Abstract
Nonlinear Gaussian filters are usually developed from numerical quadrature rules to approximate the mean and covariance. However, the Gaussian assumption may not be viable after propagation of the estimate through nonlinear dynamics, which may lead to degraded performance. In this brief, we propose an enhanced nonlinear Gaussian quadrature filter in which the quadrature points/weights are generated by a data-driven arbitrary polynomial chaos (aPC) method without relying on the Gaussian assumption. A set of Monte Carlo samples are first propagated through nonlinear dynamics. The statistic moments can be calculated directly from these Monte Carlo samples. The enhanced quadrature points/weights are generated from these moments using the aPC method. Since such quadrature points contain higher order statistic information of the propagated distribution, they can better represent the state distribution and provide a more accurate estimate. Numerical examples show the effectiveness of the proposed filter.
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