Abstract
The measurement update stage in the nonlinear filtering is considered in the viewpoint of information geometry, and the filtered state is considered as an optimization estimation in parameter space has been corresponded with the iteration in the statistical manifold, then a recursive method is proposed in this paper. This method is derived based on the natural gradient descent on the statistical manifold, which constructed by the posterior probability density function (PDF) of state conditional on the measurement. The derivation procedure is processing in the geometric viewpoint, and gives a geometric interpretation for the iteration update. Besides, the proposed method can be seen as an extended for the Kalman filter and its variants. For the one step in our proposed method, it is identical to the Extended Kalman filter (EKF) in the nonlinear case, while traditional Kalman filter in the linear case. Benefited from the natural gradient descent used in the update stage, our proposed method performs better than the existing methods, and the results have showed in the numerical experiments.
Highlights
Nonlinear filtering is a significant issue in the field of signal processing, such as target tracking, navigation and audio signal processing
The measurement update has been considered as an optimization estimation in the view of information geometry, and the estimation in the parameter space has been corresponded with the iteration procedure in a statistical manifold
We have constructed the statistical manifold based on the posterior probability density function (PDF) of state under the condition of measurement in the Bayesian framework
Summary
Nonlinear filtering is a significant issue in the field of signal processing, such as target tracking, navigation and audio signal processing. Motivated by the recursively estimation for nonlinear measurement update in the Bayesian filtering, we propose a method by using the natural gradient descent method in the statistical manifold constructed by the posterior PDF for measurement update in the nonlinear filtering. Based on the fact that the Fisher information matrix (FIM) is the inverse of Cramer-Rao Limit Bounds(CRLB) with respect to the estimation, the natural gradient descent, which has used FIM as metric in the statistical manifold, may achieve the better performance of estimation. With the better performance and fast convergence, the measurement update with natural gradient descent may be achieved better and faster Based on this measurement update stage, we can construct the different nonlinear filtering method with different state prediction method.
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