Inertial performance: Enhanced tightly coupled dead reckoning

June 13, 2017  - By and 0 Comments

Exploring IMU specifications and correlating them to performance of a final product can be daunting, as differences between MEMS sensors are not always apparent. This article presents achievable performances in fusion technology across a range of IMUs among the best in their respective performance categories. 

The number of available options in inertial navigation systems (INS) has grown substantially over the last several years. Major advances have been made not only in inertial measurement unit (IMU) technology, but also in the ability to exploit sensor information to its fullest extent. In both cases, the largest impact can be seen in the micro-electrical-mechanical systems (MEMS) sensors. MEMS sensors are typically much smaller, lower power and less expensive than traditional IMUs. The net result of these improvements is a proliferation of INS systems at much lower cost than were previously available and, therefore, greatly increased accessibility to technology that has historically seen limited deployment. Selecting the appropriate sensor and fusion solution for a particular application can be very challenging due to the large and confusing spectrum of solutions.

The IMUs will be examined in the context of new enhancements to sensor fusion algorithms such as the use of INS profiles. The concept of INS profiles applies environment specific constraints to improve performance in certain types of vehicles, or motion profiles. External sensors such as odometers and dual antenna operation can also aid the solution considerably, but will be unused in this analysis except for occasional comparisons. These external aiding sensors are extremely helpful in many cases and are available to use with a proprietary tightly coupled GNSS+INS solution called SPAN, but this paper seeks to evaluate what performance can be achieved without such aids.

Real-world test results will be examined using a selection of IMUs with the latest SPAN algorithms to illustrate what kind of performance can be achieved with different sensors in difficult conditions. Despite their major advances over the past few years, there are many challenges involved with utilizing MEMS technology to provide a robust navigation solution, particularly during limited GNSS availability or low dynamics. The measurement error characteristics of these devices have improved dramatically, but are still much larger and more difficult to estimate than traditional sensors. Advancements in SPAN sensor fusion algorithms have enabled these smaller sensors to achieve remarkable performance, especially in applications where environmental conditions allow for additional constraints to be applied.

This testing focuses on the land profile, meaning the constraints applied to a fixed-axle vehicle. The test scenarios were selected in such a way as to provide results for ideal, poor and completely denied GNSS coverage.

INS Profiles

GNSS and IMU sensors are only one part of the overall INS system performance. The sensor fusion algorithms used to exploit the available sensor data to its utmost capability are equally as important. In this regard, several improvements have been made to the SPAN INS algorithms to enhance performance under a variety of scenarios.

The largest addition to the SPAN product line is the introduction of INS profiles. That is, environment- and vehicle-specific modeling constraints can be utilized to enhance the filter performance. For example, the land profile, which will be examined in depth in this article, is intended for use with ground vehicles that cannot move laterally. The assumptions introduced for land vehicles, however, are not necessarily valid for different forms of movement, such as those experienced by a helicopter. Therefore, profiles have been implemented via command, and controlled as required by the user, allowing for maximum performance depending on the application at hand.

The land profile is analogous to what has historically been identified as dead reckoning. It is a method that uses a priori knowledge of typical land vehicle motion to help constrain the INS error growth. In other words, it makes assumptions on how land vehicles move to simplify inertial navigation from a six-degree-of-freedom system to something closer to a distance/bearing calculation. The land profile takes the concept of dead reckoning, models it as an update type into the inertial filter and adds a few additional enhancements.

Velocity Constraints / Dead Reckoning. Amongst other optimizations, the land profile enables velocity constraints based on the assumption of acceptable vehicle dynamics. This includes limiting the cross track and vertical velocities of the vehicle. Of all the enhancements, this is the one most colloquially referred to as dead reckoning.

In its simplest form, dead reckoning is the propagation of a position without any external input. In this forum, external input generally refers to GNSS satellites. Without external input, dead reckoning is inherently dependent on assumptions of velocity and heading to propagate the position. These solutions have evolved by integrating inertial and directional sensors to provide more local input and improve the solution propagation. This also is not a perfect method, however, as inertial sensors have their own errors that grow exponentially over time. The land profile velocity constraints explain the bulk of optimizations SPAN has made to enable dead-reckoning performance in extended GNSS outage conditions.

Explaining the velocity updates involves using the current INS attitude (  ); the vehicle attitude (  ) is estimated by applying the measured or estimated IMU body to vehicle direction cosine (  ). From this, the pitch and azimuth for the vehicle is estimated.Using the magnitude of the measured INS velocity in conjunction with the derived vehicle orientation, the vehicle velocity is computed, allowing the expected vertical velocity and cross-track to be constrained.

