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Nonlinear filter design using Fokker-Planck-Kolmogorov probability density evolutions

机译:使用Fokker-Planck-Kolmogorov概率密度演化的非线性滤波器设计

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The Fokker-Planck-Kolmogorov equation (FPKE) in conjunction with Bayes conditional density update formula provides optimal estimates for a general continuous-discrete nonlinear filtering problem. It is well known that the analytical solution of FPKE and Bayes formula are extremely difficult to obtain except in a few special cases. Hence, we address this problem using numerical approaches. The efficient numerical solution of FPKE presented relies on the key issue of adaptively calculating the domain over which the state probability density function is to be evaluated, which is done using Chebyshev's inequality. Application to a passive tracking example shows that this approach can provide consistent estimators when measurement nonlinearities and noise levels are high.
机译:Fokker-Planck-Kolmogorov方程(FPKE)结合贝叶斯条件密度更新公式可为一般的连续离散非线性滤波问题提供最佳估计。众所周知,除少数特殊情况外,FPKE和贝叶斯公式的解析解极难获得。因此,我们使用数值方法解决了这个问题。提出的FPKE的有效数值解依赖于关键问题,即自适应地计算将要评估状态概率密度函数的域,这是使用切比雪夫不等式完成的。在无源跟踪示例中的应用表明,当测量非线性和噪声水平很高时,该方法可以提供一致的估计。

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