PERFORMANCE ANALYSIS OF AN AKF BASED TIGHTLY-COUPLED INS/GNSS INTEGRATED SCHEME WITH NHC FOR LAND VEHICULAR APPLICATIONS

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1 PERFORMANCE ANALYSIS OF AN AKF BASED TIGHTLY-COUPLED INS/GNSS INTEGRATED SCHEME WITH NHC FOR LAND VEHICULAR APPLICATIONS Kun-Yao Peng, Cheng-An Lin and Kai-Wei Chiang Department of Geomatics, National Cheng Kung University, Tainan County, Taiwan ICETI 2012-A1008_SCI No. 13-CSME-37, E.I.C. Accession 3495 ABSTRACT INS/GNSS integrated scheme can overcome the shortcoming of INS or GNSS alone to provide superior performance. AKF is based on the maximum likelihood criterion for choosing appropriate weight and thus to adjust factors online. The primary advantage of AKF is that the filter has less relationship with priori statistical information. There are two NHC available for land navigation which the velocity of vehicle in the plane perpendicular to the forward direction is zero. To validate the performance of proposed scheme, the preliminary results illustrated AKF based tightly-coupled INS/GNSS integrated scheme can provide more stable solutions combined with NHC during GNSS outages. Generally speaking, the improvement ratio of 3D positioning reach 40% compared to EKF. Keywords: INS/GNSS; AKF; non-holonomic constraints. ANALYSE DE PERFORMANCE D UN SCHÉMA DE BASE AKF DU SYSTÈME INS DE GÉOLOCALISATION ET DE NAVIGATION INS/GNSS DE COUPLAGE SERRÉ AVEC NHC APPLIQUÉ À UN VÉHICULE TERRESTRE RÉSUMÉ Un schéma INS/GNSS intégré peut surmonter la faiblesse INS ou GNSS seul pour fournir une performance supérieure. AKF est basé sur des critères de probabilités maximales pour choisir les facteurs appropriés et les rectifier en ligne. L avantage principal de AKF est que le filtre est moins en relation avec les informations statistiques à priori. Il y a deux NHC pour la navigation terrestre pour laquelle la vitesse du véhicule sur un plan perpendiculaire à la direction avant est zéro. Pour valider la performance du schéma proposé, les résultats préliminaires mettent en évidence que le schéma AKF de base d un système INS/GNSS peut procurer des solutions plus stables en combinaison avec NHC pendant des pannes de GNSS. En général, le ratio d amélioration de positionnement 3D atteint 40% si on compare à EKF. Mots-clés : INS/GNSS ; AKF ; contraintes non-holonomiques. 503

2 Fig. 1. The limitations of INS based navigation systems. 1. INTRODUCTION Inertial Navigation System (INS) is widely used in many applications for navigating of moving platforms. Low-cost INS can experience large position and attitude errors over short term duration in comparison with high-grade systems. Due to the advances in fiber optic gyroscope and micro-electro-mechanical systems (MEMS) technologies, tactical-grade and low-cost Inertial Measurement Units (IMU) have gained great interests in both civilian and commercial fields recently. It has been proved through numerous researches that the INS/GNSS integrated is the ideal technique for seamless vehicular navigation. The stand-alone INS is self-contained and independent of external signals. Providing acceleration, angular rotation and attitude data at high sampling rates is the primary advantage of using an INS. However, the disadvantage of using an INS is that its accuracy degrades rapidly because of nonlinear errors and noises from inertial sensors including accelerometers and gyros growing quickly with time, as shown in Fig. 1. Therefore, an INS is used in the short-term case if no other navigation system or navigational aids is available. On the contrary, GNSS receivers require direct line-of-sight (LOS) signals to the GNSS satellite to provide solutions with long-term stability; consequently, it is capable of providing continuous and reliable positioning with uninterrupted signal reception. However, GNSS leaves two scenarios to be considered in the land environment. The first scenario is intermittent signal reception, as for instance in heavily forested areas or in urban canyons. The other scenario is no signal reception at all, as for instance in buildings, tunnel or underground. In the first case, GNSS has to be integrated with other sensors to bridge periods of no signal reception. In the second case, GNSS has to be replaced by another navigation system that can provide continuous navigation solutions in above environments during no GNSS signal reception. The integrated system consisted of INS and GNSS takes advantage of the complementary attributes of both systems and outperforms either stand-alone system operated [1]. There are different integrated schemes including loosely-coupled and tightly-coupled INS/GNSS integrated strategies, have been researched and developed since the last decade [2]. The sustainability of INS/GNSS integrated system using current commercially available MEMS inertial technology in typical GNSS denied environments is fragile. However, the progress of MEMS inertial sensors is advanced rapidly thus the inclusion of MEMS inertial sensors for general land vehicular navigation is bright in the future. In addition to waiting for the advanced development process of MEMS inertial sensor, some measures have been taken to increase the sustainability of MEMS INS/GNSS integrated systems for vehicular applications during frequent signal blockages in software aspect [3, 4]. In other words, aiding INS with other complementary sensors is critical to improve the accuracy of inertial based navigation systems. Choosing an appropriate estimation method is a key issue in developing an aided INS [5]. 504

