Jaafar AlMutawa

The interval versions of the Kalman filter and the EM algorithm

In this paper, we study state space models represented by interval parameters and noise. We introduce an interval version of the Expectation Maximization (EM) algorithm for the identification of the interval parameters of the system. We also introduce a suboptimal interval Kalman filter for the identification and estimation of the state vectors. The work requires the introduction of the concept of interval random variables which we also include in this work together with a study of their interval statistical properties such as expectation, conditional expectation and variance. Although the interval Kalman filter introduced here is suboptimal, it successfully recovers the state vectors to a high precision in the simulation examples we have run.

Filtering and identification of a state space model with linear and bilinear interactions between the states

In this paper, we introduce a new bilinear model in the state space form. The evolution of this model is linear-bilinear in the state of the system. The classical Kalman filter and smoother are not applicable to this model, and therefore, we derive a new Kalman filter and smoother for our model. The new algorithm depends on a special linearization of the second-order term by making use of the best available information about the state of the system. We also derive the expectation maximization (EM) algorithm for the parameter identification of the model. A Monte Carlo simulation is included to illustrate the efficiency of the proposed algorithm. An application in which we fit a bilinear model to wind speed data taken from actual measurements is included. We compare our model with a linear fit to illustrate the superiority of the bilinear model.

Continuous and discrete wavelet transforms based analysis of weather data of North Western Region of Saudi Arabia

The present study utilizes daily mean time series of meteorological parameters (air temperature, relative humidity, barometric pressure and wind speed) and daily totals of rainfall data to understand the changes in these parameters during 17 years period i.e. 1990 to 2006. The analysis of the above data is made using continuous and discrete wavelet transforms because it provides a time-frequency representation of an analyzed signal in the time domain. Moreover, in the recent years, wavelet methods have become useful and powerful tools for analysis of the variations, periodicities, trends in time series in general and meteorological parameters in particular. In present study, both continues and discrete wavelet transforms were used and found to be capable of showing the increasing or decreasing trends of the meterorological parameters with. The seasonal variability was also very well represented by the wavelet analysis used in this study. High levels of compressions were obtained retaining the originality of the signals.

Identification of errors-in-variables models using the EM algorithm

Abstract This paper advocates a new subspace system identification algorithm for the errors-in-variables (EIV) state space model via the EM algorithm. To initialize the EM algorithm an initial estimate is obtained by the errors-in-variables subspace system identification method: EIV-MOESP (Chou et al. [1997]) and EIV-N4SID (Gustafsson [2001]). The EM algorithm is an algorithm to compute the maximum value for the likelihood function that is consists of two steps; namely the E- and M-steps. The E- and M-steps in the EM algorithm are calculated by computing the conditional expectation under the assumption that the input-output data is completely observed. Numerical example shows that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods.

Diagnostics subspace identification method of linear state-space model with observation outliers

The authors propose a diagnostic technique for the state-space model fitting of time series by deleting some observations and measuring the change in the parameter estimates. They consider this approach in order to distinguish an observational outlier from an innovational one. Thus, they present a robust subspace identification algorithm that is less sensitive to outliers. A Monte Carlo simulation for a vibrating structure model demonstrates the effectiveness of the proposed algorithm and its ability to detect outliers in the measurements as well as the dynamical state.

Robust Kalman filter and smoother for errors-in-variables model with observation outliers

Abstract In this paper, we propose a robust Kalman filter and smoother for the errors-invariables (EIV) state space model subject to observation noise with outliers. We introduce the EIV problem with outliers and then we present the minimum covariance determinant (MCD) estimator which is highly robust estimator to detect outliers. As a result, a new statistical test to check the existence of outliers which is based on the Kalman filter and smoother has been formulated. Since the MCD is a combinatorial optimization problem the randomized algorithm has been proposed in order to achieve the optimal estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimate, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.

Robust maximum likelihood estimation for stochastic state space model with observation outliers

The objective of this paper is to develop a robust maximum likelihood estimation (MLE) for the stochastic state space model via the expectation maximisation algorithm to cope with observation outliers. Two types of outliers and their influence are studied in this paper: namely,the additive outlier (AO) and innovative outlier (IO). Due to the sensitivity of the MLE to AO and IO, we propose two techniques for robustifying the MLE: the weighted maximum likelihood estimation (WMLE) and the trimmed maximum likelihood estimation (TMLE). The WMLE is easy to implement with weights estimated from the data; however, it is still sensitive to IO and a patch of AO outliers. On the other hand, the TMLE is reduced to a combinatorial optimisation problem and hard to implement but it is efficient to both types of outliers presented here. To overcome the difficulty, we apply the parallel randomised algorithm that has a low computational cost. A Monte Carlo simulation result shows the efficiency of the proposed algorithms.

Stochastic subspace identification of linear systems with observation outliers

We propose a diagnostic for the state space model fitting time series formed by deleting observations from the data and measuring the change in the estimates of the parameters. A method is proposed for distinguishing an observational outlier from an innovational one. Thus we present a robust subspace system identification algorithm that is less sensitive to outliers. We give a numerical result to show effectiveness of the proposed method.

Diagnostics of data outliers using subspace identification

Abstract We propose a diagnostics technique for the state space model fitting formed by deleting observations from the data and measuring the change in the estimates of the parameters. A method is proposed for distinguishing an observational outlier from an innovational one. The presented subspace system identification algorithm is robust and less sensitive to outliers. We give a numerical result to show effectiveness of the proposed method.