Linear optimal state estimation in systems with independent mode transitions

Abstract—A generalized state space representation of a dy-namical system with random modes is presented. The dynamics equation includes the effect of the state’s linear minimum mean squared error (LMMSE) optimal estimate, representing the behavior of a closed loop control system featuring a state esti-mator. The measurement equation is allowed to depend on past LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement position and not from the entire surveillance region. The matrices comprising the system’s mode constitute an independent stochastic process. It is shown that the proposed formulation generalizes several important problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered general problem and is shown to reduce, in some special cases, to some well known classical algorithms. The new concept, as well as the derived algorithm, are demonstrated for the problem of target tracking in clutter, and are shown to attain performance that is competitive to that of several popular nonlinear methods. I

Improvement of Vector Autoregression (VAR) estimation using Combine White Noise (CWN) technique

Previous studies revealed that Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH) outperformed Vector Autoregression (VAR) when data exhibit heteroscedasticity. However, EGARCH estimation is not efficient when the data have leverage effect. Therefore, in this study the weaknesses of VAR and EGARCH were modelled using Combine White Noise (CWN). The CWN model was developed by integrating the white noise of VAR with EGARCH using Bayesian Model Averaging (BMA) for the improvement of VAR estimation. First, the standardized residuals of EGARCH errors (heteroscedastic variance) were decomposed into equal variances and defined as white noise series. Next, this series was transformed into CWN model through BMA. The CWN was validated using comparison study based on simulation and four countries real data sets of Gross Domestic Product (GDP). The data were simulated by incorporating three sample sizes with low, moderate and high values of leverages and skewness. The CWN model was compared with three existing models (VAR, EGARCH and Moving Average (MA)). Standard error, log-likelihood, information criteria and forecast error measures were used to evaluate the performance of the models. The simulation findings showed that CWN outperformed the three models when using sample size of 200 with high leverage and moderate skewness. Similar results were obtained for the real data sets where CWN outperformed the three models with high leverage and moderate skewness using France GDP. The CWN also outperformed the three models when using the other three countries GDP data sets. The CWN was the most accurate model of about 70 percent as compared with VAR, EGARCH and MA models. These simulated and real data findings indicate that CWN are more accurate and provide better alternative to model heteroscedastic data with leverage effect

Bayesian algorithms for mobile terminal positioning in outdoor wireless environments

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