Optimal filtering for systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements
Optimal filtering for systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements
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DOI：
10.1016/j.cnsns.2015.08.015
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Dongyan Chen;Long Xu;Junhua Du
中科院分区：
文献类型：
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作者：
Dongyan Chen;Long Xu;Junhua Du
研究了一类具有有限步自相关过程噪声、随机一步传感器延迟和缺失测量值的离散随机系统的最优滤波问题。系统中存在的随机干扰以乘性噪声为特征，随机出现传感器延迟和测量缺失现象。随机传感器延迟和缺失测量用两个条件概率已知的伯努利分布随机变量来描述。利用状态增强方法，将原系统转化为一个新的离散系统，其中传感器输出中存在随机的一步延迟和缺失测量值。新的过程噪声和观测噪声由原来的随机项组成，过程噪声仍然是自相关的。然后，基于最小均方误差（MMSE）原理，设计了一种新的线性最优滤波器，使得对有限步自相关过程噪声、随机一步传感器延迟和缺失测量的估计误差最小。通过求解递归矩阵方程，设计了滤波器增益。最后，通过仿真实例验证了所提滤波方案的可行性和有效性。
The optimal filtering problem is investigated for a class of discrete stochastic systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements. The random disturbances existing in the system are characterized by the multiplicative noises and the phenomena of sensor delay and missing measurements occur in a random way. The random sensor delay and missing measurements are described by two Bernoulli distributed random variables with known conditional probabilities. By using the state augmentation approach, the original system is converted into a new discrete system where the random one-step sensor delay and missing measurements exist in the sensor output. The new process noises and observation noises consist of the original stochastic terms, and the process noises are still autocorrelated. Then, based on the minimum mean square error (MMSE) principle, a new linear optimal filter is designed such that, for the finite-step autocorrelated process noises, random one-step sensor delay and missing measurements, the estimation error is minimized. By solving the recursive matrix equation, the filter gain is designed. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed filtering scheme.