Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

The article is devoted to Bayes optimization problems of nonlinear observable stochastic systems (NLOStSs) based on wavelet canonical expansions (WLCEs). Input processes (StPs) and output StPs considered nonlinearly StSs depend random parameters additive independent Gaussian noises. For synthesis we use a approach with the given loss function minimum risk condition. WLCEs are formed by covariance expansion coefficients two-dimensional orthonormal basis compact carrier. New results: (i) common Bayes’ criteria algorithm for NLOStSs WLCE presented; (ii) partial algorithms three (minimum mean square error, damage accumulation probability error exit outside limits) given; (iii) an approximate statistical linearization; (iv) test examples. Applications: parameter calibration in complex measurement control systems. Some generalizations formulated.