Minimal Number of Sensor Nodes for Distributed Kalman Filtering

Finding and identifying the minimal number of sensor nodes for a sensor network is one of the most basic problems for the implementation of distributed state estimators. Despite a plethora of research studied sensor networks, most of them ignored this problem or assumed the considered sensor network comes with an ideal number of sensor nodes. We revisit this problem in the current paper. To this end, the minimal number of sensor nodes problem is first formalized and a novel observability condition, namely, minimal nodes uniform observability (MNUO), is then proposed. Next, this MNUO is applied to study the stability issues of the distributed Kalman filtering algorithm. In what follows, under the condition of MNUO, conditions to ensure its stability are given and the results about the relation of the filtering performance before and after selecting the minimal number of sensor nodes are obtained. Finally, optimization solutions and an example are given to find the minimal number of sensor nodes for a sensor network.