Erik K. Larsson

Brief Identification of continuous-time AR processes from unevenly sampled data

When identifying a continuous-time AR process from discrete-time data, an obvious approach is to replace the derivative operator in the continuous-time model by an approximation. In some cases, a linear regression model can then be formulated. The well-known least-squares method would be very desirable to apply, since it enjoy good numerical properties and low computational complexity, in particular for fast or nonuniform sampling. The focus of this paper is the latter, i.e., nonuniform sampling. Two consistent least-squares schemes for the case of unevenly sampled data are presented. The precise choice of derivative approximation turns out to be crucial. The obtained results are compared to a prediction error method.

Identification of Continuous-Time ARX Models From Irregularly Sampled Data

The problem of estimating the parameters in a continuous-time ARX process from unevenly sampled data is studied. A solution where the differentiation operator is replaced by a difference operator is suggested. In the paper, results are given for how the difference operator should be chosen in order to obtain consistent parameter estimates. The proposed method is considerably faster than conventional methods, such as the maximum likelihood method. The Crameacuter-Rao bound for estimation of the parameters is computed. In the derivation, the Slepian-Bangs formula is used together with a state-space framework, resulting in a closed form expression for the Crameacuter-Rao bound. Numerical studies indicate that the Crameacuter-Rao bound is reached by the proposed method

Using continuous-time modeling for errors-in-variables identification

Abstract Continuous-time identification is applied to an errors-in-variables setting. A continuous-time model is fitted to data consisting of discrete-time noise corrupted input and output measurements. The noise-free input is modelled as a continuous-time ARMA process. It is described how the Cramer-Rao lower bound for the estimation problem can be computed. Several parameter estimation approaches for the problem are presented, and also illustrated in a short numerical study.

Continuous-time AR parameter estimation by using properties of sampled systems

Abstract Consider the problem of estimating the parameters in a continuous-time autoregressive (CAR) model from discrete-time samples. In this paper a simple and computationally efficient method is introduced, and analyzed with respect to bias distribution. The approach is based on replacing the derivatives by delta approximations, forming a linear regression, and using the least squares method. It turns out that consistency can be assured by applying a particular prefilter to the data; the filter is easy to compute and is only dependent on the order of the continuous-time system. Finally, the introduced method is compared to other methods in some simulation studies.

The CRB for parameter estimation in irregularly sampled continuous-time ARMA systems

We derive novel and compact formulas for the Cramer-Rao bound (CRB) associated with the identification of the parameters in a continuous-time autoregressive moving-average (ARMA) model, given nonuniformly sampled data. Our approach is based on a state-space formulation of the ARMA model, which facilitates a derivation of the CRB in closed form. Numerical examples illustrate our results.

Limiting sampling results for continuous-time ARMA systems

The objective of this paper is to present some general properties of discrete-time systems originating from fast sampled continuous-time autoregressive moving average (CARMA) systems. In particular, some results concerning the zero locations and the innovations variance of fast sampled CARMA systems will be stated. Knowledge of these properties is of importance in various fast sampling applications, such as discrete-time simulation of continuous-time systems and identification of continuous-time systems using discrete-time measurements. The main contribution, however, is to provide a mean to evaluate limiting properties for various problems. For example, how to determine the accuracy of approximate sampling schemes, how to describe the characteristics of different estimators, and how to examine the behaviour of the dynamics of a fast sampled system. The results are illustrated by an extensive set of examples.The objective of this paper is to present some general properties of discrete-time systems originating from fast sampled continuous-time autoregressive moving average (CARMA) systems. In particular, some results concerning the zero locations and the innovations variance of fast sampled CARMA systems will be stated. Knowledge of these properties is of importance in various fast sampling applications, such as discrete-time simulation of continuous-time systems and identification of continuous-time systems using discrete-time measurements. The main contribution, however, is to provide a mean to evaluate limiting properties for various problems. For example, how to determine the accuracy of approximate sampling schemes, how to describe the characteristics of different estimators, and how to examine the behaviour of the dynamics of a fast sampled system. The results are illustrated by an extensive set of examples.

On possibilities for estimating continuous-time ARMA parameters

Abstract The problem of estimating the parameters in continuous-time ARMA processes from discrete-time data is considered. Three different approaches, based on the prediction error method, the instrumental variable method and an approximate maximum likelihood method, respectively, arc studied. All three techniques provide reliable solutions to the estimation problem. A general discussion of the inherent difficulties of the problem is given together with an extensive numerical study.

Fast estimators for large-scale fading channels from irregularly sampled data

The problem of estimating the power attenuation dynamics for large-scale lognormal fading channels in wireless communication systems, when the model is described as a mean reverting Ornstein-Uhlenbeck process, is studied in the paper. Fast and accurate estimators for the model parameters from irregularly sampled data are suggested for both offline and online applications. The Crameacuter-Rao bound for the estimation of the model parameters is derived, and the qualities of the proposed estimators are evaluated with respect to the bound

Cramer-Rao bounds for continuous-time AR parameter estimation with irregular sampling

Consider the problem of estimating the parameters in a continuous-time autoregressive (AR) model given measurements taken at arbitrary time instants. In this paper the Cramer-Rao bound for this problem is derived by using a technique based on the Slepian-Bangs formula and residue calculus. Furthermore, we investigate by means of numerical experiments how different sampling schemes can affect the accuracy. Interestingly enough, however, for the examples studied, the estimation accuracy is relatively insensitive to the choice of sampling strategy.

Fast and approximative estimation of continuous-time stochastic signals from discrete-time data

A fast and approximative method for estimating continuous-time stochastic disturbance signals, described as continuous-time autoregressive moving average processes, from discrete-time data is presented. First, it is shown how these processes can be regarded as continuous-time autoregressive processes and the relation between the two types of processes is derived. The relation is then used for mapping estimated autoregressive parameters from an instrumental variable approach onto autoregressive moving average parameters. The procedure provides a solution to the estimation problem that preserves the continuous-time parameterization.