3 Fig. 2. Loosely-coupled INS/GNSS integration architecture (closed loop). 2. PROBLEM STATEMENTS It is common practice to use an Extended Kalman Filter (EKF) to accomplish the data fusion. Several architectures for EKF implementations are known [6]. The most common integrated scheme used today is loosely-coupled integrated scheme. It is the simplest way of integrating a GNSS processing engine into an integrated navigation system. The GNSS processing engine calculates position fixes and velocities in the local level frame and then send those solutions as measurement update to the main INS EKF. By comparing the navigation solutions provided by INS mechanization with those solutions provided by GNSS processing engine, those navigation states can be optimally estimated, as shown in Fig. 2, the primary advantage of loosely-coupled architecture is the simplicity of its implementation, because no advanced knowledge of GNSS processing is necessary. The disadvantage of implementation is that the measurement update of the integrated navigation system is only possible when four or more satellites are in view. On the other hand, the tightly-coupled integration scheme uses a single KF to integrate GNSS and IMU measurements. In the tightly-coupled integration, the GNSS pseudo-range and delta-range measurements are processed directly in the main KF, as shown in Fig. 3. For some references, the aiding of the receiver tracking loops using velocity information provided by the INS is an essential characteristic of tightlycoupled scheme, too. The primary advantage of this integration is that raw GNSS measurements can still be used to update the INS when less than four satellites are available. This is of special benefit in a hostile environment such as downtown areas where the reception of the satellite signals is difficult due to obstruction when the vehicle navigates in urban or suburban area. However, according to Chiang and Huang [4], the EKF implemented with a tightly-coupled scheme may come with serious problems concerning the quality of GNSS raw measurements. In other words, EKF based tightly-coupled architecture is sensitive the quality of GNSS raw measurements. This scenario usually takes place in urban and suburban areas because of the impact of reflected GNSS measurements. Therefore, this study applied the Adaptive Kalman Filter (AKF) as the core estimator of a tightly-coupled INS/GNSS integrated scheme by tuning the measurement noise matrix R adaptively. The idea of AKF is based on the maximum likelihood criterion for choosing the most appropriate weight and thus the Kalman gain factors. The conventional EKF implementation suffers uncertain results while the update measurement noise matrix R and/or the process noise matrix Q does not meet the case. 505

4 Fig. 3. Tightly-coupled INS/GNSS integration architecture (closed loop). Fig. 4. IAE computing procedure. 3. THE IMPLEMENTATION OF AKF SCHEMES This study implements AKF by innovation-based adaptive estimation (IAE). IAE needs to calculate the innovation sequence, which is obtained by the difference between real measurement received by the filter and predicted value. At the current epoch k, not only the new measurement but the predicted value provides the new information. Hence, the innovation sequence represents the information satisfy the new measurement and considered as the most relevant source of the adaptive filter. The primary advantage of AKF is that the filter has less relationship with the priori statistical information because the R matrix varies with time. In this study, the innovation sequence is used to derive the measurement weights through the covariance matrix R in this study, and the covariance matrix R is adapted when measurements update with time. A window based approach is implemented to update the quality of GNSS pseudo-range measurements by adaptively replace the measurement weights through the latest estimated covariance matrices R. Figure 4 depicts the implementation of IAE procedure. In the IAE approach, the measurement covariance matrix R and system noise covariance matrix Q are tuned by measurements of different time. The study focuses on the influence of the qualities of measurements, so only the measurement covariance matrix R is variable. The formulations of AKF are shown below (R-only) [7]. Ĉ vk = 1 N k j= j 0 v j v T j (1) v k = Z k H k x k( ) (2) 506

