The measurement of the traditional time difference of arrival positioning technology is not accurate. In order to improve the situation of LED indoor positioning, this paper proposes an improved position estimation algorithm based on bounded grid. The algorithm in this paper firstly uses the hyperbolic positioning method to locate the signal source by time difference of arrival (TDOA). Boundary of the area where the signal source may exist at the time to be measured was set, and the area was meshed. The grid was weighted with a prior time. Through Bayesian filtering, the probability that the signal emission source may exist at the time to be measured is obtained. Thus, the position information of the signal emission source was obtained. On this basis, the speed of the signal source was estimated by combing the arrival frequency difference. The simulation results show that compared with the least-weighted squares positioning algorithm and the Chan algorithm combined with Kalman filtering, the algorithm in this paper has obvious advantages in the accuracy and stability of position and velocity measurement.