A solution of the problem of nonlinear parametric identification based on generalized probability criteria

Intelligent processing of temporal data based on hybrid fuzzy-stochastic models

“…k z we use the generalized probability criteria that, in the general case, nonlinearly depend on the a posteriori density of the state variables (6) where V(y) is a known nonlinear analytic function and X is the given region of the state space.…”

“…Various modifications of the criterion function V(y) cover a rather wide class of probabilistic optimality criteria [5,6]: the criterion of minimum deviation of the a posteriori density from a given reference func tion, the criterion of minimum (maximum) probability that the state parameters exist in a certain region of the state space, various information criteria, etc. It should be noted that the statistical criteria used in presently available identification methods [7][8][9] are only special cases of the generalized nonlinear criteria used to implement the proposed preprocessing method.…”

“…is the N dimensional conditional density of the vector which is determined accord ing to equation (4); and is the likelihood function for the multivariate observation of form (5), which is determined at the current step of the algorithm [6,11].…”

Adaptive Stochastic Filtration Based on the Estimation of the Covariance Matrix of Measurement Noises Using Irregular Accurate Observations

“…The use of filtration theory approaches including the Kalman filter [20], for the assessment of dynamic stochastic processes assumes an accurate initialization of the random noises of these processes [14,16]. At the same time, in real information and control systems exposed to various disturbing effects, the meters' stochastic noises are recognized, as a rule, approximately or fluctuate randomly [10,19,[21][22][23][24][25][26][27]. As a consequence, one of the very critical Kalman filter characteristics is the Covariance Matrix of Measurement Noises (CMMN), which straightforwardly influences the filter gain change and, consequently, the rate of convergence of the filtration process.…”