Enhanced Direct Quadrature Based Method of Moments for Nonlinear Filtering
نویسندگان
چکیده
The optimal estimation of a general continuous-discrete system can be achieved through the solution of the Fokker-Planck equation and the Bayesian update. However, solving the Fokker-Planck equation numerically is prohibitive in most cases. Recently a nonlinear filtering algorithm using a direct quadrature method of moments was proposed by the authors, in which the associated Fokker-Planck equation can be propagated efficiently and accurately. This approach involves a representation of the state conditional probability density function in terms of a finite collection of Dirac delta functions. The weights and locations (abscissas) in this representation are determined by moment constraints. Although this approach has demonstrated its promising in the field of nonlinear filtering in several examples, the “degeneracy” phenomenon, similar to that which exists in a typical particle filter, occasionally appears because only the weights are updated in the modified Bayesian rule in this algorithm. Therefore, in this paper to enhance the performance, a more stable measurement update process based upon the update equation in the Extended or Unscented Kalman filters and a more accurate initialization and re-sampling strategy for weight and abscissas are proposed. As demonstrated by a standard bearing-only tracking problem, the advantages of the method are: (1) the proposed approach could lead to a significant reduction in computational cost, as compared to finite difference and other equivalent methods, without compromising the estimation accuracy; (2) the estimation performance under less frequent measurement updates is superior to Extended or Unscented Kalman filters in terms of accuracy.
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تاریخ انتشار 2009