS/INS integration is a significantly simplified modeling of state transition. Inertial errors are propagated over time instead of propagating navigation states themselves. In this case, the process noise covariance matrix, Q, is completely defined by the stability of INS sensor biases, as well as sensor noise characteristics. On the contrary, modeling of actual motion generally needs to accommodate different motion segments (such as a straight flight versus a turn maneuver), which can require ad hoc tuning. An adaptive tuning of the Q matrix may be required to optimize the performance. 

To illustrate this benefit, Figures 2 through 4 show example simulation results. A filtering of noisy GNSS position is considered. The motion trajectory includes two straight segments and a 180 degree turn maneuver. Figures 2 and 3 show outputs of a Kalman filter that does not use the INS and model navigation states instead (more specifically, a constant-velocity motion model is applied). In Figure 2, a smaller value of the system noise matrix (Q-matrix) is used. This allows for an efficient smoothing of GNSS measurement noise. However, during the turn (when non-zero acceleration is introduced and the constant-velocity motion model becomes invalid), position errors increase substantially. Increasing the system noise matrix increases the measurement feedback into the Kalman filter and helps to mitigate the divergence during the turn as shown in Figure 3. However, it comes at a cost of increased estimation noise.

The dynamic modeling/noise smoothing trade-off is eliminated when a complementary GNSS/INS Kalman filter is applied as shown in Figure 4. In this case, the system (i) substantially suppresses the measurement noise (similarly to Figure 2), and (ii) accurately follows the motion dynamic (similarly to Figure 3). 

Another benefit of the complementary estimation is the ability to linearize the state propagation and use computationally efficient linear estimation techniques. Specifically, propagation of navigation states through INS mechanization is a non-linear process. In contrast, time-propagation of inertial errors into navigation outputs can be efficiently linearized. As a result, the complementary filter can benefit from linear filtering techniques (such as an extended Kalman filter) without the need for nonlinear estimation methods such as an unscented Kalman filter and particle filter.

Observability of Error States 

State observability of the complementary sensor-fusion is one of the key aspects influencing system performance. To provide an insight into it, this section considers a two-dimensional (2D) simulation of a loosely coupled GNSS/INS, which is illustrated in Figure 5. 

GNSS position updates are used for INS drift mitigation. Acceleration due to gravity is in the direction opposite to the z-axis. The platform has a constant absolute velocity value of 20 m/s. The trajectory starts with a straight motion segment, follows it by a climb (with turning of the IMU body-frame), and completes with a straight motion. 

Inertial sensor errors were simulated as follows:

• Gyro drift: first-order Gauss-Markov process, standard deviation is 50 deg/hr, correlation time is 1000 s;

• Accelerometer bias: first-order Gauss-Markov process, standard deviation is 1 mg, correlation time is 1000 s.

GNSS position errors were simulated as zero-mean Gaussian processes with a standard deviation of 1 cm. This position performance corresponds to a carrier phase-based RTK solution. INS and GNSS update rates were 100 Hz and 1 Hz, respectively.

Figure 6 shows estimates of angular errors (attitude and gyro drift) and accelerometer biases. 

As shown in Figure 6, attitude error and x-accelerometer bias cannot be estimated separately (residual estimation errors remain) during the initial straight segment. Their estimates converge to true values after the climb starts and sufficient motion dynamics are accumulated for the error state separation. 

The plots provide initial insight into the influence of motion dynamics on the observability of INS error states. As shown in Figure 6, there is a residual attitude error that remains uncompensated during the straight motion phase. The estimate of the z-accelerometer bias rapidly converges to its true value while its x-accelerometer counterpart cannot be estimated. Both attitude error and x-accelerometer bias estimates converge to their true values shortly after the climb starts at about 30 seconds into the simulation.

This phenomenon can be explained as follows. Essentially, the Kalman filter numerically differentiates position error states into acceleration error and then separates the latter into attitude and bias error terms. For simplicity, consider a 2D case where (i) body-frame is aligned with the navigation frame; and, (ii) accelerometer biases, b, and angular orientation error, δα, are constant. INS does not take advantage of the known angular orientation (i.e., the fact that body and navigation frames are aligned with each other) and integrates gyro measurements into attitude. In this case, the navigation-frame acceleration error is:

For constant-velocity motion:

The z-bias component can be directly estimated from the z-acceleration error, which, in turn, is estimated from position error observations. However, observations of the x-acceleration error over time are rank-deficient. This does not allow for the separation between bias and attitude error terms. The filter balances their contribution into acceleration error but cannot estimate them individually. 

When time-varying acceleration is applied along the z-axis, the observation model in Equation 8 changes into:

When this system is observed over time, it has a full rank and bias and attitude error terms can now be estimated separately. This is what happens in Figure 6 after the platform starts climbing. 

Clearly, when centimeter accurate GNSS position is available all the time, it is not critical to estimate individual INS error terms. However, the observability aspect becomes more critical when GNSS outages are present. To illustrate, we consider two outage scenarios as shown in Figure 7. 

Outage 1 starts before the climb when attitude and bias errors cannot be separated. Outage 2 starts during the climb after the sufficient error state convergence is achieved. Figure 8 compares GNSS/INS position performance for these two outage cases. 

