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A transform coding data compression method is developed for the case of making estimates from data collected using two sensors. We focus on the transfer of data from one sensor to another sensor, where the shared data is then used with the local data to estimate a parameter. Particular attention is paid to the case where neither sensor alone can estimate the parameter from its data. The method uses an operational rate-distortion viewpoint together with a distortion measure based on the Fisher information (FI) of the estimation problem. Explicit means of using the transformed data to compute operational measures of the FI are given. An integer optimization version of the Lagrange multiplier method is used to efficiently determine the optimal operating point of the transform compression algorithm. The advantages of the method lie in its ability to use transform coding to effectively capture the impact of compression on estimation accuracy in a way that lends itself to efficient optimization within the operational rate-distortion viewpoint. The applicability and effectiveness of the method are demonstrated for two illustrative examples: 1) estimation of time-difference-of-arrival (TDOA), and 2) estimation of frequency-difference-of-arrival (FDOA). In these two cases it is shown that the Fisher-information-based method outperforms the standard mean-square error (MSE) approach.