State Estimation Using Parallel Extended Kalman Filters on Nonlinear Measurements

摘要

The extended Kalman filter applied to state estimation using nonlinear measurements has demonstrated divergence in many applications involving large initial uncertainties because of invalid linearizations performed by the filter on the nonlinear measurement functions. No quantitative results can be found as to how invalid these linearizations must be before divergence occurs. An attempt is made to fill this void by deriving the extended Kalman filter as an approximate nonlinear least squares estimator, through the minimization of a measurement squared error function. The convergence of the extended Kalman filter is then determined by examining the squared error function and verifying the usefulness of this function through Monte Carlo simulation. The results of this analysis are then used to specify parameters for the Gaussian sum approximation. Simulation results for nonlinear measurements generated by harmonic and Gauss-Markov processes demonstrate that successful state estimation occurs using the Gaussian sum approximation, through proper parameter specification obtained by the convergence analysis. This technique is then applied to estimating the errors in an inertial navigation system through the use of nonlinear radar altimeter measurements and terrain elevation data. The results of applying this technique to terrain-aided navigation demonstrate that the Gaussian sum approximation provides good terrain-aided navigation performance for large initial uncertainties. (ERA citation 05:022819)