As shown in Figure 8, INS drift during the second outage is reduced significantly due to the ability to separate attitude and bias error states during the climb maneuver. Particularly, the maximum error growth is reduced (from 2.7 m and 5 m for x and z position components to 0.5 m and 2 cm, respectively) for the second outage scenario. This error reduction is due to the ability to separately estimate angular and linear INS error terms by using the motion dynamics.

Conclusion

Complementary sensor fusion is the most efficient approach to fuse INS with aiding sensors. The methodology (i) models inertial error dynamics rather than modeling full motion states, and (ii) applies differences between actual measurements and their INS-based predictions as estimation observables. One of the key benefits is the ability to use computationally efficient linear estimation techniques (such as an extended Kalman filter) for the error-state propagation. Another benefit is a straight-forward choice of the system noise matrix (that is fully defined by INS error models) without the need to make a trade-off between the system’s ability to suppress the measurement noise and accurately follow a platform’s motion (e.g., during a straight flight and a turn maneuver) dynamics. This column also illustrated that the observability of inertial error states is generally impacted by the motion dynamics, which can have substantial influence on navigation performance during GNSS outages. 

The post The Inertialist: Complementary Sensor Fusion appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

The main principals of fusing inertial navigation with other sensors. 

As discussed in previous columns, inertial navigation systems (INS) enable a fully self-contained navigation capability. Yet, integration is a fundamental operation of INS mechanization. Input measurements of nongravitational acceleration (also referred to as specific force) and angular rate vectors are integrated into attitude, velocity and position outputs. Measurement errors are integrated as well, which leads to the output drift over time. As a result, even the highest-quality inertial systems must be periodically adjusted.

To mitigate inertial drift, INS has been coupled with other navigation aids. GNSS is the most popular one, but numerous other aiding sources also have been applied such as electro optical (EO) sensors (vision and LiDAR), radars (including synthetic aperture radar), terrain data bases, magnetic maps, vehicle motion constrains, and radio frequency (RF) signals of opportunity (SOOP) to name a few. In this column, we consider the main principles of fusing inertial navigation with other sensors.

Sensor Fusion Architecture 

Figure 1 illustrates the sensor-fusion approach.

INS is used as a core sensor. It is augmented by aiding navigation data sources (such as GNSS or LiDAR) to mitigate the drift in inertial navigation outputs. Aiding sources generally rely on external observations or signals that may or may not be available. Therefore, they are treated as secondary sensors. 

When available, aiding measurements are applied to reduce the drift in inertial navigation outputs. In turn, inertial data can be used to improve the robustness of an aiding sensor’s signal processing component, which is generally implemented in a form of motion compensation. For instance, INS-based motion compensation can be used to adjust replica signal parameters inside a GNSS receiver’s tracking loops to increase the signal accumulation interval, thus recovering weak signals and mitigating interference (jamming, spoofing and multipath). Another example is compensation of motion-induced distortions in EO imagery. 

To mitigate inertial drift, sensor fusion uses the complementary estimation approach, which is illustrated in Figure 2. 

As shown in Figure 2, differences between INS and aiding observations (zˆ_INS and zˆ_Aiding) are applied to estimate inertial error states instead of navigation states. Error state estimates are then subtracted from the INS solution, thus providing the overall navigation output. Specific structure of the observation vector z depends on the integration mode.

The complementary formulation estimates INS error states rather than estimating full navigation states. As compared to the full-state formulation, the main benefit of complementary estimation is a significantly simplified modeling of state transition. Inertial errors are propagated over time instead of propagating navigation states themselves. In this case, the process noise is completely defined by stability of INS sensor biases, as well as sensor noise characteristics. On the contrary, modeling of actual motion generally needs to accommodate different motion segments (such as a straight flight versus a turn maneuver), which can require ad hoc tuning to optimize the performance. Moreover, propagation of navigation states through INS mechanization is a non-linear process. 

In contrast, time propagation of inertial errors into navigation outputs can be efficiently linearized. As a result, complementary filters can generally rely on computationally efficient linear filtering techniques such as an extended Kalman filter (EKF) while reserving non-linear estimation approaches, such as particle filters and factor graphs, only to cases where aiding measurements are non-linear/non-Gaussian by nature, such as database aiding updates. 

The integrated system operates recursively on the inertial update cycle. Every time a new measurement arrives from an inertial measurement unit (IMU), INS navigation computations are performed followed by the prediction update of the complementary filter. If an aiding navigation output becomes available after the previous IMU update, it is used to compute complementary filter observables and apply them for the estimation update. Otherwise, error estimates are assigned their predicted values and computations proceed to the next inertial update. 

Integration Modes

The three main sensor fusion modes include loose coupling, tight coupling and deep coupling. They perform sensor fusion at the navigation solution level, measurement level and signal processing level, respectively. Their key features are:

Loose coupling 

Figure 3 shows a high-level diagram of a loosely coupled system mechanization that fuses inertial and aiding data at the navigation solution level.

Aiding sensors generally include a signal processing part and a navigation solution part. The signal processing part receives navigation related signals and measures their parameters. For example, GNSS receiver tracking loops measure parameters (pseudoranges, Doppler frequency shift and carrier phase) of received GNSS signals. Another example is a LiDAR time-of-flight measurement that is directly related to the distance between the LiDAR and a reflecting object. Signal parameter measurements are then applied to compute the navigation solution. For example, GNSS pseudoranges are used to compute the GNSS receiver position. Changes in distances to reflecting stationary objects are exploited to compute the change in the LiDAR’s position. 

