Abstract
This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.
Highlights
This paper describes a recursive algorithm based on a nonlinear approach to parameter estimation
The most common procedure applied for nonlinear estimation is the extended Kalman filter (EKF) [1, 2, 3]
The performances were evaluated in terms of normalised root mean square error (NRMSE) of 100 time samples over 50 runs
Summary
This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. The densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms. Keywords and phrases: nonlinear estimation, nonlinear adaptive filter, exponential distribution, maximum entropy, nonGaussian signal processing
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