5 Fig. 5. The two non-holonomic constraints in the b-frame. and R k = C vk H k P k( ) H T k (3) where v k represents the innovation sequence and Ĉ vk is the covariance of innovation sequence at epoch k. j 0 is the first epoch of estimation window, and it would be calculated by j 0 = k N + 1 and N is the size of window. This way of updating measurement covariance matrix R is derived from EKF, but it still produces new R with different time and different measurements. Because of those characteristics, it could be regarded as a modified version of AKF. The integrated algorithm in this study is applied for land vehicle navigation. Therefore, the velocity of land vehicle navigation constraints is derived assuming that the vehicle does not slip, which is a close representation for travel in a constant direction. A second assumption is that the vehicle stays on the ground, i.e., it does not jump of the ground. If both assumptions are true, non-holonomic constraints (NHC) are defined as the fact that unless the vehicle jumps off the ground or slides on the ground, the velocity of the vehicle in the plane perpendicular to the forward direction is almost zero [8 10]. Figure 5 shows the scenario of non-holonomic constraints in the b-frame. Therefore, two constraints can be considered as measurement updates to the Kalman filtering navigation: { v b y 0 v b z 0. (4) The body frame velocity can be given as: Perturbing Eq. (5) expresses: ˆv b = Ĉ b n ˆv n = (Ĉ b n) T ˆv n. (5) v b + δv b = [(I E n )C n b ]T (v n + δv n ) = C b n(i E n )(v n + δv n ). (6) Collecting terms to the first order, the velocity error dynamics can be written as: Then the measurement matrix can be given as: δv b = C b nδv n +C b ne n v n = C b nδv n C b n(v n ) n. (7) z NHC k = [ δv b y δv b z ] T (8) and [ H NHC 01 3 C k = 12 C 22 C 32 v D C 22 + v E C 32 v D C C 13 C 23 C 33 v D C 22 + v E C 32 v D C ]. (9) 507

6 Fig. 6. INS-based tightly-coupled integrated systems with NHC. Fig. 7. Trajectory in this field scenario. where C i j is the (i, j) elements from the DCM Cb n. In general, the velocity output of the inertial navigation mechanization v n can be transformed to the body frame velocity v b by the attitude error dynamics DCM Cb n. And the znhc k is used as the measurements in the Kalman filter. The estimated errors will be fed back to the mechanization then. Finally, the implementation of the Kalman filters with non-holonomic constraints in INS-based tightly-coupled integrated systems can be illustrated as Fig RESULTS AND DISCUSSIONS To validate the performance of proposed algorithm, a field test was conducted in the downtown area of Tainan. The total trajectory distance is 5 km and the work time is 20 min. The trajectory can be displayed in Google earth as shown in Fig. 7, and Fig. 8 shows the building distribution and scenes beside the roads went through in this field scenario. The test platform was mounted on the top of a land vehicle. The IMUs applied includes SPAN-CPT (1 deg/hr in run gyro bias) from NovAtel, which was used as the reference 508

7 Fig. 8. Scenes in this field scenario. Fig. 9. The experiment platform. system, and test IMU, C-MIGITS III (3 deg/hr in run gyro bias). The GNSS measurements were collected by a dual-frequency receiver, NovAtel OEMV-3 (geodetic), and a single frequency receiver, Ublox AEK-4T (low-cost). The set up of the test platform is illustrated in Fig. 9. Figure 10 depicts the trajectories estimated by EKF, EKF+NHC, AKF, AKF+NHC and reference trajectory. As shown in this figure, the EKF estimated trajectory deviated from the reference trajectory when the vehicle traveled through urban area where the quality of GNSS signals became relatively poor. On the other hand, those trajectories estimated AKF based schemes have shown relatively stable results because the impact of bad pseudo-range measurements have been reduced through changing the measurement covariance R adaptively to reflect the quality of GNSS measurements and increase the robustness of the tightly coupled scheme. The reference trajectory was produced using the raw measurements of SPAN-CPT and dual frequency GNSS carrier phase measurements in differential mode with RTS smoothing implemented in tightly-coupled mode. The test IMU data sets provided by C-MIGITS III an were processed with GNSS raw measurement collected by Ublox AEK-4T using the conventional tightly-coupled scheme shown in Fig. 3 and proposed AKF based tightly-coupled schemes, respectively. 509

