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.

Directional splitting of Gaussian density in non‐linear random variable transformation

“…A feasible approach to prevent the violation of the Gaussianity assumption of the transformed variable is an approximation of the Gaussian PDF of the to-be-transformed variables by a mixture of Gaussian PDFs, each with a smaller covariance matrix than the original Gaussian PDF [1,2,4,10,[17][18][19][20][21][22]. Decreasing the covariance matrix (and thus narrowing the region where the nonlinear function is assessed) inherently results in an asymptotic reduction of the MoNL corresponding to each term of the GM.…”