Robust Kalman Filtering Under Model Uncertainty: The Case of Degenerate Densities

Yi, Shenglun; Zorzi, Mattia

doi:10.1109/tac.2021.3106861

Cited by 27 publications

(20 citation statements)

References 37 publications

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“…It follows from the proof of Lemma 2 (see Appendix A) that the constant c depends on δ. The conditions (21) and (22) suggest that δ should be chosen appropriately so that both the conditions could be satisfied simultaneously. However, the exact bounds on δ depend on other bounds assumed on the system matrices in Theorem 1.…”

Section: A Forward Soekf Stabilitymentioning

confidence: 99%

“…Then, the estimation error of I-SOEKF given by ( 23) is exponentially bounded in mean-squared sense if the estimation error is bounded by a suitable constant > 0 and the bound constants also satisfy the equivalent conditions of (20), (21), and (22) for the inverse filter dynamics.…”

Section: B Inverse Soekf Stabilitymentioning

confidence: 99%

“…The uncertainty in system parameters or noise statistics may result in large estimation errors or even filter divergence [17,18]. Prior works [17,[19][20][21][22] proposed various adaptive filters to reduce the sensitivity of KF to system uncertainties. However, the general non-linear filtering problem is not considered.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

Singh¹,

Chattopadhyay²,

Mishra³

2022

Preprint

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Recent counter-adversarial system design problems have motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman filter tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). In a companion paper (Part I), we developed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. To address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cramér-Rao lower bound as a benchmark.

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Section: A Forward Soekf Stabilitymentioning

confidence: 99%

Section: B Inverse Soekf Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

Singh¹,

Chattopadhyay²,

Mishra³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, their framework dynamically competes with object birth/death and survival through correlated nonparametric processes. Yi, S. et al [ 11 ] considered the robust state space filtering problem in the case where the transition probability density is unknown and possibly degenerate. The resulting robust filter has a Kalman-like structure and solves a minimax game; the least popular model is then naturally selected in the prescribed ambiguity set, which also contains non-Gaussian probability densities, while the other participants design the best filters for the least popular models.…”

Section: Introductionmentioning

confidence: 99%

A Two-Stage Feature Point Detection and Marking Approach Based on the Labeled Multi-Bernoulli Filter

Yang

Liu

2022

Sensors

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In recent years, various algorithms using random finite sets (RFS) to solve the issue of simultaneous localization and mapping (SLAM) have been proposed. Compared with the traditional method, the advantage of the RFS method is that it can avoid data association, landmark appearance and disappearance, missed detections, and false alarms in Bayesian recursion. There are many problems in the existing robot SLAM methods, such as low estimation accuracy, poor back-end optimization, etc. On the basis of previous studies, this paper presents a labeled random finite set (L-RFS) SLAM method. We describe a scene where the sensor moves along a given path and avoids obstacles based on the L-RFS framework. Then, we use the labeled multi-Bernoulli filter (LMB) to estimate the state of the sensor and feature points. At the same time, the B-spline curve is used to smooth the obstacle avoidance path of the sensor. The effectiveness of the algorithm is verified in the final simulation.

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“…One player, say nature, selects the least favorable model in this prescribed "ball", and the other player designs the optimum estimator for the least favorable model. It is worth noting that many extensions of this paradigm have been proposed such as: the case with different ambiguity sets [20,21,22,23]; the distributed case [24,25]; the case with external input [26]; the case of degenerate densities [27,28].…”

Section: Introductionmentioning

confidence: 99%

Robust fixed-lag smoothing under model perturbations

Su¹,

Zorzi²

2022

Preprint

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A robust fixed-lag smoothing approach is proposed in the case there is a mismatch between the nominal model and the actual model. The resulting robust smoother is characterized by a dynamic game between two players: one player selects the least favorable model in a prescribed ambiguity set, while the other player selects the fixed-lag smoother minimizing the smoothing error with respect to least favorable model. We propose an efficient implementation of the proposed smoother. Moreover, we characterize the corresponding least favorable model over a finite time horizon. Finally, we test the robust fixed-lag smoother in two examples. The first one regards a target tracking problem, while the second one regards a parameter estimation problem.

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Robust Kalman Filtering Under Model Uncertainty: The Case of Degenerate Densities

Cited by 27 publications

References 37 publications

Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

A Two-Stage Feature Point Detection and Marking Approach Based on the Labeled Multi-Bernoulli Filter

Robust fixed-lag smoothing under model perturbations

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