Department of Physics, University of Otago, Dunedin, New Zealand.
Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.
Phys Rev E. 2018 Jan;97(1-1):010201. doi: 10.1103/PhysRevE.97.010201.
Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.
最优序贯推断，或对确定性动力系统状态的滤波，要求对福罗贝尼乌斯-佩龙算子进行模拟，这可以表述为连续性方程的解。对于低维、平滑系统，有限体积数值方法提供了一种解决方案，该方案可保持概率并给出收敛到最优连续时间值的估计，而柯朗-弗里德里希斯-莱维型条件则确保中间离散化解决方案保持正密度函数。该方法在一个简单摆的非线性滤波状态的示例中得到了演示，与使用无迹卡尔曼滤波器的结果进行了比较，并针对观测值秩亏导致多峰概率分布的情况进行了演示。