A velocity vector update is then applied to the inertial filter to constrain error growth. The effects of this method are expected to be most apparent in extended GNSS outage conditions when the INS solution must propagate with no external update information.

Phase Windup Attitude Updates. Some applications are inherently difficult for inertial sensors due to the fact that these systems are reliant on measuring accelerations and rotations in order to observe IMU errors. When traveling at a constant bearing and speed, separating IMU errors from measurements becomes challenging, so any application that does not provide meaningful dynamics is more demanding on inertial navigation algorithms. This type of condition commonly appears in applications such as machine control, agriculture and mining.

Gravity is a strong and fairly well known acceleration signal, so the real difficulty in this type of environment is managing the attitude, and especially azimuth, errors. Attitude parameters become difficult to observe when the system experiences insignificant rotation rates about its vertical axis.

External inputs can be used for providing input during low dynamic conditions when rotational observations are weaker. These are particularly helpful in constraining angular errors and include the same types used to assist in initial alignment: dual antenna GNSS heading, magnetometers, etc. However, as the goal of this testing is to demonstrate the achievable performance from a single antenna GNSS system, this type of external aid was specifically omitted.

Utilizing a patented technique for determining relative yaw from phase windup, the system is able to distinguish between true system rotation and unmodeled IMU errors during times of limited motion. This is a novel way to extract additional information out of existing sensors rather than adding more equipment and complexity.

The phase windup update is used to constrain azimuth error growth during low dynamic conditions that are typically not favorable to inertial navigation. However, it does require uninterrupted GNSS tracking and is therefore applicable only in GNSS benign environments. This approach is expected to show the greatest benefit in low dynamic conditions and be directly attributable to azimuth accuracy, but only in conditions where GNSS availability is relatively secure.

Equipment and Test Setup

We paired OEM-grade GNSS receiver cards with a selection of IMUs in different performance categories. Since the OEM GNSS platform is capable of tracking all GNSS constellations and frequencies, we configured each receiver to use triple frequency, quad-constellation RTK positioning. The receivers were coupled with a wideband antenna capable of tracking GPS L1/L2/L5, GLONASS L1/L2, BeiDou B1/B2 and Galileo E1/E5b signals.

Three IMUs were tested: an entry-level MEMS IMU (UUT1), a tactical-grade MEMS IMU (UUT2) and a high-performance fiber-optic gyro-based IMU (UUT3).

All GNSS receivers and IMUs were set up in a single test vehicle and collected simultaneously for all scenarios. IMUs were mounted together on a rigid frame, and all receivers ran the same firmware build that were connected to the same antenna.

The tests were conducted using a single GNSS antenna with no additional augmentation sources, such as distance measurement instrument (DMI) or wheel sensor. These are extremely helpful in aiding the solution, but as previously mentioned, this testing seeks to demonstrate the possible performance without the benefit of additional aiding sources. Dependence on aiding sources is a very important distinction when comparing such systems.

The GNSS positioning mode used was RTK via an NTRIP feed from a single base station with baselines between 5–30 kilometers. This was done to try to minimize GNSS positioning differences between the three systems. L-band correction signals were not tracked, and PPP positioning modes were not enabled.

A basic setup diagram of each system under test can be seen in Figure 1.

FIGURE 1. Equipment set-up (not to scale).


Test Scenarios

Four test scenarios will be examined using all the equipment and algorithms described above. They are: urban canyon, low dynamics, parking garage and extended GNSS outage.

The urban canyon test is designed to show the performance of the system in restricted GNSS conditions. The challenge to this scenario is to maintain a high-accuracy solution when GNSS positioning becomes intermittent or even unavailable.

The low dynamics test is intended to illustrate the benefits of the land profile, and specifically the phase windup azimuth updates in maintaining the azimuth accuracy.

The parking garage test will show the efficacy of the velocity constraint models over the different IMU classes as the extended outage provides no external information to the INS filter whatsoever. Again, no other aiding sources were used.

Urban Canyon Test. The urban canyon environment has been and remains one of the strongest arguments in favor of using GNSS/INS fusion in a navigation solution. Because urban canyons are common, densely populated and, of course, a demanding GNSS environment, they represent both an important and challenging location to provide a reliable navigation solution. Typically, they contain major signal obstructions, strong reflectors and complete blockages (depending on the city). For this reason, they provide an excellent use case for INS bridging to maintain stability of the solution.

