Kalman and particle filtering

This chapter contains sections titled: One-Dimensional Consideration Multidimensional Consideration An Alternate Derivation of the Multidimensional Covariance Prediction Equations Application of the EKF to the DIFAR Ship Tracking Case Study References

Linearization

Tracking (education)

Alpha beta filter

Unscented transform

10.1002/9781118287798.ch7

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A Few Problems with Application of the Kalman Filter

Lecture notes in statistics (1989)

Carlo Carraro

Alpha beta filter

10.1007/978-1-4612-3680-1_9

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A Generalised Extended Kalman Filter and its Application to Steel Rolling Temperature Estimation

IFAC Proceedings Volumes (1993)

Jingrong Cheng P. Stone Duncan McFarlane

Alpha beta filter

Line (geometry)

10.1016/s1474-6670(17)48546-6

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Further Development of the Kalman Filter

Advanced textbooks in control and signal processing (1999)

Edward W. Kamen J. K. Su

The previous chapter took us from the idea of recursive estimation to the Kalman filter. This chapter contains several extensions of the Kalman filter. It begins with a discussion of the innovations, which are the estimation error for predicting the measurements. The innovations can be viewed as the “new information” about x(n) that is conveyed by z(n) and have a number of interesting and useful properties. An alternate derivation, based on the innovations, of the Kalman filter follows.

Alpha beta filter

10.1007/978-1-4471-0417-9_6

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Comparison of H_∞ Robust Filter and Kalman Filter

Systems engineering and electronics (2003)

Zhang Li-kun

In general conditions, Kalman filtering technique has been applied extensively. When there is uncertainty in dynamic model of the statistics of noise sources are not fully known or unavailable, the application of Kalman filtering is restricted. H_∞ filtering can solve the problems in the applications of Kalman filtering with high accuracy and robustness. In this paper, H_∞ filtering and Kalman filtering technique are introduced in brief, H_∞ robust filter and Kalman filter are designed, and their performances are compared and studied through three aspects.

Alpha beta filter

Robustness

Filtering problem

Source

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Special Topic: An Introduction to Kalman Filter

Graduate texts in mathematics (2022)

Rabi Bhattacharya Edward C. Waymire

Alpha beta filter

10.1007/978-3-031-00943-3_25

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An approximation of the Kalman filter equations

IEEE Transactions on Automatic Control (1968)

C.H. Wells

This correspondence presents the results of the application of the matrix inversion lemma to the Kalman filter equation. This operation eliminates the inversion process in the Kalman filter and enables one to sequentially compute the optimum estimate of the state without the use of the inversion process.

Alpha beta filter

Lemma (botany)

10.1109/tac.1968.1098931

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Modified extended Kalman filtering

Derek S. Wall F.M.F. Gaston

This paper examines a previously published modified extended Kalman (1960) filter. The modification provides better estimates than the extended Kalman filter under certain system conditions. The modification attempts to formulate a more accurate linearization of the underlying system, hence improve the state estimates. This paper investigates conditions where the algorithm outperforms the extended Kalman filter. The paper also suggests an additional modification which further improves the performance.

Alpha beta filter

Linearization

Unscented transform

10.1109/icdsp.1997.628449

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