Note the navigation solution can only be computed if a sufficient number of signal measurements is available. For example, at least four pseudoranges must be available to compute the GNSS-based position. At least two non-collinear lines must be extracted from an image of a two-dimensional (2D) LiDAR image to compute a 2D position. Depending on the aiding sensor, the observation vectors, zˆ_INS and zˆ_Aiding can include, position, velocity, attitude and their combinations. 

The loosely coupled approach operates at the navigation solution level and does not require any modifications to the aiding sensor. Yet, a key limitation of loosely coupled fusion is it cannot estimate INS error states unless a complete aiding solution is available. For instance, loosely coupled GNSS/INS cannot update inertial drift terms in an urban canyon when the GNSS position cannot be computed even though limited satellite measurements may still be available. As a result, useful aiding information is inherently lost.

Tight coupling

Tight coupling applies measurements of aiding signal parameters for the INS drift mitigation. As compared to loose coupling, the main benefit of tightly coupled systems is the ability to (partially) update INS error states even when insufficient aiding data are available to compute a full navigation solution, such as when less than four GNSS satellites are visible. 

For such cases, a GNSS only position solution cannot be calculated. As a result, loosely coupled systems experience a complete GNSS outage. In contrast, the tightly coupled method can use limited GNSS measurements, thus enabling (partial) mitigation of the INS error drift. Another example of tight coupling is an EO-aided INS where landmark features are extracted from imagery data and then applied for the INS drift mitigation. When limited landmarks are present, and the system cannot compute an EO-based position update, individual feature measurements still enable INS drift mitigation within the tightly coupled architecture. 

Figure 4 illustrates the tightly coupled approach. 

For tight coupling, the INS error estimation generally has to be augmented with the estimation of aiding sensor errors. For example, GNSS receiver clock errors (bias and drift) are included into the system state vector for the GNSS/INS integration case. Image-aided inertial augments the system states with misalignment between INS and camera (or LiDAR) sensor frames. 

Similarly to loose coupling, complementary estimation observables are formulated as differences between actual measurements and their INS-based estimates. To illustrate, for GNSS/INS, complementary pseudorange observations are formulated as differences between their INS estimates and GNSS measurements: 

In Equation 1,  is the geometrical range to the k^th satellite. It is estimated using INS position solution, xˆ_INS, and satellite position vector, :

where:

In Equation 2, x is the true position, δx_INS is the INS position error, r^(k) is the true range between the receiver and satellite k, (,) is the vector dot product, and | | is the Euclidian norm. 

The GNSS pseudorange measurement model is:

where c is the speed of light, δt_rcvr is the receiver clock bias, and ε is the pseudorange measurement error that includes thermal noise, multipath, atmospheric delays, and orbital errors.

From Equations 3 and 4, the complementary observation is formulated as:

The EKF is commonly applied to estimate INS error states and GNSS receiver clock states.

As mentioned previously, the main benefit of tight coupling is the ability to implement estimation updates even when limited signal measurements are available. As a drawback, it may require a firmware modification of the aiding sensor to enable access of its signal measurements, which are also referred to as raw measurements.

Deep coupling

Deep coupling fuses inertial and aiding data at the signal processing stage. This approach keeps measurement-domain estimation of INS error states (as in tight coupling) and adds INS-based motion compensation to robustify the signal processing component of the aiding sensor. Figure 5 shows a high-level block diagram of the deeply coupled approach. 

For GNSS/INS, various deeply integrated implementations, which are also referred to as ultra-tight coupling, have been reported in the literature. Both deep and ultra-tight systems are designed to improve the post-correlation signal to noise and interference ratio (SNIR). The distinction between deep and ultra-tight approaches can be somewhat vague. Ultra-tight coupled implementations generally maintain GNSS tracking loops and use inertial aiding to narrow their bandwidths. Deep integration operates directly with GNSS IQ samples. This is done by (i) processing IQ data with a combined pre-filter/Kalman filter scheme; or, (ii) explicitly accumulating IQ samples over an extended time interval (i.e. beyond the unaided receiver implementation). 

Deep coupling maximizes the benefits of sensor fusion as it fuses inertial and aiding data at the earliest processing stage possible, thus eliminating any inherent information losses. However, it generally requires modification of the aiding sensor signal processing component. Yet, in some cases, these modifications still can be implemented via a firmware upgrade, for example, by providing access to high-frequency (1 kHz or similar) IQ outputs of GNSS correlators. 

This section considers two example cases that illustrate benefits of INS-centric sensor fusion. The first example is the integration of GNSS and inertial for ground vehicle applications. Figure 6 shows example test results that compare loosely and tightly coupled system mechanizations. The system integrates a consumer-grade GNSS chipset, consumer-grade MEMS INS and vehicular motion constraints.

Cumulative error distribution results shown in Figure 6b clearly demonstrate the benefits of tight coupling over the loosely coupled approach. For example, the 90% bound of the horizontal position error is reduced from 15 meters to 6.5 meters, while the 95% error bound is reduced from 40 meters to 7.5 meters. 

Example Benefits

The second example illustrates the benefits of deep integration. Deep coupling for GNSS/INS (including weak signal recovery and interference mitigation) has been discussed by various research papers (including the first issue of The Inertialist column where we illustrated applications of deep integration for jamming and spoofing mitigation). In this section, example benefits are extended to non-GNSS aiding of inertial navigation. 

