Iterative Identification for Multivariable Systems with Time-Delays Based on Basis Pursuit De-Noising and Auxiliary Model

Abstract

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm.

ECG Signal Denoising and Reconstruction Based on Basis Pursuit

“…The measurement matrix plays an important role in CS and signal reconstruction. The reconstruction error is smaller if the performance of the measurement matrix is better [42]. The measurement matrix M makes the dimension of ECG signals reconstructed from L measured values such as Figure 1.…”

A Novel Identification Method for a Class of Closed-Loop Systems Based on Basis Pursuit De-Noising

“…where λ is a non-negative parameter and can be set as λ = σ √ 2 log(n) [17]. Two non-negative vectors u o and v o are introduced to convert the problem in (12) into a quadratic program [18], [23], and let u oj := (θ oj ) + , v oj := (−θ oj ) + and (θ o ) + := max{0, θ o } for all j = 1, 2, • • • , n, where θ oj , u oj and v oj represent the j-th element of the vectors θ o , u o and v o , respectively. Then the parameter vector θ o can be expressed as…”

“…Convex optimization algorithms such as the basis pursuit, the basis pursuit de-noising (BPDN) can recovery sparse signals with the advantages of high stability and strong applicability [17]. In the literature of system identification, the BPDN criterion was combined with the auxiliary model idea to jointly estimate the parameters and time-delays of multivariable output-error systems [18]. In the current paper, the BPDN criterion is used to identify the parameters and time-delays of a class of closed-loop systems simultaneously due to its robustness.…”

Joint parameter and time-delay estimation for a class of Wiener models based on a new orthogonal least squares algorithm

“…Chen et al derived a biased compensation recursive least squares threshold algorithm for a time-delay rational model [18]. A typical method to tackle the unknown time-delays is the over-parameterization method [12,19]. By introducing a sufficient regression length, the system can be represented as a high-dimensional sparse model that contains redundant information products [20].…”

“…Two kinds of methods are discerned to obtain an approximation for such sparse models, namely the convex optimization methods and the greedy methods. Many convex optimization schemes, such as the basis pursuit de-nosing (BPDN) [19] and the least absolute shrinkage and selection operator (LASSO) [21], can obtain the sparse solution with high stability and strong applicability, but computationally expensive. The greedy schemes, such as the orthogonal LS (OLS), the orthogonal matching pursuit (OMP) [23,25] and their variations, are stepwise inference processes that start from a null model and make the locally optimal choice at each step [22], which have received much attention due to the charming computational advantage.…”