Abstract

The optimal procedure for estimating of time-varying parameters in the multi-input, multi-output, discrete time d,namical system described by the state and observation equations is discussed. The system's output and state are contaminated by independent discrete Gaussian noises with completely known statistics. The maximum likelihood (M. L.) approach is used to obtain the estimation algorithm fot the time-varying parameters (elements of the transition and input matrices) . The time-varying parameters can have an arbitrary form of nonrandom discretized time functions. The iterative estimation algorithm utilizes the conjugate gradient method. The recurrent expressions for the gradient with respect to discrete values of the parameters to be estimated are developed on an analitical way. The proposed procedure of the gradient calculation utilizes direct computational method of dynamical optimization. Numerical results of digital computer simulations, which illustrate theoretical considerations, are presented.

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