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Application of new data compression schemes to aided inertial navigation systems is presented. The need for data compression is motivated by the fact that the external aiding system generates frequent but inaccurate position measurements, which have to be processed by a processor whose computation capability is limited. Two new data compression techniques are presented and their efficiency is demonstrated through covariance simulation runs as well as computational complexity analysis. These schemes are characterized by their ability to process batches of measurements recursively and efficiently. It is demonstrated that the resulting estimation accuracy is comparable to that produced by a Kalman filter which processes optimally the same amount of data, while the required computational effort is reduced.