Bayesian fault detection method for linear systems with outliers

A novel approach for monitoring the accuracy of the Bayesian estimate of linear Gaussian state-space model is introduced, based on the monitoring of the propagation of the errors in the Kalman filter algorithm. The effect of the sensor errors on the Kalman filter estimate is explicitly computed and compensated. A marginalized particle filter is used to compute the posterior distribution of the sensor errors. Using a target tracking simulation it is shown that the proposed method has improved performance over the standard detection-identification-adaptation (DIA) method.

[1]  Weihua Zhuang,et al.  Nonline-of-sight error mitigation in mobile location , 2005, IEEE Trans. Wirel. Commun..

[2]  A F Smith,et al.  Monitoring renal transplants: an application of the multiprocess Kalman filter. , 1983, Biometrics.

[3]  Irwin Guttman,et al.  Optimal collapsing of mixture distributions in robust recursive estimation , 1989 .

[4]  P.J.G. Teunissen Quality control in integrated navigation systems , 1990, IEEE Symposium on Position Location and Navigation. A Decade of Excellence in the Navigation Sciences.

[5]  W. Baarda,et al.  A testing procedure for use in geodetic networks. , 1968 .

[6]  H. Sorenson,et al.  Recursive bayesian estimation using gaussian sums , 1971 .

[7]  Michèle Basseville,et al.  Detection of Abrupt Changes: Theory and Applications. , 1995 .

[8]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[9]  Jean-Yves Tourneret,et al.  A Particle Filtering Approach for Joint Detection/Estimation of Multipath Effects on GPS Measurements , 2007, IEEE Transactions on Signal Processing.

[10]  Henri Pesonen A Framework for Bayesian Receiver Autonomous Integrity Monitoring in Urban Navigation , 2011 .

[11]  Fredrik Gustafsson,et al.  Adaptive filtering and change detection , 2000 .

[12]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[13]  Ba-Ngu Vo,et al.  The Gaussian Mixture Probability Hypothesis Density Filter , 2006, IEEE Transactions on Signal Processing.

[14]  H. Sorenson,et al.  Nonlinear Bayesian estimation using Gaussian sum approximations , 1972 .

[15]  Olivier Julien,et al.  Detection of Variance Changes and Mean Value Jumps in Measurement Noise for Multipath Mitigation in Urban Navigation , 2010 .

[16]  F. Gustafsson The marginalized likelihood ratio test for detecting abrupt changes , 1996, IEEE Trans. Autom. Control..

[17]  Robert Piche,et al.  Bayesian positioning using Gaussian mixture models with time-varying component weights , 2011 .

[18]  R. Grover Brown,et al.  A Baseline GPS RAIM Scheme and a Note on the Equivalence of Three RAIM Methods , 1992 .

[19]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[20]  A. Willsky,et al.  A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems , 1976 .

[21]  J.-Y. Tourneret,et al.  Detection of variance changes and mean value jumps in measurement noise for multipath mitigation in urban navigation , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.