In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.
Multiple targets tracking is a major issue in the intelligent applications. Numerous methods have been presented for the multiple targets tracking to capture the targets trajectory in a video sequence in order to increase intelligence and reduce human error. In this paper, a method is proposed based on combining the Extended Kalman Filter (EKF) and Particle Swarm Optimization (PSO) to construct an intermediate tracker and track targets more accurately. The EKF solves targets collision problem, and PSO reduces the covariance of measured noise. Finally, the Joint Probabilistic Data Association (JPDA) filter is used to reduce the number of multiple hypotheses and create a one-to-one correspondence between targets and measurements. To detect targets, frames subtracting along with background modeling and canny edge detector are used. To reduce running time of the proposed method, number of video frames per second (fps) is reduced from 30 to 10 and the sampling rate is also reduced. Despite of this reduction, simulation reults of the proposed method show the multiple targets tracking with 98% accuracy at an acceptable running time compared to the similar methods. In addition, by using the proposed method, the number of assignment states is reduced in the targets tracking process. Overall, the proposed method not only can be used in the intelligent applications, but also in the video compression applications as well.
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