During most urban canyon environments, it is typically rare to incur total GNSS outages of more than 30 seconds. Therefore, this scenario examines the stability of the solution in continuously degraded, but not generally absent, GNSS. In this case, the coupling technique of the inertial algorithms rather than quality of the IMU dominates achievable position accuracy.

The receiver platform is capable of tracking all GNSS constellations and frequencies. This provides a significant benefit to test scenarios, such as the urban canyon, where the amount of visible sky is significantly restricted. In this case, the more satellites that are observable, the more the tightly coupled architecture can exploit the partial GNSS information.

Though position accuracy between IMUs is less apparent in this condition, attitude results remain separated by IMU quality, which is a major consideration for some mapping applications such as those using lidar or other sensors where a distance/bearing calculation must be done for distant targets.

Test data for this scenario was collected in downtown Calgary, Canada. The trajectory (Figure 2) includes several overhead bridges for brief total outages and some very dense urban conditions.

FIGURE 2. Urban canyon test trajectory.

Table 1 shows the RMS error results of the three systems running both the default and land profiles. The first thing to notice is that the errors are differentiated by IMU category, though the differences are fairly small in the position domain thanks to the tightly coupled architecture. However, because GNSS information is partially available, the differences seen in activating the land profile are fairly modest, especially as the IMU performance rises.

TABLE 1. RTK RMS errors for urban canyon.

As the clearest benefits of the land profile are seen on the entry-level MEMS IMU (UUT1), these will be explored graphically in Figures 3 and 4. Figure 3 shows the position domain, and the RMS differences can be seen in a few cases where the default mode errors increased faster than the land profile. An example of this divergence is most obvious around the 1500-second mark of the test during periods GNSS is most heavily blocked.

Low Dynamics Test. The low dynamics test is designed to emulate conditions experienced by machine control, agriculture and mining applications. In this situation, GNSS availability is generally not the limiting factor and can be used to control the low frequency position and velocity errors of the INS system. The difficulty is managing the attitude, especially azimuth, errors because attitude parameters are very hard to observe without significant rotations or accelerations (Figures 5 and 6).

The low dynamics test was collected in an open-sky environment and consisted of traveling in a straight line on a rural road for roughly 2 km at an average speed of 10–15 km/h.

As this type of scenario provides little physical impetus, the azimuth and gyroscope biases are not observable. The reason for this is due to the use of the first-order differential equations to estimate the navigation system errors. Essentially, the differential equations define how the position, velocity and attitude errors change (grow) over time based on each other and the IMU errors. The observability of a particular update is tied to additional states through the off-diagonal elements of the derived transition matrix with the accelerations and rotations experienced by the system.

The overall RMS solution errors for RTK are provided in Table 2. As evident by the results presented, the position and velocity errors are clearly constrained by the continuous RTK-level GNSS position regardless of whether the land profile is enabled or not. The real differentiator in the land profile is the attitude performance due to the use of phase windup as a constraint. Moreover, the attitude improvements are certainly tied to IMU quality.

TABLE 2. RTK RMS errors for low dynamics.

TABLE 3. RTK RMS errors, parking garage (500s).

UUT1 exhibited a noticeable improvement in the attitude performance, while the higher performance IMUs did not. This is not entirely unexpected as the precision of the phase windup is lower than that of the higher grade IMUs.

Looking at the data graphically, Figure 7 shows the effect of land profile on positioning performance in this scenario. The two solutions are indistinguishable on the plot, and are all within standard RTK-level error bounds as was indicated in the RMS table.

Figure 7 shows the attitude accuracy with and without the land profile enabled. Again, the largest gains are seen on the entry-level UUT1, so this is the graphic shown below. This shows how the error peaks of the azimuth estimates are constrained. All the sharp corrections in each plot correspond to the vehicle turning around at the end of each 2-Km line and illustrates how much more powerful a rotation observation can be in azimuth accuracy overall.

FIGURE 7. UUT1 attitude error (std vs. land).

Parking Garage Test. This test was carried out at the Calgary International Airport and was selected to show the INS solution degradation during extended complete GNSS outages. The test consisted of an initialization period in open sky conditions to allow the SPAN filter time to properly converge, followed by a 500-second period within the parking garage. During the interval within the parking garage there were no GNSS measurements available.

Figure 8 provides a trajectory of the test environment. The time spent inside the parking structure is evident on the center bottom of the image.

FIGURE 8. Parking garage test trajectory.

