The least-squares identification of FIR systems subject to worst-case noise (original) (raw)

The cost of complexity in identification of FIR systems

2008

In this paper we investigate the minimum amount of input power required to estimate a given linear system with a prescribed degree of accuracy, as a function of the model complexity. This quantity is defined to be the 'cost of complexity'. The degree of accuracy considered is the maximum variance of the discrete-time transfer function estimator over a frequency range [−ω B , ω B ]. It is commonly believed that the cost increases as the model complexity increases. The objective of this paper is to quantify this dependence. In particular, we establish several properties of the cost of complexity. We find, for example, a lower bound for the cost asymptotic in the model order. For simplicity, we consider only systems described by FIR models and assume that there is no undermodelling.

FIR System Identification Using Feedback

Journal of Signal and Information Processing, 2013

This paper describes a new approach to finite-impulse (FIR) system identification. The method differs from the traditional stochastic approximation method as used in the traditional least-mean squares (LMS) family of algorithms, in which we use deconvolution as a means of separating the impulse-response from the system input data. The technique can be used as a substitute for ordinary LMS but it has the added advantages that can be used for constant input data (i.e. data which are not persistently exciting) and the stability limit is far simpler to calculate. Furthermore, the convergence properties are much faster than LMS under certain types of noise input.

Frequency domain identification of FIR models from noisy input – output data

2019

This paper describes a new approach for identifying FIR mode ls from a finite number of measurements, in the presence of additive and uncorrelated white noise. In particular, two different frequency domain algorithms are proposed. The first algorit hm is based on some theoretical results concerning the dynamic Frisch scheme. The second algorithm maps the FIR identification problem into a quadratic eigenvalue problem. Both methods resemble in many aspects some other identification algorithms, originally developed in the time domain. The fe atures of the proposed methods are compared with each other and with those of some time domain algorithms by means of Monte Carlo simulations.

Error assessment of the estimated coefficients obtained in system identification technique

Signal, Image and Video Processing, 2014

System identification technique plays an important role in many electrical devices. In this technique, an adaptive filter models the unknown system with a Finite Impulse Response (FIR) or an Infinite Inverse Response (IIR) filter. This paper concentrates on the system identification technique based on the least squares criterion and evaluates the relationship between each estimated coefficient (obtained by the adaptive filter) and its corresponding coefficient in the unknown system. By logically classifying the variables, the amount of error between these two corresponding coefficients is evaluated and precisely expressed based on the auto-correlation lags of the input signal of the system and the coefficients of the unknown system. Also, the computed error is simplified for two particular cases in which the input signal of the system is an ideal zero-mean white Gaussian noise or a windowed (short-time) zero-mean white Gaussian noise. Experimental results provided in the simulation part verify the arithmetic expressions presented in the paper.

Closed-loop identification of unstable systems using noncausal FIR models

2013 American Control Conference, 2013

Noncausal finite impulse response (FIR) models are used for closed-loop identification of unstable multi-input, multi-output plants. These models are shown to approximate the Laurent series inside the annulus between the asymptotically stable pole of the largest modulus and the unstable pole of the smallest modulus. By delaying the measured output relative to the measured input, the identified FIR model is a noncausal approximation of the unstable plant. We present examples to compare the accuracy of the identified model obtained using least squares, instrumental variables methods, and prediction error methods for both infinite impulse response (IIR) and noncausal FIR models under arbitrary noise that is fed back into the loop. Finally, we reconstruct an IIR model of the system from its stable and unstable parts using the eigensystem realisation algorithm.

FIR system identification using higher-order statistics

2009

In this paper, new approaches for the identification of FIR systems using HOS are proposed. The unknown model parameters are obtained using optimization algorithms. In fact, the proposed method consists first in defining an optimization problem and second in using an appropriate algorithm to resolve it. Moreover, we develop a new method for estimating the order of FIR models using only the output cumulants. The results presented in this paper illustrate the performance of our methods and compare them with a range of existing approaches.

Optimal input design for worst-case system identification in

Systems & Control Letters, 1993

In this paper, we examine optimal sequences that generate worst-case parameters estimation errors in the 11,12 and l~ norm context for algorithms identifying linear, timeinvariant, discrete-time, finite impulse response systems excited by bounded sequences and with I~ norm measurement error.

System Identification Using Composite FIR/IIR Models

2018 Annual American Control Conference (ACC)

Since physical systems usually have infiniteimpulse-response (IIR) dynamics, IIR models are widely used for system identification. Using IIR models, however, requires knowledge of the system order, which, if chosen incorrectly, may yield poor parameter estimates. On the other hand, finiteimpulse-response (FIR) models of sufficiently high order can approximate asymptotically stable systems without knowledge of the system order. However, FIR models cannot approximate systems with poles located outside the open unit disk. In this paper we introduce a composite FIR/IIR (CFI) model, which is the product of a possibly noncausal FIR model and a poleonly IIR model. CFI models are shown to more accurately approximate systems with arbitrary poles under the condition that a lower bound on the number of poles located outside the open unit disk is known.

Maximum likelihood identification of noisy input–output models

Automatica, 2007

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cràmer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations. ᭧