In this paper, in addition to investigation and analyzing the dynamic model of a maneuver target, a new method based on the Interaction Multiple Model (IMM) method is presented to solve the tracking problem in presence of measurement noise. In this procedure, two models are used along with an extended Kalman filter for each model, for estimation of the states related to stochastic target model. To this end, a specific weight is calculated adaptively for each model and the final estimation of the target is obtained from the weighted sum of the modes related to each model. In this paper, second order Markov models are used to better describe the system behavior which leads to a decrease in the number of required motion models. This means that the previous two models are used to decide on the next model, and a much better algorithm is provided than the first-order IMM algorithm.

Drought is an inseparable part of climatic fluctuations which caused to lot of damages to different sections annually. Therefore, drought prediction can effectively reduce its damages. Markov Chain method is one of the drought prediction methods. In this study, the effect of Markov Chain order (orders 1, 2 and 3) were evaluated in drought forecasting accuracy (based on SPEI index), using Markov Chain method on climatological data of five synoptic stations of Iran with different climatic conditions during 1967 to 2014. Based on the results, transition probability from all drought classes to class 4 (normal) had the most frequency and to class 1 (extreme wet) had the lowest frequency. Results demonstrated that when observed and predicted drought classes have no difference, Markov order 3 has the best results. When observed and predicted drought classes have one class of difference, in 60% of cases Markov order 3 and in 40% of cases Markov order 2 has the best results. When observed and predicted drought classes have difference of two or three classes, Markov order 3 has the best results. Therefore, it is recommended to use Markov order 3 and Markov order 2, respectively with SPEI index and Markov Chain method, for drought forecasting.

The present work focuses on the second order Markov chain model which arises in a variety of settings and is well-suited to be modeled in many applications. The efficiency of the maximum quasi-likelihood estimators with the full maximum likelihood estimators for second order Markov chain models are given, besides the limiting normality results on the asymptotic properties of the associated estimates. Some efficiency calculations are also given to discuss the feasibility and computational complexity of the QL approach relative to the full likelihood approach.

In a finite stationary Markov chain, transition probabilities may depend on some explanatory variables. A similar problem has been considered here. The corresponding posteriors are derived and inferences are done using these posteriors. Finally, the procedure is illustrated with a real example.

In spite of the fact that the principles of impinging stream reactors have been developed for more than half a century, the performance analysis of such devices, from the viewpoint of the mathematical modeling, has not been investigated extensively. In this study two mathematical models were proposed to describe particulate matter drying in tangential impinging stream dryers. The models were developed based on Markov-Chain analysis and the theory of stirred tanks in series. The required parameters for each model were determined by using RTD data obtained in a tangential impinging stream dryer and then the governing equations were solved numerically.Comparing the models with available experimental data shows that the stirred tanks in series model successfully explains the drying behavior in impinging stream dryers.Nevertheless, the developed results of the model that is based on Markov-Chain analysis, are not in exact agreement with corresponding experimental data. Also, the effects of some operating parameters on performance of such dryers were investigated. The results indicate that the moisture removal efficiency of dryer increases when the solid to gas ratio and initial moisture content of particles decreases and the temperature of carrier gas increases.