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This work studies the problem of tracking signal-emitting mobile targets using navigated mobile sensors based on signal reception. Since the mobile target's maneuver is unknown, the mobile sensor controller utilizes the measurement collected by a wireless sensor network in terms of the mobile target signal's time of arrival (TOA). The mobile sensor controller acquires the TOA measurement information from both the mobile target and the mobile sensor for estimating their locations before directing the mobile sensor's movement to follow the target. We propose a min-max approximation approach to estimate the location for tracking which can be efficiently solved via semidefinite programming (SDP) relaxation, and apply a cubic function for mobile sensor navigation. We estimate the location of the mobile sensor and target jointly to improve the tracking accuracy. To further improve the system performance, we propose a weighted tracking algorithm by using the measurement information more efficiently. Our results demonstrate that the proposed algorithm provides good tracking performance and can quickly direct the mobile sensor to follow the mobile target.