8 Fig. 10. The trajectories. Fig. 11. PDOP and visible satellites of the geodetic GNSS receiver. Fig. 12. PDOP and visible satellites of the low-cost GNSS receiver. Figures 11 and 12 compare the number of visible satellites and PDOP values provided by the reference GNSS receiver, a geodetic grade dual frequency GNSS receiver and a test receiver, a consumer grade single frequency GNSS receiver. 510

9 Fig. 13. E-errors. Fig. 14. N-errors. Fig. 15. U-errors. Figures 13 to 15 illustrate positional errors of those approaches in East, North and Height components. Generally speaking, the positional errors estimated by NHC are significantly smaller than those estimated by EKF and AKF in East direction in most of the cases. On the other hand, the positional errors of north components estimated by AKF+NHC are slightly smaller than those estimated by EKF in North direction in most of the cases. Similar trend can be founded in height components. Tables 1 and 2 illustrate the statistical summary of the numerical comparisons between EKF, EKF+NHC, AKF and AKF+NHC in field scenarios. In the case of EKF based INS/GNSS tightly-coupled integration with NHC, all the results of the two integrated systems in this field scenario have 40% up improvement in horizontal positional error and 30% averaged improvement in 3D positional error from EKF to EKF with NHC. In the other case of AKF based INS/GNSS tightly-coupled integration with NHC; the results show the 25% averaged improvement in 3D positional error. Therefore, the aid of NHC to Kalman filters applied in land vehicles can be reveal here, especially during no GNSS signals. 511

10 Table 1. RMS and improvement ratio. KF RMS (m) Improv. (%) E N U E N U EKF EKF+NHC AKF AKF+NHC Table 2. Maximum error. KF Maximum error (m) E N U EKF EKF+NHC AKF AKF+NHC CONCLUSIONS The case of the 17-state EKF based tightly-coupled INS/GNSS integrated system can reach 30% averaged improvement in 3D position error with NHC. The other case of 17-state AKF based tightly-coupled INS/GNSS integrated system can reach 25% averaged improvement in 3D position error with NHC. Especially, the NHC can be the aid for the stand-alone INS to decrease the position drift during the GNSS obstructions over 1 minute in those two cases of the INS integrated with the geodetic GNSS receiver and the low-cost GNSS receiver. Therefore, the AKF based INS/GNSS tightly-coupled integrated algorithm with NHC can provide more stable navigation solutions than EKF and AKF based integration algorithms applied in a hostile environment. In the combination of NHC and the Kalman filters, the attitude dynamics are the essential matrices to convert the n-frame to b-frame. The NHC are implemented in the b-frame and it can be regarded as providing the more accuracy velocity measurement update. Therefore, other sensors such as odometers providing the horizontal velocities and barometers providing vertical velocities possibly can be applied as velocity measurement update for INS/GNSS integrated systems. REFERENCES 1. Yang, Y., Tightly coupled MEMS INS/GPS integration with INS aided receiver tracking loops, Dissertation, Department of Geomatics Engineering, University of Calgary, Canada, Petovello, M.G., Real-time integration of tactical grade IMU and GPS for high-accuracy positioning and navigation, PhD Thesis, Department of Geomatics Engineering, University of Calgary, Canada, Chiang, K.W., Noureldin, A. and El-Sheimy, N., A new weight updating method for INS/GPS integration architectures based on neural networks, Measurement Science and Technology, Vol. 15, No. 10, pp , Chiang, K.W. and Huang, Y.W., An intelligent navigator for seamless INS/GPS integrated land vehicle navigation applications, Applied Soft Computing, Vol. 1, pp , Shin, E.H., Estimation techniques for low-cost inertial navigation, PhD Thesis, Department of Geomatics Engineering, University of Calgary, Canada, Wendel, J. and Trommer, G.F. Tightly coupled GPS/INS integration for missile applications, Aerospace Science and Technology, Vol. 8, pp , Schwarz, K.P. and Mohamed, A.H., Adaptive Kalman filtering for INS/GPS, Journal of Geodesy, Vol. 73, pp ,

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