Properties of Distributed Filtering Under Scaled Noise Covariances

This paper investigates the properties of the distributed filter under scaled noise covariances. Initially, three performance indices, along with three auxiliary indices, are introduced to evaluate the performance of the distributed filter. By providing the specific assumptions on the scaled parameters, the proportional relations among three performance indices are revealed. The relations of the gain matrices under the nominal and actual parameter scenarios are also examined. Furthermore, the impact of the fusion step on these relations is elucidated. These results provide guidance for designing the nominal noise covariance and evaluating the performance of the distributed filter under the scaled noise covariances. The theoretical results are validated through simulations.