Target Tracking With Constraints In Wireless Sensor Network

Wireless sensor networks(WSN), composed of the sensor nodes, are deployed in the monitoring area and can receive a variety of information. Because of its low cost, self-organization, distribution, robustness, real-time and other features, wireless sensor networks have been widely applied in many areas of military defense, environmental monitoring, urban management, health care, space exploration, emergency rescue, disaster relief and so on.The locating and tracking of moving target is one of the main applications of WSN. The trajectory of the moving target can be estimated by measuring and fusing the target signal parameters. This paper will study the tracking algorithm based on the Kalman filtering. In recent years, the constrained Kalman filtering has received extensive attention in fault diagnosis, robot control, multi-target tracking, navigation and other different areas. In the actual WSN target-tracking system, we can usually get some priori information about the target motion. This paper mainly focuses on how to use the second-order equality constraints to improve the target tracking accuracy in the Kalman filtering.In this paper, the target-tracking algorithms in the WSN with constraint information are discussed in the following aspects. By comparing with the existing methods, it will prove that the algorithms proposed in this paper have more superiority.1) This paper investigates the target-tracking model based on the target signal time difference of arrival(TDOA) and frequency difference of arrival(FDOA) measurements obtained at sensors. The number of sensors available for the geolocation task is more than sufficient and their locations are subject to random errors. This paper derives the constrained Cramér-Rao lower bound(CCRLB) of the target position and on the basis of the CCRLB analysis, an approximately efficient constrained maximum likelihood estimator(CMLE) for geolocating the target is established.2) Based on the maximum likelihood(ML) function, a closed-form approximate solution can be obtained. This paper develops an improved approximate maximum likelihood(AML) algorithm, updating the cost function with receiver uncertainty, which can allow real-time implementation as well as global convergence. And a new iterative algorithm for solving the CMLE is then proposed, where the updated target position estimate is shown to be the globally optimal solution to a generalized trust region sub-problem(GTRS) and it can be found via a simply bisection search.3) A new target-tracking algorithm based on Kalman filtering with quadratic equality constraints is proposed in this paper. The proposed algorithm firstly utilizes newly obtained positioning measurements and the unconstrained Kalman filtering to produce an updated state estimation and then refines it using a maximum likelihood estimator with quadratic equality constraints. When solving the constrained maximum likelihood estimator, this paper formulates it as a GTRS in order to obtain its globally optimal solution. Simulation results show that the proposed algorithm outperforms previously developed nonlinear Kalman filtering algorithms with quadratic equality constraints in terms of enhanced target tracking accuracy.4) A first-order mean square error(MSE) analysis is conducted to quantify the performance degradation when the known target altitude is assumed to be precise but it indeed has some unknown and deterministic errors. Computer simulations are used to verify the validity of the MSE analysis.