Figure 7 shows example test results for a LiDAR-aided inertial. In this case, inertial data is fused with measurements of line features that are extracted from images of a 2D scanning LiDAR. The tightly coupled implementation assumes the LiDAR scanning plane remains horizontal, which leads to distortions in the cross-track direction as shown in the left-hand plot. Deep coupling applies inertial data to adjust LiDAR images for tilting, thus improving the cross-track performance as shown in the right-hand plot of Figure 7.

Conclusion 

INS-centric sensor fusion uses self-contained inertial navigation as its core sensors and applies aiding data from other navigation aids to reduce drift in inertial navigation outputs. The complementary fusion enables seamless addition of aiding data (when and if available); PNT continuity in various environments; and robust, resilient state estimation with outlier mitigation (e.g., non-line-of-sight GNSS and SOOP multipath in urban environments) via INS-based statistical gating of aiding measurements. 

The three main fusion strategies include loose, tight and deep coupling that subsequently increase the level of interaction between inertial and aiding sensors’ navigation and signal processing components. Progressing from loose to deep coupling improves the navigation accuracy and robustness. It may require modifications on the aiding sensor side, which in many cases can be accomplished via firmware upgrades.

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Errors in inertial sensor measurements are accumulated over time, leading to drift in INS navigation outputs. While gyro bias is the main contributor, other factors, such as accelerometer bias and noise, are important to consider for balancing the overall error budget. 

A key benefit of inertial navigation is its self-contained nature as the system can maintain navigation continuity while other navigation aids are (temporarily) unavailable. For example, GNSS/INS mechanization can coast on inertial solution when GNSS is jammed. Yet, as described in the previous column on inertial fundamentals, integration is the main computational operation of the INS: sensor measurements (angular rates and non-gravitational acceleration components also referred to as specific forces) are integrated into navigation outputs (attitude, velocity and position). Measurement errors are integrated as well, which leads to a drift in navigation solution over time. As a result, inertial can be used to bridge over continuity gaps (such as GNSS interference areas), but over a limited time.

Understanding inertial error behavior is a critical component of the overall system design. It is addressed in this column.

Influence of Accelerometer Bias 

We start with a simple one-dimensional (1D) case where a platform moves along the x-axis of the horizontal frame. In this case, the double integration scheme completely defines the INS navigation mechanization because attitude determination, gravity addition and coordinate transformation are not required. A constant bias, b_accel, in accelerometer measurements propagates into velocity and position errors (δv and δr, respectively) as follows:

Influence of Gyro Bias

Gyro bias is first integrated into attitude errors and then propagates into velocity and position errors through coordinate transformation. To understand the error propagation mechanism, let’s consider a simplified two-dimensional (2D) case that is illustrated in Figure 1. 

In Figure 1(a) the relative angle, α, between the body-frame (x_b, z_b) and the navigation frame (x_N, z_N) is perfectly known. In this case, body-frame non-gravitational acceleration is translated exactly into its navigation frame components, a_x and a_z. When gyro bias, b_gyro, is present, it is integrated into the attitude error, δα, during the attitude determination step:

where δα is the initial attitude error. As a result, instead of being computationally aligned with the actual navigation frame, the body-frame is rotated into a tilted frame as shown in Figure 2 (b). In this case, the non-gravitational acceleration transforms as: 

or using the small angle approximations (i.e., cos(δα)≈1 and sin(δα)≈δα):

Hence, the error in the coordinate transformation, δα, leads to acceleration-domain errors, a_zδα and -a_xδα, that are then double integrated into position error. This leads to cubic growth of position error due to gyro bias. To illustrate, consider a stationary case where:

In this case, the coordinate transformation error, δa, is:

When integrated into position error, it becomes:

For a general 3D case, the consideration is substantially more involved mathematically. Yet, the nature of error propagation remains the same: gyro bias-induced position error growths proportionally to time³.

The Shuler Effect 

These considerations show accelerometer and gyro drift lead to unlimited error growth in INS navigation outputs. However, when navigating over the Earth surface, the horizontal error component becomes limited due to a Shuler effect. This effect introduces negative feedback (via the gravity addition step) into the error propagation mechanism, thus transforming the polynomial error growth into an oscillatory behavior. The oscillation period is rather large (about 84 minutes as we will see later in this section). As a result, it does not have much benefit for lower-grade inertial systems as their errors grow to unacceptable levels before the Shuler effect kicks in. Yet, Shuler oscillations effectively limit horizontal errors of a high-quality system such as a navigation-grade INS. Figure 2 illustrates the Shuler effect.

As shown in Figure 2, position error δx leads to the wrong gravitational acceleration vector being applied for the gravity addition step. This creates an acceleration error: 

Because the acceleration error is the second derivative of the position error , Equation 5 can be rewritten as:

Equation 6 is a well-known differential equation of a harmonic oscillator. Thus, the position error has an oscillatory behavior with its (Shuler) oscillation period, T_S, defined as: 

Table 1 shows the INS error propagation mechanism for different error sources when the Shuler effect is taken into account. 

It is noted that for time intervals that are significantly shorter than the Shuler period, the error behavior is well approximated by polynomials: e.g., ~t² and ~t³ for accelerometer and gyro bias components, respectively, as we derived previously. It is also worth mentioning that gyro bias is the only error source that leads to unlimited position error growth (even though over longer periods of time the growth becomes linear rather than cubic thanks to the Shuler feedback mechanism).

