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A compressive sensing-based approach to solve the problem of tracking targets in the deployment area of the wireless networks without the need of equipping the target with a wireless device has been proposed. We present a dynamic statistical model for relating the change of the received signal strength between the node pairs to the spatial location of the target. On the basis of the model, the problem is formulated as a sparse signal reconstruction problem, and we propose a novel Bayesian greedy matching pursuit (BGMP) algorithm to tackle the signal reconstruction problem even from a small set of measurements. The BGMP iteratively seeks the contribution of each pixel for multi-times to compensate for the inaccuracy of the measurement matrix, and builds the enumeration region based on the past estimations to speed up the algorithm and improve its reconstruction performance simultaneously. Experimental results demonstrate the effectiveness of our approach and confirm that the BGMP algorithm could achieve satisfactory localisation and tracking results.