Fault Identification in Linear Dynamic Systems by the Method of Locally Optimal Separate Estimation

In this article, the synthesis of two-stage structure recursive filter is carried out. The filter is resistant to unknown disturbances and is able to simultaneously evaluate both the state of the system and the malfunction has arisen in it. The presented synthesis method is based on the assumption that there is no a priori information about the dynamics of operating faults and disturbances. The provided synthesis method is based on assumption of the lack prior data about fault dynamics and perturbations. In this case, it is assumed that faults affect both the state of the system and the output variables, and disturbances affect only the state variables. Synthesis of the recursive filter was made in two options. In the first case, it was assumed that the distribution matrix of faults in the observation channel is a full rank matrix, then the result obtained was generalized to the case of an arbitrary rank matrix. The proposed filters are locally optimal in the sense of forming separate unbiased fault estimates and states with minimal variance. For these purposes, a matrix version of the Lagrange multiplier method was used. The operability of the considered method was tested on the example of an aircraft landing system. A comparative analysis of the qualitative variables of the proposed filter with the corresponding variables of the standard Kalman filter has been carried out. Solving this task is very important to improving the stability of operation and reliability of different communication equipment in the emerging networks, both local and global, both fixed and wireless.