Unlike the horizontal channel, the vertical INS channel is inherently unstable. The reason is that gravitational acceleration reduces as the distance from the Earth surface increases. As a result, vertical position error is further amplified through the gravity addition rather than being dampened by it (as in the horizontal channel case). For this reason, higher-quality inertial systems that are designed to maintain stand-alone navigation over long periods of time are commonly augmented with a barometric altimeter to stabilize the vertical channel. 

Sensor Noise and First-Order Gauss-Markov Models

Approximation of accelerometer and gyro measurement errors by a constant bias is good for providing an insight into the key principles of INS error growth. Yet, for practical cases, it is too simplistic even for low-grade MEMS sensors. More adequate modeling of sensor measurement errors includes slow-varying bias and noise terms. Noise is represented by a zero-mean Gaussian random process. Slow-varying time bias is approximated by the first-order Gauss-Markov process. This process has an exponential autocorrelation function:

where 1/β is a time constant that is inversely proportional to the correlation time as illustrated in Figure 3. 

It is noted that for gyroscopes, the noise measurement is commonly characterized by a random angular error, n_δα, that is accumulated over time:

where n_δw is the rate measurement noise and ∆t is the measurement update interval. Accumulated noise is often referred to as a random walk akin to accumulating steps of random (positive and negative) lengths. Assuming uncorrelated noise samples at different measurement instances, the random walk variance is:

where n_δw is the rate measurement noise and ∆t is the measurement update interval. Accumulated noise is often referred to as a random walk akin to accumulating steps of random (positive and negative) lengths. Assuming uncorrelated noise samples at different measurement instances, the random walk variance is:

Other Error Sources 

Other sensor-related error sources that can contribute into the inertial error budget include scale-factors, g-sensitive errors and non-linearity sensitivity errors (e.g., squared acceleration scale factors). There are also two important error sources that are not related to sensor imperfections. The first one is packaging error, more specifically misalignment of sensitive axes from a perfect mutually orthogonal sensor orientation assumed by strapdown mechanization algorithms.

The second non-sensor error source is gravity modeling errors. For consumer-grade INS, a simple gravitational model assumes a downward pointed gravity with the absolute value of 9.8 m/s². As the quality of inertial sensors improves, a more precise gravitational model has to be used to balance the overall error budget. In this case, the orientation and absolute value of the gravity vector are modeled as a function of position. Modeling errors are characterized by gravity anomaly and gravity deflections as illustrated in Figure 4.

Both packaging errors and gravity modeling errors can lead to substantial navigation drift even in a (hypothetical) case where perfect accelerometers and gyroscopes are used. 

Example Error Models

Table 2 shows typical error parameters for different INS grades.

Examples of INS Error Budgets

This final section provides two examples of the INS error budget. The first example is shown in Figure 5 for a consumer-grade INS. Stand-alone inertial functionality over a 1-minute interval is considered.

In this case, gyro bias is clearly the largest contributor into the position error drift, while contributions of other error sources are about an order of magnitude lower. 

The second example is coasting with navigation-grade INS over a GNSS jamming region. In this case, a simulated flight scenario includes (a) an initial INS alignment segment where the GNSS is available (10 minutes), and (b) a complete GNSS outage (10 to 30 minutes). The inertial is first pre-calibrated using GNSS measurements (pseudoranges and carrier phase) and then switches into a stand-alone mode after GNSS becomes jammed. 

Figure 6 shows the contribution of different error sources, which also includes errors in the gravitational model, with modeling parameters illustrated in Figure 4. Interestingly, in this case, gravitational errors are the major 
contributor into the INS error budget after 10 minutes of coasting. Their contribution becomes more balanced with the gyro drift after 30 minutes of GNSS-denied operations. Nevertheless, in this example case, improving INS sensor performance will not significantly improve the overall system accuracy because the gravitational model has to be improved first. 

Conclusion

To summarize, errors in inertial sensor measurements are accumulated over time into drift in INS navigation outputs (position, velocity and attitude). Position errors grow proportionally to (i) time³ due to gyro biases, and (ii) to time² due to biases in accelerometer measurements. This polynomial error growth is stabilized by the Schuler effect for the horizontal channel when duration of stand-alone INS operation is comparable to 84 minutes. 

Gyro bias can be generally considered as the main error contributing factor, especially for longer coasting intervals. Yet, other error sources (accelerometer bias, gyro and accelerometer noise, scale-factors and non-linearity errors) are also important for balancing the overall error budget. In addition, 
sensor packaging and gravity modeling errors must be accounted for in INS error models. For example, a gravitational model error can be the main contributing factor for navigation-grade GNSS/INS when coasting over GNSS outages during relatively limited intervals of 10 to 30 minutes.

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In this second column we consider fundamental principles of inertial navigation that derive position, velocity and angular orientation from measurements of accelerometers and gyroscopes.

The key concept of inertial navigation originates from the first two laws of Newtonian physics. The first law states that an object will continue to move with a constant velocity unless disturbed by an external force. According to the second law, a non-zero net external force will result in an acceleration in the same direction with that force, and inversely proportional to the mass of the object. Hence, if we can measure the external force, it can be directly related to acceleration. Figure 1 shows how acceleration can be then integrated into velocity and position.

