Presence Of Output Noise Research Articles

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems’ fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this article, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise-level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise-level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.

Identification of a Wiener System via Semidefinite Programming

This paper presents a new method for the identification of Wiener systems in the presence of output noise. The Wiener system identification problem is formulated as a convex Semidefinite Programming (SDP) problem by constraining a finite dimensional time dependency between signals. The main contribution of this paper is that the proposed method is robust to output noise and neither the Gaussian assumption of the input signal nor the invertibility of the static nonlinearity is necessary. The main assumption used in this paper is that static nonlinearity is monotonically non-decreasing. In the proposed identification method, the linear dynamical system is parametrized as a Finite Impulse Response (FIR) model and a nonparametric identification method is used to create the noise free output signal. Because both the intermediate signal and the noise free output signal are unknown, an over-parametrization technique is used. Once parameters are estimated, a Singular Value Decomposition (SVD) is used to separate the linear system parameters and the noise free output signal. The proposed identification method is applied to simulation data from a Wiener system. The effectiveness and accuracy of the proposed method are verified via numerical simulations.

Optimized Excitation Signals for MIMO Frequency Response Function Measurements

Many different excitation signals can be chosen for the nonparametric frequency response function measurements of a linear multiple-input-multiple-output (MIMO) system. In the presence of output noise they will result in different signal-to-noise ratios (SNRs) of the frequency response function measurements. In this paper, these effects are analyzed and compared for three classes of multisine excitations: random multisines, approximately orthogonal random multisines, and orthogonal random multisines, taking also into account the crest-factor minimization. It is shown that the orthogonalization of the inputs yields an essential increase in the measured SNR

A new algorithm for the identification of multiple input Wiener systems.

Multiple-input Wiener systems consist of two or more linear dynamic elements, whose outputs are transformed by a multiple-input static non-linearity. Korenberg (1985) demonstrated that the linear elements of these systems can be estimated using either a first order input-output cross-covariance or a slice of the second, or higher, order input-output cross-covariance function. Korenberg's work used a multiple input LNL structure, in which the output of the static nonlinearity was then filtered by a linear dynamic system. In this paper we show that by restricting our study to the slightly simpler Wiener structure, it is possible to improve the linear subsystem estimates obtained from the measured cross-covariance functions. Three algorithms, which taken together can identify any multiple-input Wiener system, have been developed. We present the theory underlying these algorithms and detail their implementation. Simulation results are then presented which demonstrate that the algorithms are robust in the presence of output noise, and provide good estimates of the system dynamics under a wide set of conditions.

A new form of stable adaptive observer

A new form of adaptive observer which is guaranteed to be globally stable via hyperstability theories is presented. Its main advantage over existing designs is that asymptotic unbiased estimates are obtained in the presence of output noise. Experimental results are given to demonstrate the performance of this observer.