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SELECTED BIBLIOGRAPHY 135

multi-modal due to the uncertainty of the moment at which the on/off
control switches its state.
In contrast with the Kalman filter, the particle filter is able to
estimate the fluctuations of the volume. In addition, the estimation
of the density is much more accurate. The price to pay is the compu-
tational cost.

MATLAB functions for particle filtering
Many MATLAB users have already implemented particle filters, but no
formal toolbox yet exists. Section 9.3 contains a listing of MATLAB code
that implements the condensation algorithm. Details of the implementa-
tion are also given.

4.5 SELECTED BIBLIOGRAPHY

Some introductory books on Kalman filtering and its applications are
Anderson and Moore (1979), Bar-Shalom and Li (1993), Gelb et al.
(1974), Grewal and Andrews (2001). Hidden Markov models are
described in Rabiner (1989). Tutorials on particle filtering are found in
Arulampalam et al. (2002) and Merwe et al. (2000). These tutorials also
describe some shortcomings of the particle filter, and possible remedies.
Seminal papers for Kalman filtering, particle filtering and unscented
Kalman filtering are Kalman (1960), Gordon et al. (1993) and Julier
and Uhlmann (1997), respectively. Linear systems with random inputs,
among which the AR models, are studied in Box and Jenkins (1976). The
topic of statistical linearization is treated in Gelb et al. (1974). The
condensation algorithm is due to Isard and Blake (1996). The Baum-
Welch algorithm is described in Rabiner (1986).

Anderson, B.D. and Moore, J.B., Optimal Filtering, Prentice Hall, Englewood Cliffs, NJ,
1979.
Arulampalam, M.S., Maskell, S., Gordon, N. and Clapp, T., A tutorial on particle filters
for online nonlinear/non-Gaussian Bayesian tracking, IEEE Transactions on Signal
Processing, 50(2), 174–88, February 2002.
Bar-Shalom, Y. and Li, X.R., Estimation and Tracking – Principles, Techniques, and
Software, Artech House, Boston, 1993.
Box, G.E.P. and Jenkins, G.M., Time Series Analysis: Forecasting and Control, Holden-
Day, San Francisco, 1976.
Gelb, A., Kasper, J.F., Nash, R.A., Price, C.F. and Sutherland, A.A., Applied Optimal
Estimation, MIT Press, Cambridge, MA, 1974.
Gordon, N.J., Salmond, D.J. and Smith, A.F.M., Novel approach to nonlinear/nonGaussian
Bayesian state estimation, IEE Proceedings-F, 140(2), 107–13, 1993.