Clearly, integration requires initial conditions: i.e., initial velocity and position have to be determined. The initialization is commonly accomplished using external aids such as GNSS.

Acceleration is measured by accelerometers whose operational concept can be represented by a proof mass on a spring (Figure 2). An accelerometer measures projection of nongravitational acceleration (i.e., a difference between the acceleration due to motion and acceleration due to gravity) on its sensitive axis. In textbooks, this nongravitational acceleration is also referred to as specific force. To integrate accelerometer measurements into velocity and position, the INS first needs to relate orientation of sensors’ sensitive axes to a navigation frame of reference (where navigation outputs are computed). Second, gravitation acceleration needs to be added.

Gimballed and Strapdown 

There are two approaches to relate measured projections of non-gravitational acceleration with the navigation frame. The first, referred to as gimballed, is to mechanically align accelerometer sensitive axes with the axes of navigation frame. For the second, referred to as strapdown, accelerometers are rigidly attached to the (rotating) body frame and the angular alignment is performed computationally. The gimbaled approach allows for a very precise angular alignment. However, it results in larger size, higher cost and reduced reliability (increased mean time before failure) of inertial navigation as compared to strapdown implementations. Hence, most modern inertial systems utilize a strapdown approach wherein sensor’s sensitive axes are rigidly attached to the body frame and stabilized computationally rather than mechanically. Here, gyroscopes measure angular rates, which are then applied to compute relative attitude between body and navigation frames. Attitude estimates then computationally transform components of the non-gravitational acceleration vector from body into navigation frame.

In addition, Newton’s laws are valid only in a non-rotating inertial frame. For the majority of navigation applications, navigation solution needs to be determined relative to an Earth-related frame of reference such as a local-level East, North Up (ENU) frame. These rotating frames are non-inertial by nature. Hence, compensation of non-inertial effects has to be added to the INS navigation mechanization.

System Components 

Summarizing, the main principle of inertial navigation (illustrated in Figure 1) needs to be extended to include (i) attitude stabilization, (ii) addition of gravity; and (iii) compensation of non-inertial effects. Figure 3 shows a respective high-level diagram of strapdown INS mechanization.

In Figure 3, solid lines indicate components that are required for any type of INS. System components with dotted-lines can be omitted by some inertial implementations, particularly, when lower-grade MEMS sensors are used. These components are related to compensation of non-inertial effects, including (1) the Earth rate (rotation of the Earth), (2) the transport rate (rotation of the local-level frame due to platform’s motion along the Earth surface), (3) Coriolis acceleration and (4) centripetal acceleration (which is often incorporated into addition of gravity). Their compensation requires knowledge of velocity and position states, as well as angular orientation. Hence, a feedback from velocity, position and attitude computations is included in Figure 4. Compensation of non-inertial effect is a more advanced INS concept that can be found in textbooks on inertial navigation and is not further considered as a part of this description of inertial fundamentals. In addition, for lower-grade IMUs, non-inertial effects stay below the level of sensor errors (biases and noise). Table 1 shows this with numerical estimates for an example case where a ground vehicle is moving with a speed of 60 mph at a 45 deg Northern latitude. The table demonstrates that higher-grade inertial systems (tactical and navigation grade) must compensate for non-inertial effects; these can be considered second-order, excluded from INS mechanization, when consumer-grade IMUs are used.

Angular Orientation 

As shown in Figure 3, gyro angular rates are integrated into angular orientation for computational alignment of accelerometer sensitive axes with the navigation frame. Angular orientation is commonly represented by Euler angles, quaternions and direction cosine matrix (DCM). There is no one particular attitude parametrization that would provide substantial advantages over others (in terms of computational savings or reduced error propagation) and all three methods can be used interchangeably. We will apply DCM to represent INS attitude due to its intuitive use for coordinate transformation. The notation is for the DCM that corresponds to the coordinate transformation from body (b) into navigation (N) frame.

Unfortunately, finite rotations do not commute in three dimensions (Figure 4). This complicates INS attitude updates. Gyro angular rates cannot be simply integrated into rotation angles around x, y and z axes and then converted into attitude, since the sequence of rotations matters. Fortunately, infinitesimally small rotations commute, producing an attitude differential equation. For the case of DCM, this equation is:

where is the skew-symmetric matrix comprised of body-frame angular rates:

Equation (1) is an exact continuous-time relationship between the DCM and angular rates. Its exact discrete-time solution can be obtained for a case where orientation of the angular rate vector stays constant between consecutive IMU updates: 

where is the matrix exponential function, and is the skew symmetric matrix of body-frame angular increments over the IMU update interval. Some IMUs output gyro measurements in the form of angular increments (delta Thetas), which can be directly used for DCM updates. Otherwise, gyro rates can be numerically integrated into angular increments, using, for example, a trapezoidal rule: 

Equation (3) is the exact DCM solution, assuming that angular rate vector does not change orientation between consecutive IMU updates (the vector’s absolute value can change). When this does not hold, computational errors are introduced, referred to as coning errors, to be considered in future columns.

Similar to integration of acceleration into velocity and position, INS attitude requires initialization: i.e., initial value of the DCM, needs to be estimated. It can be then propagated recursively over time using equation (3). Initial attitude is estimated based on vectors whose components are known in body and navigation frames: body frame is computationally rotated such that body and navigation frame components of these vectors are aligned with each other. 

