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The problem of the existence of redundancy in the data in a recursive estimation problem is investigated. Given a certain data rate, should the estimator be run at the same rate? It is shown that under certain conditions there is redundancy in the data and the estimator can be run at a lower rate using compressed data with practically the same performance as when no data compression is utilized. It is also pointed out that, although at the higher rate there is redundancy in the data, the performance deteriorates noticeably when the data rate is lowered. Conditions for the existence of redundancy in the data and the procedure to remove it are presented. The procedure to compress the data is obtained such as to preserve the information in the sense of Fisher. The effect of data compression is a reduction in the computation requirements by a factor equal to the compression ratio. Such a reduction might be important in real-time applications in which the computing power is limited or too expensive. The application of this technique to the tracking of a reentry vehicle with a linearized filter is discussed in more detail and simulation results are presented.