Active adaptation of a distributed multi-sensor filtering system

A multi-sensor filtering system is characterized mathematically as a result of the solution to the problem of synthesizing the multi-dimensional discrete system of filtering a single signal from heterogeneous data sources. The stationary problem statement has three variants of its solution: by Kolmogorov–Wiener, Kalman covariance, and Kalman information forms. In the body of the paper, we actualize a problem of these solutions under uncertainty conditions. Aimed at the Active Principle of Adaptation, we have found a method to form an instrumental performance index to substitute the inaccessible original performance index (filtering error mean square) by that criterion functional we created. This substitution makes it possible to apply for system adaptation all apparatus and tools of practical optimization methods, first of all, the gradient and Newton-like methods.
Our findings follow:
– Stretching one-step prediction and measurement update operations are wise to perform at the Decision Making Center; computation operations aimed to minimize the instrumental performance index are to be done in this place, too.
– Uncompounded procedures of adaptive data scaling are advisable to complete at the sensors' location in the network.
– Adaptation algorithms may be implemented based for filter structures taken in different forms: Kolmogorov–Wiener, Kalman covariance, or Kalman information forms.
– Computational operations for minimizing the instrumental performance index would be beneficial to develop as versions to implement the modern practical optimization methods of different levels of complexity.