When at least two non-collinear vectors are available, a unique rotation exists that defines initial value of the DCM. Most commonly, gravity and Earth rate vectors are applied for the initial alignment. Their body-frame components are measured by accelerometers and gyros, respectively, when the IMU is stationary; while navigation-frame components are obtained using GNSS position estimate (gravity is derived from a model and Earth-rate is projected into the ENU frame for a given location). 

However, for lower-grade IMUs, Earth rate (15 deg/hr) stays below gyro errors and cannot be measured reliably. In this case, the following initialization method can be used. First, angular orientation is partially aligned using gravitational acceleration while the platform is stationary. Next, a straight motion segment is exercised during which velocity vector is applied to complete the alignment procedure. Navigation frame components of velocity are estimated from GNSS data. Body-frame components are defined from a motion model: for example, assuming that velocity is aligned with the vehicle’s forward axis.

Figure 3 shows angular orientation used to transform body-frame nongravitational acceleration into navigation frame:

Coordinate transformation is followed by the addition of gravity:

Gravity addition uses a model of gravitational acceleration vector. The simplest model is to assume that this vector is pointer downward and its absolute value is equal to 9.8 m/s2. This model’s accuracy is sufficient for lower-grade inertial systems. However, more accurate gravitational models are required for higher-grade INS. In this case, gravitational model represents direction and magnitude of gravity as a function of position.

Finally, navigation-frame acceleration is numerically integrated into velocity and position outputs:

Note that more advanced integration schemes (i.e., quadratic or higher-order) can be used to reduce numerical errors in high dynamic-motion environment.

Complete Algorithm

To summarize basic INS mechanization, Figure 5 shows a MATLAB implementation of inertial algorithm that follows main computational steps.

INS implementation in Figure 5 does not include compensation of non-inertial effects. As discussed previously, these effects stay below IMU sensor errors for lower-grade inertial systems (such as consumer-grade MEMS). As a result, the algorithm in Figure 5 has been successfully used by various INS-centric sensor-fusion systems, such as for example tightly and deeply coupled GNSS/INS mechanizations that were discussed in the first issue of the Inertialist column.

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Inside GNSS’s resident inertial expert examines coasting over GNSS outages, navigation in challenged environments and interference mitigation in a sensor-fusion environment.

As positioning experts search for ways to fill GNSS vulnerability gaps, many alternative navigation sources and sensors present themselves, each with their own limitations. No single technology provides accurate and reliable positioning, navigation, and timing anywhere anytime. Instead, we must combine complementary benefits of different navigation aids via sensor fusion.

How do we build a sensor-fusion system? Nearly all nav aids derive information from some external sources that may not be always available. One notable exception provides a completely self-contained solution. It is inertial navigation. An inertial navigation system (INS) measures non-gravitational accelerations and angular rates and integrates them into navigation outputs. The underlying physical effects are always there, and the system can operate in any environment at any time. 

As a result, robust and reliable positioning anywhere anytime can be enabled by INS-centric sensor fusion that seamlessly ties together various navigation aids around inertial. In this case, INS servesas a core sensor to provide navigation outputs while other (environment-dependent) navigation sensors provide aiding data to reduce drift in inertial navigation outputs. Such complementary fusion enables 

• seamless addition of aiding data, when and if available; 

• solution continuity in various environments; 

• and robust and resilient state estimation in contested environments where corrupted measurements (e.g., non-line-of-sight GNSS multipath) are mitigated using INS-based screening. 

Recent advances in inertial navigation technology and, especially in micro-electromechanical inertial measurement units (MEMS IMUs), make it possible to find a suitable IMU option for a wide range of applications, from a $2-3 level consumer-grade to tactical-grade to navigation-grade. As a result, inertial navigation is already at the core of many existing systems and its use will continue to expand in the future. 

In the first issue of this column, we look more closely at the claim that there is an INS option for every budget. 

Sure, there are relatively expensive IMUs that can be used, but are there any navigation-related benefits of inertial sensors that cost only a few dollars? 

Benefits of Consumer-Grade MEMS 

Fortunately, performance of consumer-grade MEMS sensors has continued to improve. To illustrate, Figure 1 shows stability of an industrial-grade MEMS gyroscope.

The turn-on drift value can be still quite large. Yet this drift is stable and can be efficiently calibrated out during the initialization phase, when the system is at rest. Residual stochastic variations stay at a 20 deg/hr level, which is sufficient to enable substantial benefits from the navigation perspective. These include: 

• Coasting over GNSS outages; 

• Reliable navigation in harsh GNSS environments such as dense urban canyons; and,

• Interference mitigation, including jamming suppression and protection against spoofing attacks. 

Figure 2 illustrates these benefits for ground-vehicle applications, showing a high-level architecture of an example INS-centric sensor-fusion system. 

This system combines inertial with GNSS measurements (pseudoranges, Doppler, carrier phase) and ground-vehicle motion constraints (including zero velocity updates, as well as zero lateral and vertical velocity constraints). The integration filter fuses INS with aiding sources utilizing a complementary sensor-fusion concept. Instead of estimating navigation states themselves, it estimates errors in navigation states. 

This process

• enables efficient linearization of system relations such that the integration filter can be implemented in a form of computationally-efficient extended Kalman filter (EKF); 

• and substantially simplifies dynamic-state modeling since slowly-changing INS errors can be modeled much more reliably as compared to fast-changing navigation states. 

