A constrained extended Kalman filter based on LS-VCE formulated by condition equations with prediction of cross-covariances

摘要

A constrained extended Kalman filter (CEKF) based on least-squares variance component estimation (LS-VCE) is generally developed by condition equations since the proper prediction of dispersion matrices is one of the main bottlenecks in the KF algorithms. Here we investigate four problems which have not been simultaneously considered yet. These problems are examination of non-linearty of dynamic model, VCE, general non-linear state constraints and fairly general stochastic model. Although a few contributions proposed some adaptive KF in particular based on Helmert's VCE method, they developed their filters for special problems with some restrictive conditions such as independence of all variables and/or linearity of the dynamic model. Also some of these filters did not apply VCE methods to all parts of the dynamic model. In this contribution, we try to overcome all of these restrictions. Moreover, LS-VCE method gives some added advantages over other VCE methods. First the new formulation of CEKF is developed by condition equations with prediction of all possible cross-covariances as algorithm 1. Then the LS-VCE method is applied to it after some modifications which results in an adaptive constrained extended Kalman filter (ACEKF) as the second algorithm.