Optimal evaluation in dynamic systems subjected to waveform disturbances

The tools of the conditional Markov process theory solve the problem of optimal evaluation for the state of a dynamic system subjected to noise-like and waveform disturbances. By replacing the variables the problem is reduced to optimal evaluation of a dynamic system of random structure. For the a posteriori probability of a waveform disturbance and for auxiliary conditional probability densities of the system states real time equations are obtained. These lead to the current evaluation of the system state in Gaussian approximation. Approximate equations are provided fir r.m.s. optimal estimate in the case of a linear model of waveform disturbances, a linear model of the dynamic system, and linear observations. The resultant optimal filtering algorithm is discussed with reference to evaluating the state of a scalar system with an allowance for possible stepwise change of the state at a random time.