Target Tracking Algorithm Based On Nonlinear Observer

In recent years, Wireless Sensor Networks (WSN) have been studied intensely as one of the hottest research fields. Due to low-cost, low-power, small size, self-organizing ability and other characteristics, WSN have broad application prospects in military defense, environment monitor, urban transport and so on.Compared with traditional networks, target tracking problems with WSN have more important application advantages because WSN are more reliable, more concealed and more efficient. In real environments, the state equation of the target and the observation equation of the sensors are generally nonlinear and noisy. At the same time, the target’s dynamics is partially unknown, which makes the problem more challenging. Therefore, it’s crucial to design and apply nonlinear filtering algorithms to estimate the state of the target.EKF algorithm is the most popular filter for nonlinear systems. Based on the Kalman filter theory, Taylor series expansion is applied to first-order linearization of the nonlinear system. However, the quality of EKF is often poor for intrinsically nonlinear systems. UKF algorithm is combined with unscented transform and the Kalman filter, and the filtering precision is higher than EKF algorithm. To deal with the non-Gaussian random variable problem, the most commonly-used way is particle filter (PF) algorithm. The algorithm is simple and realized easily. However, the amount of calculation is so large that PF may be difficult to be applied in WSN. The degenerating problem of the sample points is also hard to be dealt with.In condition of these above, an observer-based nonlinear target tracking algorithm is proposed in this paper. In order to solve the tracking problem, which the input of the state equation is partly unknown, and the observation equation is nonlinear and noisy, state observer is designed. Lyapunov stability and exponentially bounded in mean square of stochastic process are applied to get a feedback gain matrix, which makes the estimated trajectory to be similar with the real trajectory. So the target tracking problem can be solved.At the same time, in accordance with the limited sensing range, mobile sensors are applied to develop a stable formation control strategy, which makes the target can be monitored by sensors at any time. First, a directed tree graph is developed. Then, according with the dynamics of mobile agents, inspired by the idea of virtual sensor approaching and control thesis, a neighbor-based formation control algorithm is developed to ensure the sensors can track the target in a long time. And the stability of the algorithm is analyzed.At last, some numerical simulations are presented to validate the observer-based nonlinear filter algorithm and the formation control algorithm.