Recurrent algorithms for detection of stochastic signals in the state space

The paper is devoted to synthesis of recurrent algorithms for detection of stochastic signals given in state space. The structure of the algorithms synthesized is shown to be close to that of the Kalman filter. Analysis of one of the algorithms synthesized is carried out. Illustration of connection between weight coefficients of processing system, which are formed in implicit form, is given. Dynamics of amplification and feedback coefficients of the system is studied; calculation of its detection characteristics is fulfilled. Synthesis of the filters is also carried out for the continuous time. The algorithms synthesized are extended to the case of a mixture of stochastic correlated interferences and white noise. Modification of one of the algorithms is made which enables its use for solving problems of multialternative detection.

💡 Research Summary

The paper addresses the problem of detecting stochastic signals that are described in a state‑space form, and it proposes a family of recursive detection algorithms whose structure closely resembles that of the Kalman filter. The authors begin by formulating the signal‑plus‑noise model as

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