Sensitivity analysis for nonlinear Kalman filters in navigation signal parameter estimation

Nonlinear estimation methods are used for filtering navigation signals, the quality of which depends on the accuracy of the chosen state and observation models. In situations where model parameters are unknown or change during observation, it is necessary to resort to adaptive filtering algorithms. The need for more complex approaches is determined by how much the deviation of a particular parameter affects the filtering result. To assess the quality of filtering, criteria such as signal-to-noise ratio gain or root mean square error are typically used; however, these are not intended to determine the influence of the magnitude of parameter deviations from their true values on the estimation error variance, unlike a quality indicator such as sensitivity. The article discusses the analysis of filtering sensitivity to changes in observation and state parameters under the influence of white noise for Kalman filters of various accuracy orders and a filter optimal by the criterion of maximum a posteriori probability density. Simulation is carried out by numerical methods. The derivation of the large-scale sensitivity equation for the nonlinear Kalman filter in analytical form is presented. As a result, dependencies of sensitivity on the magnitude of the discrepancy between the true and assumed models were obtained, as well as the stability of the filtering algorithms to this discrepancy. The results can be used to formulate requirements for permissible model parameter deviations and to check the filtering quality under conditions of their a priori uncertainty.

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