Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems

Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

“…For the uncertain multisensor system (1)-(3) with Assumptions 1 to 4, if Φ is a stable matrix, applying Lemma 8, then the solutions X(t) and X(t) to the time-varying generalized Lyapunov equations (10) and (11) with any initial conditions X(0) ≥ 0 and X(0) ≥ 0 converge respectively to the unique positive semidefinite solutions X ≥ 0 and X ≥ 0 for the following steady-state generalized Lyapunov equations:…”

“…7,8 The input white noise estimation problem for stochastic systems is called white noise deconvolution, which has important applications in oil seismic exploration 9 and occurs in many fields, including communications, signal processing, and state estimation. There exist several approaches to the deconvolution problem in the literature, for example, the Kalman filtering approach, 9 the modern time-series analysis method, 10 and the polynomial approach. 11 The optimal white noise deconvolution estimators with application to oil seismic exploration were presented in the work of Mendel.…”

“…11 The optimal white noise deconvolution estimators with application to oil seismic exploration were presented in the work of Mendel. 9 A unified white noise estimate theory based on the modern time-series analysis approach was presented in the work of Deng et al, 10 which not only includes input white noise estimators but also includes measurement white noise estimators. Concerning with the H ∞ deconvolution problems, the optimal estimators were derived via a polynomial approach.…”

“…Concerning with the H ∞ deconvolution problems, the optimal estimators were derived via a polynomial approach. 11 However, the aforementioned works 9,10 and the work of Zhang et al 11 are all confined to the single-sensor systems. For multisensor systems, based on the Kalman filtering approach, many researches have been reported in the past few decades on the design of information fusion white noise deconvolution estimators.…”

“…It includes the robust CF and WMF time-varying white noise estimators, and their robustness, equivalence, accuracy relations, complexity analysis and convergence analysis, fictitious noise technique and Lyapunov equation approach. The optimal and self-tuning white noise deconvolution estimation theory [9][10][11][12][13][14][15][16][17] have been developed to robust white noise deconvolution estimation theory for uncertain systems. The robust fused Kalman filtering theory in the aforementioned work [32][33][34] is extended to design the robust fused white noise estimators for multisensor systems with uncertain-variance multiplicative noises and linearly correlated white noises.…”