Novel approach to nonlinear/non-Gaussian Bayesian state estimation
An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which 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 simulation example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
- A.H. Jazwinski . (1970) , Stochastic processes and filtering theory.
- D.L. Alspach , H.W. Sorenson . Nonlinear Bayesian estimation using Gaussian sum approximation. IEEE Trans. Auto. Control , 439 - 447
- C.J. Masreliez . Approximate non-Gaussian filtering with linear state and observation relations. IEEE Trans. Auto. Control , 107 - 110
- M. West , P.J. Harrison , H.S. Migon . Dynamic generalised linear models and Bayesian forecasting (with discussion). J. Amer. Statistical Assoc. , 73 - 97
- R.S. Bucy . Bayes theorem and digital realization for nonlinear filters. J. Astronaut. Sci. , 80 - 94
- S.C. Kramer , H.W. Sorenson . Recursive Bayesian estimation using piece-wise constant approximations. Automatica , 6 , 789 - 801
- H.W. Sorenson , J.C. Spall . (1988) Recursive estimation for nonlinear dynamic systems, Bayesian analysis of time series and dynamic models.
- G. Kittagawa . Non-Gaussian state-space modelling of non-stationary time series (with discussion). J. Amer. Statistical Assoc. , 1032 - 1063
- Pole, A., West, M.: `Efficient numerical integration in dynamic models', 136, Research report, 1988.
- B.P. Carlin , N.G. Polson , D.S. Stoffer . A Monte-Carlo approach to nonnormal and nonlinear state space modelling. J. Amer. Statistical Assoc. , 493 - 500
- M. West , J.M. Bernardo , J.O. Berger , A.P. Dawid , A.F.M. Smith . (1992) Modelling with mixtures (with discussion), Bayesian statistics 4.
- P. Muller . Monte Carlo integration in general dynamic models. Contemp. Math. , 145 - 163
- B.W. Silverman . (1986) , Density estimation for statistics and data analysis.
- A.F.M. Smith , A.E. Gelfand . Bayesian statistics without tears: a sampling-resampling perspective. Amer. Stat. , 84 - 88
- Y.C. Ho , R.C.K. Lee . A Bayesian approach to problems in stochastic estimation and control. IEEE Trans. Auto. Control. , 333 - 339
- P.J. Harrison , C.F. Stevens . Bayesian forecasting (with discussion). J. R. Stat. Soc. B , 205 - 247
- V.J. Aidala , S.E. Hammel . Utilization of modified polar coordinates for bearings-only tracking. IEEE Trans. Auto. Control , 3 , 283 - 294