Integrity Algorithm to Protect against Sensor Faults in Tightly-coupled KF State Prediction

Jinsil Lee, Minchan Kim, Dongchan Min, and Jiyun Lee

Abstract:	Recently, autonomous vehicles including self-driving cars, or autonomous drones are getting a great deal of attention with the expectation that they can partially replace or augment human performance while improving operational efficiency and increase the range of applications. There are many technical issues to solve for realizing the mission including mechanical and electrical problem, control and path planning, and navigation. Among the required technologies, navigation is one of the essential components for the development of autonomous vehicles because vehicles conduct control and path following operations autonomously by trusting the given navigation information. In this response, multi-sensor navigation systems have been actively developed to improve navigation accuracy as well as continuity under various operational conditions. Currently, various sensors including Global Navigation Satellite System (GNSS), Inertial Measurement Unit (IMU), vision sensor, barometer, magnetometer, and LIDAR (for cars) are integrated to provide the navigation solution. Many studies developed the integration algorithms of these sensors, and the accuracy and continuity are significantly improved. As the many inputs from various sensors are integrated, navigation solutions are more often exposed to potential sensor faults. For the practical use of the autonomous vehicle in a ‘real world’ environment, navigation safety in addition to the navigation accuracy and continuity is critical to ensure the safe operation of the autonomous vehicles. This raises the most obvious and important question which is “How can we prove that the solution from the multi-sensor navigation system is safe to use?”. This study leverages the concept of navigation integrity which is carried out in civil aviation navigation. Integrity is a measure of trust in navigation solutions, and integrity algorithm detects navigation sensor faults causing unacceptably large positioning error and computes position error bound (protection level, PL) against undetected sensor faults. In civil aviation, integrity algorithms have been developed for different types of GNSS standalone and augmentation systems including Receiver Autonomous Integrity Monitoring (RAIM), and Satellite or Ground Based Augmentation Systems (SBAS or GBAS) to ensure navigation integrity to the extremely high level of integrity (of the order of from 10-7 to 10-9). In an integrity algorithm, the PL is computed by quantifying the impact of undetected sensor faults which propagates through a filter estimation algorithm. Thus, a PL derivation algorithm should be designed depending on estimation filters. The developed integrity algorithms for civil aviation (reviewed in the previous paragraph) is designed based on the weighted least square (WLS) filter algorithm which is a snapshot estimator in accordance with the positioning algorithm. In contrast, the multi-sensor navigation systems mostly use a Kalman filter (KF), which is a ‘recursive’ filter, for estimating navigation solutions. The recursive filter utilizes all previous sensor information in addition to the current time sensor input to determine the state estimates. This means sensor faults occurred in the previous measurements affect the position estimates as well as sensor faults in the current time measurements. This fault propagation characteristic in a recursive KF should be carefully considered when designing a KF based integrity algorithm. This raises the need for the new integrity algorithm for multi-sensor navigation systems which utilizes KF for sensor integration. The KF based integrity algorithms that quantify the fault impact on state estimates are actively being discussed in recent publications [1]-[3]. One assumption made in the previous studies is that faults occur in the GNSS measurement sequence which is used for the KF measurement update. Studies in [1] and [2] quantified the worst-case integrity risk of KF estimates by determining the worst-case fault vector in an analytical approach based on the relationship between state error and range residual based monitor test statistics. [2] specifically applied the KF based integrity algorithm to evaluate the integrity risk against a GNSS spoofing within a GNSS/IMU integrated system with an assumption that the IMU is a fault-free sensor. As another approach, [3] proposed to compute a real-time PL equation for KF estimates. To improve real-time capability, it applied an external snapshot based WLS RAIM monitor for fault monitoring and computed PL by simulating the impact of remaining fault on KF estimates through the KF algorithm that users are utilizing for their positioning. Based on the fact that there are two main filtering steps which are a state prediction and measurement update, the integrity algorithm for the sensor faults occurring in the state prediction step is also required in multi-sensor navigation systems to fully assure the system safety. In the state prediction step, an estimated state in a previous epoch is propagated to the next epoch based on a given static model or using sensor measurements which provide information for the state prediction. In multi-sensor navigation systems, sensors which provide the information for vehicle motions are used for the state prediction step. There are sensors generally applied in state prediction step including IMU, and vision sensor. Those sensors are also vulnerable to faults [4]-[5], and integrity against those sensors should be considered within the system integrity algorithms. In [6], we illustrated how an unexpected step type IMU faults (potentially due