Iterative parameter identification algorithms for transformed dynamic rational fraction input–output systems

A coupled recursive least squares algorithm for multivariable systems and its computational amount analysis by using the coupling identification concept

“…In the future work, the further investigation is to combine the identification algorithms proposed in this article with other methods, [116][117][118][119][120][121][122] such as the multi-innovation identification theory, to enhance their ability to track time-varying parameters and to improve the efficient data utilization. Furthermore, combining the coupling identification concept with other identification methods [123][124][125][126][127][128] such as the Bayesian approach, the maximum likelihood method and the Kalman filter technique to study more complex parameter identification problems is also an interesting research direction in the future.…”

Filtered generalized iterative parameter identification for equation‐error autoregressive models based on the filtering identification idea

“…The proposed iterative algorithms in this article can combine other identification approaches [70][71][72][73][74][75] to investigate new parameter estimation methods of some stochastic systems with colored noises [76][77][78][79][80][81] and can be applied to signal processing and chemical process control. [82][83][84][85][86][87] The calculation amount of the F-GLSI algorithm in ( 71)-( 85) at each iteration is displayed in Table 2, and the steps of computing the parameter estimates are as follows.…”

“…(2) Gather the observation data u(t) and y(t), form the output information vector 𝝋 c (t) and the input information vector 𝝓 c (t) using ( 81)-( 82), t = 1, 2, … , l + L. For the stacked output vector Y(l, L) using ( 72) and the stacked output information matrix 𝜱 c (l, L) using ( 77). ( 3) Form the filtered output information vector φaf,k (t) using ( 79), the filtered input information vector φbf,k (t) using (80), and the filtered input information vector φk (t) using ( 78), t = 1, 2, … , l + L. (4) Form the stacked information matrix Φk (l, L) using (74), or form the stacked output information matrix Φaf,k (l, L) and the stacked input information matrix Φbf,k (l, L) using ( 77)- (77), and form the stacked information matrix Φk (l, L) using ( 74). ( 5) Update the parameter estimation vector θk using (71).…”

Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

“…The proposed parameter estimation algorithms in this article can combine other identification algorithms [78][79][80][81][82][83] to explore new parameter estimation methods of different dynamic stochastic systems [84][85][86][87][88][89] and can be applied to signal processing and chemical process control. [90][91][92][93][94][95][96] The steps of computing the P-REG parameter estimation vector θ(t) in ( 19)-( 26) are listed in the following.…”