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The measurements of full tensor gradiometer include a lot of white noise and red noise�� The tradi- tional digital filter can only removes the noise completely when it in a specify frequency band��but when the noise and the gradient signal have the same frequency band�� the traditional filter cannot separate the noise from the gradi- ent signal well�� In order to filter the white noise and red noise simultaneously��the authors use the Kalman filter with augmented matrix convert to estimate the red noise in full tensor gravity gradient data��which achieved the aim that restraining the white noise and separating the red noise with the gradient signal��and combine the advantages of the digital filter and Kalman filter to get higher quality gradient signal�� Model data have been used to identify the a- bility of the filters��which have satisfied the high precision requirements of processing the gravity gradient data��