用KL散度选出最可信的系统状态估计结果
A Kullback-Leibler divergence method for input-system-state identification
- 通过比较前后分布的KL散度筛选最优初始参数
- 在线性、非线性及信息有限场景下均表现更优
- 适合需要可靠状态估计的系统监控场景
本文在卡尔曼滤波框架内检验一种新型KL散度方法，用于在多个初始参数猜测下选择最可信的输入-参数-状态估计结果。该方法利用数据从先验到后验分布的信息变化来解决因初始参数不同导致结果不一致的问题。首先对多个初始参数集执行卡尔曼滤波，得到系统输入-参数-状态估计；其次，使用KL散度同时比较各后验分布与先验分布的差异；最后，选取KL散度最小的识别结果作为最可信解。该方法在线性、非线性及信息受限场景中均能有效选出表现更优的估计，为系统监控提供了有力工具。
原文摘要 · Abstract (English)
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from the uncertainty related to obtaining different results from different initial parameter set guesses, and the examined approach uses the information gained from the data in going from the prior to the posterior distribution to address the issue. Firstly, the Kalman filter is performed for a number of different initial parameter sets providing the system input-parameter-state estimation. Secondly, the resulting posterior distributions are compared simultaneously to the initial prior distributions using the Kullback-Leibler divergence. Finally, the identification with the least Kullback-Leibler divergence is selected as the one with the most plausible results. Importantly, the method is shown to select the better performed identification in linear, nonlinear, and limited information applications, providing a powerful tool for system monitoring.
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