Unlike urban canyon environments that contain partial GNSS information, this exhibits an extended period of complete GNSS outage. During this type of scenario, the IMU specifications become much more significant. IMU errors directly translate to the duration the solution can propagate before the accumulated low-frequency errors of the IMU grow to unacceptable levels. System performance during the outage degrades according to the system errors at the time of the outage and the system noise. The velocity errors increase linearly as a function of attitude and accelerometer bias errors. The attitude errors will increase linearly as a function of the unmodeled gyro bias error. The position error is a quadratic function of accelerometer bias and attitude errors.

Position results from each IMU are shown for UUT 1 in Figure 9. This plot shows the error with the land profile on and off. Without the land profile, the second-order position degradation in an unconstrained system is clearly visible.

FIGURE 9. UUT1 position error (std vs. land ).

By enabling the land profile, the filter constrains IMU errors by utilizing a velocity model for wheeled vehicles. With the constraints, the position errors are startlingly reduced for UUT1 and then progressively less impactful as the IMU quality increases in UUT2 and UUT3, respectively. This makes sense as the IMU error growth is progressively smaller in those IMUs, so the effect of mitigating them is also reduced.

Extended GNSS Outage Test. An extension of the parking garage test is to evaluate the performance in a much longer outage. Instead of 10 minutes, an outage of one hour was tested. Also, due to the extremely long GNSS outage bridging, the effects of adding a DMI sensor (odometer) will also be explored as they are able to be used as a major additional aiding source.

Table 4. Percent error / distance traveled over 1-hour GNSS outage.

The most common measure of dead-reckoning performance is error over distance traveled (EDT). Due to the very long duration outages in this test, the errors will be reported in error over distance traveled to conform to the typical reporting method. This test was conducted in a mixture of highways and suburban streets with an average speed of 65 Km/h, incorporating a moderate amount of dynamics.

This effect can be seen over the duration of the entire outage as well in Figure 9. In this case, the points are the RMS error over several tests. and the light background shroud represents the one-sigma confidence as time progresses. The confidence increases over time as the overall distance traveled also increases.

FIGURE 10. Land profile EDT with and without DMI aid over 1-hour GNSS outage.

Results and Conclusions

In testing a range of IMUs in some challenging scenarios, this paper has sought to illustrate what kind of performance is achievable using each kind of system. An added complexity is looking at what effect certain inertial constraint algorithms have on this solution.

Although low-cost MEMs IMUs are continuing to greatly improve in quality and stability, the end application is still highly correlated to the overall performance of a selected INS system. For a great many applications, the MEMS devices in combination with a robust inertial filter can meet requirements and provide excellent value. However, some applications continue to require higher end sensors, and possibly post-processing to meet their needs.

The ability of SPAN to utilize partial GNSS measurements such as pseudorange, delta phase and vehicle constraints means even low-cost MEMs are capable of providing a robust solution in challenging GNSS conditions. However, this tightly coupled integration is limited in cases where GNSS is completely denied or when in low dynamic conditions.

INS profiles using velocity constraints, phase windup and robust alignment routines have been shown to provide substantial aid to the INS solution in tough conditions, such as GNSS denied or low dynamics. These improvements were shown to exhibit greater impact as the IMU sensor precision decreases. These abilities, in conjunction with the existing tightly coupled architecture of SPAN and the ever-increasing accuracy of MEMS, IMUs indicate that robust GNSS/INS solutions will continue to proliferate at lower cost targets. However, very precise applications such as mapping will continue to rely on higher quality sensors to meet strict accuracy requirements.


The authors thank Trevor Condon and Patrick Casiano of NovAtel for collecting and helping to process the data presented in this article, and to Sheena Dixon for her tireless editing.


NovAtel SPAN technology on the NovAtel OEM7 receiver is the testing and development platform for this research. NovAtel OEM7700 GNSS receiver cards and a NovAtel wideband Pinwheel antenna were employed. The inertial units under test were an Epson G320 (low-power, small-size MEMS IMU); Litef μIMU-IC (larger tactical-grade performance IMU still based on MEMS sensors); and a Litef ISA-100C (near navigation-grade IMU using fiber-optic gyros (FOG). Although all are excellent performers in their class and capable of providing a navigation-quality solution, the intent is to show the potential limitations that might arise due to the intended application.

RYAN DIXON is the chief engineer of the SPAN product line at NovAtel Inc., leading a highly skilled team in the development of GNSS augmentation technology. He holds a BSc. in geomatics engineering from the University of Calgary.

MICHAEL BOBYE is a principal geomatics engineer at NovAtel and has participated in a variety of research projects since joining in 1999. Bobye holds a BSC. in geomatics engineering from the University of Calgary.

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