In this paper, we study the dynamic bandwidth allocation problem for target tracking based on quantized sensor data in wireless sensor networks. At each time step, the fusion center distributes the available bandwidth among the sensors in such a way that the posterior Cramér-Rao lower bound (PCRLB) on the mean squared error (MSE) is minimized. Since the optimal solution requires a combinatorial search, we seek computationally efficient suboptimal methods for dynamic bandwidth allocation. In order to minimize the estimation error, our objective is to maximize the determinant of the Fisher information matrix (FIM) subject to the total rate constraint. To maximize the determinant of the FIM, we formulate an approximate dynamic programming (A-DP) algorithm and compare its performance with other suboptimal methods, including the generalized Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm and the greedy search. A-DP is computationally more efficient than the GBFOS and simulation results show that A-DP and GBFOS algorithms yield similar tracking performance in terms of the mean squared error and outperform the greedy search.