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# Discrete Kalman filter in problems of optimal receiving signals

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V.M. Sovetov – Dr. Sc. (Eng.), Main Research Scientist, 16 CRTI DoD. E-mail: sovetovvm@mail.ru

The Kalman filter (KF) as well as a matched filter or a correlator is used for solving optimal signal reception. The main problem when using KF in optimal reception is the solution of the Riccati equation to calculate the covariance matrix of the estimation error and, ac-cordingly, the weight matrix. It is known that the discrete KF for the signal of known form can be represented as the sum of the state vectors with the transformation of the state transition matrix followed by weighing the result of accumulation using a posteriori error covariance matrix estimation. In this case, it suffices to compute the weight matrix for the decision, which greatly simplifies the implementation of algorithms of reception. Represented KF as the sum state vectors, meets the dual models of the transmitted signal. Using this representation of KF, it is show that matched filtering and correlation processing are part of KF algorithm. The expression for the weight matrix obtained by solving the Riccati equation also includes a matched filtering and correlation processing. Thereby the signal component at the output of the receiver is normalized to unity, resulting in accurate estimation signal. As an example, was demonstrated the reception harmonic signal with opposite phases. This reception was carried out using a decision rule for the correlation reception, matched filtering and KF as a whole.
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