A bi-objective model with sequential search algorithm for optimizing network-wide train timetables

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

“…The methods proposed in this paper can combine some statistical optimal strategies [44][45][46][47] to study the parameter estimation algorithms of linear and nonlinear systems [48][49][50][51][52] and can be applied to other fields, [53][54][55][56][57][58][59] such as fault detection, image processing, and sliding mode control. Different from the previous linearization method like Taylor expansion, we take use of the special structure of the bilinear system and propose the state filtering algorithm to obtain the unknown states by minimizing the covariance matrix of the state estimation errors based on the extremum principle.…”

“…Finally, the convergence analysis and the simulation results show that the proposed state estimator has good performance in the state estimation of bilinear systems. The methods proposed in this paper can combine some statistical optimal strategies [44][45][46][47] to study the parameter estimation algorithms of linear and nonlinear systems [48][49][50][51][52] and can be applied to other fields, [53][54][55][56][57][58][59] such as fault detection, image processing, and sliding mode control. [60][61][62][63]…”

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

“…• The methods proposed in this paper can combine some statistical optimal strategies [47][48][49] to study the parameter estimation algorithms of linear and nonlinear systems [50][51][52][53][54][55][56] and can be extended to other fields. • The simulation results indicate that the F-ML-HLSI algorithm can generate more highly accurate estimates of bilinear systems and has a faster convergence speed than the F-ML-HGI algorithm, the GI algorithm, and the MISG algorithm developed in the work of Meng.…”

“…Therefore, the proposed identification methods in this paper can be used to build highly-precise models for the practical industrial process (eg, the rare earth cascade extraction process) for their uncertainty and complexity. • The methods proposed in this paper can combine some statistical optimal strategies [47][48][49] to study the parameter estimation algorithms of linear and nonlinear systems [50][51][52][53][54][55][56] and can be extended to other fields. [57][58][59][60][61][62][63][64][65][66][67][68][69]…”

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

“…The multi-innovation identification principle is an effective method to improve the accuracy of the identification algorithms. The methods proposed in this paper can combine other mathematical tools [52][53][54] to study the parameter identification problems of different systems with colored noise [55][56][57] and can be applied to other fields such as information processing and communication. [58][59][60][61][62][63][64][65][66][67]…”