In this paper, we consider a special case of the one dimensional heat diffusion across a homogeneous wall. This physical system is modeled by a linear partial differential equation, which can be thought of as an infinite dimensional dynamic system. To simulate this physical system, one has to approximate the underlying infinite order system by a finite order approximation. In this paper we first construct a simple and straightforward approximate finite order model for the true system. The proposed approximate models may require large model order to approximate the true system dynamics in the high frequency regions. To avoid the usage of higher order models, we use a scheme similar to singular perturbations to further reduce the model order.
In this paper, we consider a special case of the one dimensional heat diffusion across a homogeneous wall. This physical system is modeled by a linear partial differential equation, which can be thought of as an infinite dimensional dynamic system. To simulate this physical system, one has to approximate the underlying infinite order system by a finite order approximation. In this paper we first construct a simple and straight forward approximate finite order model for the true system. The proposed approximate models may require large model order to approximate the true system dynamics in the high frequency regions. To avoid the usage of higher order models, we use a scheme similar to singular perturbations to further reduce the model order.
Most existing work so far on continuous-time AR (CAR) parameter estimation concentrates on the noiseless measurement case. When measurement noise is present, our previous results on CAR parameter estimation need to he revised accordingly. Here we model th
It is often necessary in practice to perform identification experiments on systems operating in closed loop. There has been some confusion about the possibilities of successful identification in such cases, evidently due to the fact that certain common methods then fail. A rapidly increasing literature on the problem is briefly surveyed in this paper, and an overview of a particular approach is given. It is shown that prediction error identification methods, applied in a direct fashion will given correct estimates in a number of feedback cases. Furthermore, the accuracy is not necessarily worse in the presence of feedback; in fact optimal inputs may very well require feedback terms. Some practical applications are also described.
Errors-in-variables estimation problems for single-input-single-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.
System identification for networked control is considered. Due to the time-delays in the network, it can be difficult to work with a discrete-time model and a continuous-time model is therefore chosen. A covariance function based method that relies on the second order statistical properties of the output signal, where it is assumed that the input signal samples are from a discrete-time white noise sequence, is proposed for estimating the parameters. The method is easy to use since the actual time instants when new input signal levels are applied at the actuator do not have to be known. An analysis of the networked system and the effects of the time-delays is made, and the results of the analysis motivate and support the chosen approach. Numerical studies indicate that the method is robust to randomly distributed time-delays, packet drop-outs, and additive measurement noise.
We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MS
Errors-in-variables (EIV) identification refers to the problem of consistently estimating linear dynamic systems whose output and input variables are affected by additive noise. Various solutions have been presented for identifying such systems. In this study, EIV identification using Structural Equation Modeling (SEM) is considered. Two schemes for how EIV Single-Input Single-Output (SISO) systems can be formulated as SEMs are presented. The proposed formulations allow for quick implementation using standard SEM software. By simulation examples, it is shown that compared to existing procedures, here represented by the covariance matching (CM) approach, SEM-based estimation provide parameter estimates of similar quality.
The problem of estimating the parameters in continuous-time autoregressive moving average (ARMA) processes from discrete-time data is considered. Both direct and indirect methods are studied, and similarities and differences are discussed. A general discussion of the inherent difficulties of the problem is given together with a comprehensive study on how the choice of the sampling interval influences the estimation result. A special focus is given to how the Cramer-Rao lower bound depends on the sampling interval.