类卡尔曼粒子滤波：量化新息/测量的最优估计
The Kalman Like Particle Filter : Optimal Estimation With Quantized Innovations/Measurements
摘要：
我们研究了线性系统的最优估计和控制问题，使用量化测量，重点是传感器网络的应用。我们表明，状态条件下的因果量化的测量可以表示为高斯随机向量和一定的截断高斯向量的总和。这种结构与全信息卡尔曼滤波器非常相似，因此允许我们有效地将卡尔曼结构与粒子滤波器相结合，以递归地计算状态估计。我们称由此产生的滤波器的卡尔曼粒子滤波器（KLPF），并观察到，它提供了接近最佳的性能，使用少得多的粒子比直接应用于原始问题的粒子滤波器。我们表明，条件态密度遵循一个，所谓的，广义闭偏态（GCSN）分布。我们进一步表明，对于这样的系统的经典分离性质之间的控制和估计举行，确定性等价的控制律是LQG最优的。
英文摘要：
We study the problem of optimal estimation and control of linear systems using quantized measurements, with a focus on applications over sensor networks. We show that the state conditioned on a causal quantization of the measurements can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resulting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far fewer particles than that of a particle filter directly applied to the original problem. We show that the conditional state density follows a, so called, generalized closed skew-normal (GCSN) distribution. We further show that for such systems the classical separation property between control and estimation holds and that the certainty equivalent control law is LQG optimal.
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