Structure adaptation of nonlinear filters based on non-Gaussianity measures

Abstract

The paper deals with state estimation of stochastic nonlinear dynamical systems. A structure adaptation of nonlinear filters is proposed to reduce errors stemming from approximations made by the filters. The adaptation is controlled by non-Gaussian measures which assess current working conditions of the filter. A large non-Gaussian measure indicates a possible large approximation error and results in splitting the state conditional probability density function. To limit computational complexity of the filter given by the number of terms, a reduction of this number is done by merging some terms. The algorithm of the proposed filter with structure adaptation is detailed using the extended Kalman filter relations. Performance of the filter is illustrated in a numerical example.