Distributed Kalman Filtering [chapter]

2014 Networked Filtering and Fusion in Wireless Sensor Networks  
The Kalman filter provides an efficient means to estimate the state of a linear process, so that it minimizes the mean of the squared estimation error. However, for naturally distributed applications, the construction and tuning of a centralized observer may present difficulties. Therefore, we propose the decomposition of a linear process model into a cascade of simpler subsystems and the use of a Kalman filter to individually estimate the states of these subsystems. Both a theoretical
more » ... n and simulation examples are presented. The theoretical results show that the distributed observers, except for special cases, do not minimize the overall error covariance, and the distributed observer system is therefore suboptimal. However, in practice, the performance achieved by the cascaded observers is comparable and in certain cases even better than the performance of the centralized observer. A distributed observer system also leads to increased modularity, reduced complexity, and lower computational costs. (0)15 27 88573, Fax:+31 (0)15 27 86679 Preprint submitted to Elsevier and a sequence of noisy measurements. For such a purpose, dynamic systems are often modeled in the state-space framework, using a state-transition model, which describes the evolution of states over time and a measurement model, which relates the measurement to the states. In state-estimation problems, these models may also be given in a probabilistic form. The most well-known and widely used probabilistic estimation methods are the Kalman filter and its extension to nonlinear systems, the Extended Kalman Filter (Kalman, 1960; Welch and Bishop, 2002) . While the Kalman filter has severe limitations and becomes unstable for highly nonlinear processes, for a linear process, it provides an efficient means to estimate the states so that it also minimizes the mean of the squared error. The filter supports the estimation of past, present and future states, even if a precise model of the system considered is unknown.
doi:10.1201/b17667-5 fatcat:m7zdr62rpjforc7l546jfhiyla