Zero crossing data contain information of a process in compact form and is therefore of interest in wireless sensor networks where only reduced amounts of data can be transmitted. When analyzing the properties of certain algorithms using zero crossing data, the cross-covariance between the zero crossing rates of two jointly Gaussian and stationary processes is needed. The evaluation of such a cross-covariance is considered in the paper and an exact numerical expression as well as an asymptotic expression are presented.

A sliding-window variable-regularization recursive-least-squares algorithm is derived, and its convergence properties, computational complexity, and numerical stability are analyzed. The algorithm operates on a finite data window and allows for time-varying regularization in the weighting and the difference between estimates. Numerical examples are provided to compare the performance of this technique with the least mean squares and affine projection algorithms. Copyright (c) 2015 John Wiley & Sons, Ltd.

An errors-in-variables problem where the system as well as the white measurement noises are in continuous-time is considered. Due to the intrinsic nature of the measurement noises, a strategy of lowpass filtering followed by instantaneous sampling is used for obtaining data from the system. A previously developed covariance function based parameter estimation method is first slightly improved. Thereafter, it is analyzed by evaluating the covariance matrix of the estimated parameter vector. Three different expressions for a generic element of an intermediate matrix in the expression for the covariance matrix are derived. One exact but computationally demanding, one approximate valid for small sampling intervals, and one exact for the case when the sampling interval tends to zero. The covariance matrix can be used for studying the influence of some user parameters, including the choice of the lowpass filter, on the quality of the estimated parameter vector.

Two sampling strategies are used for solving an errors-in-variables problem where the system as well as the white measurement noises are of a continuous-time nature. The sampling strategies are integrated sampling, and lowpass filtering followed by instantaneous sampling. Covariance relations are derived and systems of equations are formed for the data obtained from the two sampling strategies, and parameter estimators based on these relations and equations are proposed.

A covariance matching approach for identifying errors-in-variables systems is analyzed for the general case. The asymptotic covariance matrix of the jointly estimated system parameters, noise variances and auxiliary parameters is derived. An algorithm for how to compute this covariance matrix from given system descriptions is also provided. The results generalize previous known special cases. Using Monte Carlo analysis, we illustrate the proposed algorithm. The results suggest close agreement between the theoretical and empirical accuracy. (C) 2014 Elsevier Ltd. All rights reserved.

The parameters in a general Gaussian process, including the parameters in an additive Gaussian noise process, are estimated based on zero crossing data for the total process and arbitrarily filtered versions thereof. A nonlinear weighted least squares estimate is considered and an analysis of the asymptotic covariance matrix of the estimated parameter vector is made. The proposed estimator and the use of zero crossing data are suitable when information of a process is sent from wireless sensors to a node center for further processing due to an efficient use of available bandwidth.

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.

A continuous-time description of networked control systems is considered and the parameters are estimated. The discrete-time description is time-varying due to the random time-delays in the wireless links and therefore difficult to work with. Off-line as well as on-line situations are considered for parameter estimation. In the off-line situation, a linear regression is formed and then the parameters are estimated by the least squares method. In the on-line situation, the estimates of the parameters are recursively updated for each time instance. A comparative study of two different parameter estimation approaches is presented. In the first approach, the parameters are estimated by a simple linear regression. In the second approach, transformation of the differentiation operator to another casual and stable linear operator is made in linear regression to estimate the parameters. A numerical study of these approaches is also presented for comparison.