EKF measurement observations are formulated as differences between the actual measurements and their INS-based predictions. Furthermore, comparison of INS predictions with actual measurements provides a very efficient tool for detection and removal of outliers in aiding data (e.g., GNSS multipath or unreliable velocity constraints during sharp turns). 

In addition to fusion of inertial with aiding sources at the measurement level (commonly referred to as tight coupling), the sensor fusion architecture in Figure 2 also supports data fusion at the signal-processing level or deep coupling. Deep coupling enables extremely long coherent integration (LCI) of received GNSS signals: 1 second and beyond vs. 20 ms in a traditional receiver architecture. This

• narrows the signal processing bandwidth thus eliminating spoofing, and 

• boosts the received signal power while averaging out noise and interference. 

LCI is made possible and practical by accurate aiding of the GNSS signal accumulation from a consumer-grade INS that benefits in turn from sustained GNSS updating. 

Coasting Over GNSS Outages

Figure 3 shows example coasting performance. In this case, a tightly coupled implementation (without the deep integration component) is used. Experimental results here were produced with an off-the-shelf GNSS receiver chipset (u-blox M8T), ST Micro MEMS IMU (ISM330DHCX) and QuNav’s embedded GNSS/Inertial Vehicular Engine (GIVE) software. 

Figure 3(a) shows trajectory estimates for a tunnel test with two complete outages that lasted about 30–40 seconds. Figure 3(b) shows a significantly longer outage case, where the vehicle was driven in an underground parking garage for over 5 minutes. Position outputs from GNSS/INS and GNSS/INS/motion constraint integration options are shown.

Relatively short GNSS outages (about 30 seconds) can be reliably bridged over with INS only. However, for longer outage durations, performance starts to degrade as shown in Figure 3(b). The outage duration can be extended substantially if the INS aiding sources are further augmented with motion constraints. In this case, the system can sustain a long GNSS outage (5 minutes) while limiting position errors to a level of about 10 meters.

GNSS-Challenged Environments

Figure 4 shows example test results in dense urban environments (downtown San Francisco). Again, a tightly coupled sensor-fusion option was used with u-blox GNSS, ST Micro IMU and QuNav sensor-fusion. Position output from Novatel SPAN (using tactical grade IMU and generated in post-processing mode) was used for truthing. 

Test results demonstrate that the motion-constrained INS integration option limits position errors to 4 meters (at a 50% error bound) and 10 m (at a 99% error probability) in very difficult GNSS environments in dense urban canyons under severe multipath. 

Interference Mitigation

Deep integration of INS-centric sensor fusion with GNSS enables mitigation of jamming signals and suppression of spoofing attacks in a small form-factor system that does not need to use multi-element antenna arrays. As mentioned previously, deep integration applies inertial aiding to significantly increase the accumulation interval of received GNSS signals. For example, an LCI of 1 second can be maintained. 

The use of LCI is extremely beneficial for mitigating spoofing attacks, thus protecting open-service GNSS signals. Specifically, the signal processing bandwidth is reduced to 1 Hz or less. This makes it extremely difficult to launch a successful attack since the spoofer has to be able to

• track the receiver motion and clock states at a sub-Hz level (or, equivalently, sub-decimeter-per-second level of precision); 

• and align its signal to the authentic one at the same level of precision. 

Figure 5(a) illustrates the spoofing mitigation capability. In this case, a smart spoofing was software-injected into pre-recorded baseband signal samples of GPS Link 1 C/A signal, which were then post-processed by QuNav’s software-defined receiver (SDR) deeply integrated with consumer-grade MEMS IMU (that was used for GNSS outages and dense urban tests discussed above). 

The spoofer implemented a position push and was able to successfully hijack the signal-processing functionality of an unaided receiver. In contrast, the deeply integrated system maintained the lock on the authentic signal throughout the tests thus making the system immune to spoofing. 

LCI also provides additional 20 dB protection against jamming, including the most difficult case of matched-spectrum (broadband) jamming. To illustrate, Figure 5(b) shows test results for a ground vehicle test scenario where a 40-dB signal attenuation was introduced by a software-injection of broadband jamming into GLONASS L1 signal data. This attenuation level is 20 dB below a tracking threshold of unaided receivers. 

Sub-meter positioning capabilities were maintained using aiding from a MEMS IMU chipset. In addition to jamming suppression, extended signal accumulation is also beneficial for weak signal recovery. Specifically, the 20 dB anti-jam protection is equivalent to 20 dB gain in weak GNSS signal processing, which is directly beneficial for degraded environments such as dense urban and under multiple layers of canopy.

Conclusion

To summarize, consumer-grade MEMS inertial sensors provide substantial benefits for various GNSS-degraded environments. As illustrated with test results, tightly coupled GNSS/INS supports position continuity over relatively short GNSS outages (30-40 seconds). This outage duration can be increased (to 5 minutes or longer) if the system mechanization is augmented with other navigation aids (such as motion constraints for ground vehicles). In addition, tightly coupled solution enables reliable localization in contested GNSS environments such as urban canyons. Finally, extension of tight coupling to deep integration allows for mitigation of interference (jamming and spoofing).

In the next issue, we will look into fundamentals and discuss main principles of inertial navigation. 

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