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The problem of dynamic bit allocation for target tracking is investigated in this paper under a total sum rate constraint in sensor networks. Bits are dynamically allocated to sensors in such a way that a cost function, which is based on the Cramér-Rao lower bound evaluated at the predicted target state, is minimized. The optimal solution to this problem, namely joint bit allocation and local quantizer design, is computationally prohibitive and not realistic for real-time online implementation. Instead, a two-step optimization procedure is proposed. First, the best time independent quantizers are obtained offline by maximizing the average Fisher information about the signal amplitude, for different number of bits. With the time independent quantizers, the generalized Breiman, Friedman, Olshen, and Stone (BFOS) algorithm is employed to dynamically assign bits to sensors. Simulation results show that with the same or even less sum bit rate, the proposed dynamic bit allocation approach leads to significantly improved tracking performance, compared with the static bit allocation approach where each sensor is allocated with equal number of bits.