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This paper is concerned with the estimation problem for a dynamic stochastic estimation in a sensor network. Firstly, the quantized Kalman filter based on the quantized observations (QKFQO) is presented. Approximate solutions for two optimal bandwidth scheduling problems are given, where the tradeoff between the number of quantization levels or the bandwidth constraint and the energy consumption is considered. However, for a large observed output, quantizing observations will result in large information loss under the limited bandwidth. To reduce the information loss, another quantized Kalman filter based on quantized innovations (QKFQI) is developed, which requires that the fusion center broadcast the one-step prediction of state and innovation variances to the tasking sensor nodes. Compared with QKFQO, QKFQI has better accuracy. Simulations show the effectiveness.