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In this paper, localization problem in wireless sensor and actor networks (WSAN) is addressed. In WSAN, the performance of event detection and tracking highly depends on the exact location information of the events that must be reported along with the event features. Having precise location information of the sensor nodes, actors are able to execute actions more effectively in the region of detected events. In this context, the accurate localization of sensor nodes is essential with respect to the actors. Particularly, the problem becomes much more complicated when the sensor nodes as well as the anchor nodes (actors) are mobile. In order to localize the mobile sensor nodes relative to the actors, a novel Timing-based Mobile Sensor Localization (TMSL) algorithm is introduced. In TMSL, sensor nodes determine their distance from actors by using propagation time and speed of RF signal. In order to determine distance from the actors, actors actively broadcast reference beacons in a pattern of intervals adaptively defined according to the mobility of sensor nodes and the required level of localization accuracy. These reference beacons carry the interval numbers in which they were transmitted. The interval numbers are then used by the sensor nodes to calculate the start time of the beacons locally which is then used to determine the propagation time. TMSL does neither require nor assume any time synchronization among the sensor nodes or with the actors. Performance evaluations clearly show that TMSL is adaptive to velocity of mobile sensor and actor nodes and can be configured according to the required localization accuracy in order to avoid overhead raised due to high velocity.