Kalman filters for non-linear systems: a comparison of performance

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Abstract
The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the algorithm is often used for non-linear systems by linearizing the system's process and measurement models. Different ways of linearizing the models lead to different filters. In some applications, these ‘Kalman filter variants’ seem to perform well, while for other applications they are useless. When choosing a filter for a new application, the literature gives us little to rely on. This paper tries to bridge the gap between the theoretical derivation of a Kalman filter variant and its performance in practice when applied to a non-linear system, by providing an application-independent analysis of the performances of the common Kalman filter variants. This paper separates performance evaluation of Kalman filters into (i) consistency, and (ii) information content of the estimates; and it separates the filter structure into (i) the process update step, and (ii) the measurement update step. This decomposition provides the insights supporting an objective and systematic evaluation of the appropriateness of a particular Kalman filter variant in a particular application.

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