Robust nonlinear filter for nonlinear systems with multiplicative noise uncertainties, unknown external disturbances, and packet dropouts

This technical note is concerned with the nonlinear filtering for networked control systems. First, the modified particle filter algorithm with intermittent observations is proposed and the conditional Cramér-Rao lower (CRL) bound with packet dropouts for nonlinear non-Gaussian system is derived. Second, an upper bound for the CRL bound of the Gaussian filter with packet losses is obtained by constructing a linear Gaussian-Markovian networked system because of the complexity in direct analysis and computation. Third, a sufficient condition is given for the bounded expectation of the CRL bound, which is the necessary condition for bounded mean-square error covariance. Finally, an example illustrates the effectiveness of the proposed filter. KEYWORDSCramér-Rao lower bound, networked control systems, packet dropout, particle filter Int J Robust Nonlinear Control. 2018;28:2961-2975.wileyonlinelibrary.com/journal/rnc

Section: Introductionmentioning

confidence: 99%

Modified particle filter and Gaussian filter with packet dropouts

Yang

Fang

2018

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay, missing measurements, and uncertain‐variance multiplicative and additive white noises

Liu

Tao

Fan

et al. 2019

Summary The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

Robust estimation algorithm based on prior probability statistics

Wang

Hao

2021

For the nonlinear systems with uncertain system parameters, based on the recursive linear minimum variance estimation framework, the effect of the system parameters on the mean squared error (MSE) is analyzed, that is, the greater the system parameters deviation (whether they are positive or negative deviation) is, the greater the MSE is. Based on the analysis results and prior probability statistics (probability distributions or sampling distributions), an innovative robust estimation algorithm is proposed for nonlinear systems with uncertain system parameters. Three examples verify the effectiveness of the proposed algorithm.