ION GNSS 2011
Session E3: Robust Navigation in GNSS-Denied and GNSS-Challenged Environments 2

Title: Observability Analysis of Non-Holonomic Constraints for Land-Vehicle Navigation Systems
Author(s): Y. Li, X. Niu, Q. Zhang, C. Shi, GNSS Research Center, Wuhan University, China
Date/Time: Thursday, September 20, 2012, 8:57 a.m.
Room: Room B113-116

GNSS (Global Navigation Satellite Systems) and INS (Inertial Navigation Systems) have different advantages and can be integrated to provide variety of navigation information which is precise, reliable, and with high data rate. Especially during these decades, advances in Micro-Electro-Mechanical Systems (MEMS) technology combined with the miniaturization of electronics, have made it possible to produce chip-based inertial sensor for use in measuring angular velocity and acceleration. These MEMS chips have become ideal candidates for various applications because they are small, light-weight, low-power and are extremely low-cost and reliable. At the same time, the cost reduction of GNSS receiver has also promoted the development of low-cost navigation technique. GNSS/MEMS INS integrated systems become the most commonly used navigation techniques. However, the performances of the MEMS sensors are highly dependent on the environmental conditions such as temperature variations. During the GPS outages in challenging environments such as in urban canyons, a MEMS INS will lose its value fast due to the decrease of its performance. The accuracy limitation of low-end navigation techniques (e.g. MEMS INS, GNSS chips etc.) become the main obstacle for their development and promotion. From the perspectives of the navigation system designers, one most useful approach to solve this problem is to improve the navigation algorithms. There are lots of priori information about the navigation systems (e.g. control inputs, vehicle dynamic models, kinematic constraints, the road information etc.), which can play significant roles in generating information and reducing estimation uncertainty. Due to their independence of hardware costs, the priori information is especially valuable for the low-end navigation systems. Among various priori information, Non-Holonomic Constraint (NHC) is the most useful one in the case of Land-Vehicle Navigation (LVN). For a land-based vehicle, the yaw can be measured by extra sensors such as GPS dual antenna system or estimated by the navigation algorithms through vehicle maneuvers such as turns. However, these two ways are not always applicable. Such extra sensors are not affordable for many low-end navigation systems and the vehicles do not have sufficient maneuvers all the time. During most of the time, a car moves straightforward with small velocity variations. Under this condition, the yaw is unobservable or weakly observable even when there are GNSS updates. Once the GNSS signal was blocked, the yaw would diverge faster. The degradation of the yaw angle will affect the position estimates directly. Therefore, it is beneficial to use NHCs, which refer to the fact that unless the vehicle jumps off or slides on the ground, the velocity of the vehicle in the plane perpendicular to the forward direction is almost zero. As a kind of priori information, NHCs can be used in the navigation algorithms without any additional sensor. It had already been shown by real tests that both the position errors and the attitude errors were reduced significantly when NHCs were used. Generally speaking, NHCs are used as main means to control the navigation errors of land-based vehicles nowadays. Although it is widely known that NHCs can improve the navigation performance, there are relatively less theoretical analysis of their contributions. It seems that NHCs are useful for most of the time when combining with the low-end INS. However, it is hard to maximize the effects of NHCs as well as control the risks (they possibly have) if there is no guidance of their use based on theoretical analysis. Some quantificational analysis are given in this paper to make the use of NHCs more systematically and efficiently. The work focuses on the following points. On the one hand, we analyze the contributions of NHCs from an overall perspective. Since NHCs are essentially velocity constraints along the y-axis or z-axis in the body frame (b-frame), there influences on the Kalman filter system can be quantified. On the other hand, we analyze the observerbility of an INS/NHCs system quantificationally. This kind of analysis provides a deeper insight into the navigation algorithms. As quantificational analysis, we describe the degree of observabilities, not limit on the states are observable or not. Besides, the facts which influence the observabilities are studied as well as the strength of their effect. Some preliminary results are given as below. All the following variables project to the body frame (b-frame). (1) NHCs enhance the yaw estimate. The strength of the contribution depends on the relationship between the y-axis velocity constraint error (i.e. ?Vy) and the x-axis vehicle velocity (i.e. the forward velocity, Vx). Less ?Vy or more Vx leads to better estimate of the yaw. If the y-axis velocity constraint is exact right (i.e. the y-axis velocity is exact zero), the yaw will be completely observable. (2) The estimate of the pitch depends on the relationship between the z-axis velocity constraint error (i.e. ?Vz) and Vx. Less ?Vz or more Vx leads to better estimete of the pitch. (3) When the vehicle is moving straightforward, the unobservable parts of the y-axis accelerometer bias (i.e. bay) and that of the z-axis gyro bias (i.e. bgz) relate with each other. Their relative relationship depends on Vx. Meanwhile, the unobservable parts of the z-axis accelerometer bias (i.e. baz) and that of the y-axis gyro bias (i.e. bgy) have the similar relationship. If there is acceleration along x-axis (i.e. the vehicle changes its velocity), both bgz and bgy will become strong observable. Then the observability of both bay and baz will be improved accordingly. (4) When the vehicle is turning, the observability of both the gyro and accelerometer biases depend on both the yaw rate and the forward accelerometer of the vehicle. More dynamics of the yaw lead to better estimates of both the attitude errors and the accelerometer biases as well as relatively weaker estimates of gyro biases. These analysis have also successfully explained that NHCs have little effect under low vehicle speed or zero speed. More abundant analysis and quantificational results are given in the body of the paper. Through the theoretical studies, it can be seen clearly that NHCs would make different contributions in different cases. The studies show the performance of an INS/NHCs system, which can promote the better utilization of NHCs or other priori informations. Both simulation analysis and real tests will be taken to support the theoretical analysis.

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