© The Institution of Electrical Engineers
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.
References
-
-
1)
-
A.F.M. Smith ,
A.E. Gelfand
.
Bayesian statistics without tears: a sampling-resampling perspective.
Amer. Stat.
,
84 -
88
-
2)
-
M. West ,
J.M. Bernardo ,
J.O. Berger ,
A.P. Dawid ,
A.F.M. Smith
.
(1992)
Modelling with mixtures (with discussion), Bayesian statistics 4.
-
3)
-
G. Kittagawa
.
Non-Gaussian state-space modelling of non-stationary time series (with discussion).
J. Amer. Statistical Assoc.
,
1032 -
1063
-
4)
-
S.C. Kramer ,
H.W. Sorenson
.
Recursive Bayesian estimation using piece-wise constant approximations.
Automatica
,
6 ,
789 -
801
-
5)
-
V.J. Aidala ,
S.E. Hammel
.
Utilization of modified polar coordinates for bearings-only tracking.
IEEE Trans. Auto. Control
,
3 ,
283 -
294
-
6)
-
P. Muller
.
Monte Carlo integration in general dynamic models.
Contemp. Math.
,
145 -
163
-
7)
-
Pole, A., West, M.: `Efficient numerical integration in dynamic models', 136, Research report, 1988.
-
8)
-
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
-
9)
-
Y.C. Ho ,
R.C.K. Lee
.
A Bayesian approach to problems in stochastic estimation and control.
IEEE Trans. Auto. Control.
,
333 -
339
-
10)
-
R.S. Bucy
.
Bayes theorem and digital realization for nonlinear filters.
J. Astronaut. Sci.
,
80 -
94
-
11)
-
A.H. Jazwinski
.
(1970)
, Stochastic processes and filtering theory.
-
12)
-
B.W. Silverman
.
(1986)
, Density estimation for statistics and data analysis.
-
13)
-
H.W. Sorenson ,
J.C. Spall
.
(1988)
Recursive estimation for nonlinear dynamic systems, Bayesian analysis of time series and dynamic models.
-
14)
-
C.J. Masreliez
.
Approximate non-Gaussian filtering with linear state and observation relations.
IEEE Trans. Auto. Control
,
107 -
110
-
15)
-
P.J. Harrison ,
C.F. Stevens
.
Bayesian forecasting (with discussion).
J. R. Stat. Soc. B
,
205 -
247
-
16)
-
M. West ,
P.J. Harrison ,
H.S. Migon
.
Dynamic generalised linear models and Bayesian forecasting (with discussion).
J. Amer. Statistical Assoc.
,
73 -
97
-
17)
-
D.L. Alspach ,
H.W. Sorenson
.
Nonlinear Bayesian estimation using Gaussian sum approximation.
IEEE Trans. Auto. Control
,
439 -
447
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