Bayesian State Estimation for Tracking and Guidance Using the Bootstrap Filter

The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

[1]  G. Kitagawa.  Non-Gaussian State—Space Modeling of Nonstationary Time Series , 1987 .

[2]  Martin Abba Tanner,et al.  Tools for Statistical Inference: Observed Data and Data Augmentation Methods , 1993 .

[3]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[4]  Y. Ho,et al.  A Bayesian approach to problems in stochastic estimation and control , 1964 .

[5]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[6]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[7]  Nicholas G. Polson,et al.  A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling , 1992 .

[8]  Walter D. Grossman,et al.  Bearings-only tracking: a hybrid coordinate system approach , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[9]  V. Aidala,et al.  Utilization of modified polar coordinates for bearings-only tracking , 1983 .

[10]  C. Masreliez.  Approximate non-Gaussian filtering with linear state and observation relations , 1975 .

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

[12]  Susan M. Drake.  A Novel Approach. , 1996 .

[13]  J. Speyer,et al.  A stochastic analysis of a modified gain extended Kalman filter with applications to estimation with bearings only measurements , 1983, The 22nd IEEE Conference on Decision and Control.

[14]  Harold W. Sorenson,et al.  Recursive Bayesian estimation using piece-wise constant approximations , 1988, Autom..

[15]  Neil Gordon,et al.  Bayesian methods for tracking , 1993 .