to fracture, stiction, or delamination) affect the KF estimates when it is used for the state prediction in a GNSS/IMU integrated navigation system. It was also shown that the impact of fault on position solutions due to the IMU sensor faults could be expressed using the KF innovation vector in real-time. A PL was determined for the IMU sensor fault hypothesis using the KF innovation vector and additional noise bounding terms. In this paper, we extend the concept of integrity assurance against faults occurring in sensors used for state prediction, proposed in [6], to KF-based multi-sensor navigation systems. We analyze the key difference in the impact of faults occurring in the prediction step and the measurement update step on state estimates. Under the assumption that no simultaneous fault occurs on two integrated sensors (one for the state prediction, and the other for the measurement update), the most fundamental parameter we can utilize from a KF is a KF innovation vector. If the innovation can fully capture the recursive impact of faults on state estimates in real-time, the user PL can be formulated utilizing the innovation vector with additional uncertainty terms for noise bounding. Based on the analytical formulation of the recursive fault impact on user position under each fault condition, it is shown that the innovation vector can express the fault impact on user position only when the fault occurs in sensors used for the state prediction. In case of a fault occurring in sensors used for the measurement update step, additional information on the fault vector is required to fully express the magnitude of the resulting position error caused by the fault. In other words, the innovation vector cannot be used to compute user PL in real-time when there is a fault on sensors used for the measurement update. Table 1 summarizes the content in this paragraph. Based on the finding, this study proposes a generalized integrity architecture which can be used for a KF based multi-sensor navigation system to assure navigation integrity. In the integrity architecture, three fault hypotheses are defined which are a nominal hypothesis (H0), a fault hypothesis occurred in a sensor for the measurement update step (H1), and a fault hypothesis occurred in a sensor for the prediction step (H2). For the H0 hypothesis, nominal covariance from the KF is used for PL computation. Under the H1 fault hypothesis, an additional fault monitoring algorithm is required to detect faults and quantify the undetected fault magnitude after fault monitoring in order to compute the real-time protection level. The algorithms which use RAIM proposed by the previous study [3] can be utilized for computing a real-time PL for this fault hypothesis. Lastly, the KF innovation vector is used to detect the fault and to compute a PL for the H2 fault hypothesis. For the H2 fault hypothesis, fault detection is conducted on the user position domain by comparing the fault impact determined using the KF innovation vector in real-time with a pre-defined threshold without employing additional fault monitoring algorithms. The proposed integrity algorithm can be applied to various types of multi-sensor navigation systems to compute PL against the sensor faults occurring in the state prediction step. In this study, we verified and showed the applicability of the developed integrity algorithm using two types of KF based multi-sensor systems which are a GNSS/IMU integrated navigation system and a GNSS/vision integrated navigation system. IMU and Vision sensors were used to predict the filter state, and GNSS was used to update the filter. Three PLs are computed for each fault hypothesis. We employed the algorithm proposed in [3] for computing a real-time PL against GNSS faults within the KF. New PLs both for the IMU and vision sensor were determined using the KF innovation sequence based on the proposed integrity algorithm. The computed PLs for IMU and vision sensors well bounded the KF estimates both under no-fault condition and fault-injected condition. The proposed integrity algorithm for KF-based multi-sensor navigation systems against sensor faults in the KF prediction step can be broadly used to fully assure the safety of autonomous vehicles. References [1] M. Joerger, and B. Pervan (2013). "Kalman Filter-Based Integrity Monitoring Against Sensor Faults." Journal of Guidance, Control, and Dynamics 36(2): 349-361. [2] C. Tanil et al. (2017). "An INS monitor to detect GNSS spoofers capable of tracking vehicle position." IEEE Transactions on Aerospace and Electronic Systems. [3] Bhattacharyya, S. and D. Gebre-Egziabher (2015). "Kalman filter based RAIM for GNSS receivers." IEEE Transactions on Aerospace and Electronic Systems 51(3): 2444-2459. [4] Bhatti, Umar Iqbal, and Washington Yotto Ochieng. "Failure modes and models for integrated GPS/INS systems." The Journal of Navigation 60.2 (2007): 327-348. [5] Fu, Li et al. “Vision-Aided RAIM: A New Method for GPS Integrity Monitoring in Approach and Landing Phase” Sensors (Basel, Switzerland) vol. 15,9 22854-73. 10 Sep. 2015, doi:10.3390/s150922854 [6] J. Lee, et al., “Integrity assurance of Kalman-filter based GNSS/IMU integrated systems against IMU faults for UAV applications,” ION GNSS 2018, Miami, Florida, pp. 2484-2500.
Published in:	Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019) September 16 - 20, 2019 Hyatt Regency Miami Miami, Florida
Pages:	594 - 627
Cite this article:	Lee, Jinsil, Kim, Minchan, Min, Dongchan, Lee, Jiyun, "Integrity Algorithm to Protect against Sensor Faults in Tightly-coupled KF State Prediction," Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 2019, pp. 594-627. https://doi.org/10.33012/2019.16867
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