A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements

The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73%and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.

[1]  Lennart Ljung,et al.  Generalized Kalman smoothing: Modeling and algorithms , 2016, Autom..

[2]  Fahed Abdallah,et al.  Particle Filtering Combined with Interval Methods for Tracking Applications , 2012 .

[3]  Christian Musso,et al.  Improving Regularised Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[4]  Branko Ristic,et al.  Introduction to the Box Particle Filtering , 2013 .

[5]  Lyudmila Mihaylova,et al.  Box Particle Filtering for extended object tracking , 2012, 2012 15th International Conference on Information Fusion.

[6]  Fahed Abdallah,et al.  An Introduction to Box Particle Filtering [Lecture Notes] , 2013, IEEE Signal Processing Magazine.

[7]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[8]  Karim Dahia,et al.  A Box Regularized Particle Filter for terrain navigation with highly non-linear measurements* , 2016 .

[9]  Visakan Kadirkamanathan,et al.  Autonomous crowds tracking with box particle filtering and convolution particle filtering , 2016, Autom..

[10]  J. Norton,et al.  State bounding with ellipsoidal set description of the uncertainty , 1996 .

[11]  N. Higham COMPUTING A NEAREST SYMMETRIC POSITIVE SEMIDEFINITE MATRIX , 1988 .

[12]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[13]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[14]  E. Walter,et al.  Exact description of feasible parameter sets and minimax estimation , 1994 .

[15]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[16]  Luc Jaulin,et al.  Robust set-membership state estimation; application to underwater robotics , 2009, Autom..

[17]  F. Schweppe Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[18]  Arnold Neumaier,et al.  Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization , 1998, SIAM Rev..

[19]  Fahed Abdallah,et al.  Box particle filtering for nonlinear state estimation using interval analysis , 2008, Autom..

[20]  Shiyin Qin,et al.  A Fast Algorithm of Simultaneous Localization and Mapping for Mobile Robot Based on Ball Particle Filter , 2018, IEEE Access.

[21]  Petar M. Djuric,et al.  Resampling Methods for Particle Filtering: Classification, implementation, and strategies , 2015, IEEE Signal Processing Magazine.

[22]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[23]  Branko Ristic,et al.  Bernoulli Particle/Box-Particle Filters for Detection and Tracking in the Presence of Triple Measurement Uncertainty , 2012, IEEE Transactions on Signal Processing.