Robust weighted fusion Kalman predictors with uncertain noise variances

Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

“…Applying the convergence of self-turning Riccati equation, 43 the DESA method 44 and DVESA method, 6 similar to the proofs as shown in previous works, 6,[23][24][25] the convergence relations (109) and (110) can be proved. The details are omitted.…”

“…The proposed robust filtering methodology has developed and extended the Lyapunov equation approach [5][6][7][8] and the fictitious noise technique, 11,12,[15][16][17][18][19][20][21][22][23][24][25][26] and it was completely different from the Riccati equation approach, 11,12,15,16 LMI approach, [17][18][19] game-theoretic approach, 2 and polynomial approach. 3 The convergence theory and the method of classic Kalman filtering were developed and extended.…”

“…The convergence problem of variances was solved by the DVESA method, which was converted into the stability problem of a Lyapunov equation. The convergence problem of estimators was solved by the DESA method, which was converted into the stability problem of a different equation (see previous works [5][6][7][23][24][25]44 ).…”

“…However, only the uncertain noise variances were considered in previous works, [5][6][7][8] whereas the model parameters of the considered system were all assumed to be exactly known and the correlated noises were not considered in other works. [2][3][4][5][6][7][8] However, in many engineering applications, the correlated noises often arise. For example, the noise described by the autoregressive moving average model is autocorrelated.…”

“…Recently, for a system with uncertain noise variances, according to the minimax robust estimation principle, 4 based on the worst-case conservative system with conservative upper bounds of uncertain noise variances, the robust local and fused Kalman filters, 5 predictors, 6 smoothers, 7 and white noise deconvolution smoothers 8 have been presented by the Lyapunov equation approach, respectively, in the sense that the actual estimation error variances of each estimator are guaranteed to have a minimal upper bound for all the admissible uncertainties. However, only the uncertain noise variances were considered in previous works, [5][6][7][8] whereas the model parameters of the considered system were all assumed to be exactly known and the correlated noises were not considered in other works. [2][3][4][5][6][7][8] However, in many engineering applications, the correlated noises often arise.…”