Abstract: In order to inplementing underwater gravity aided inertial navigation on Kalman filter, the modeling of gravity measurements and their errors is requred. Due to that background a new pattern of gavity aided navigation which is based on local gravity field modeling is given in this paper. In this paper, a fast Fourier series based local gravity field modeling is firstly introduced, and by which the difference between measured gravity and indicated gravity is then expressed as continual analytical equation. After that, the extended Kalman filter is introduced, with the gravity difference used as measurement, to optimum estimate the position error of INS. At the end of this paper a simulation is done on gravity anomaly database, and form the results we can see that the mean error of local gravity field modeling is less than 0.1331mGal, and the mean location error in longitude and latitude is 0.1975 and 0.2499 nautical mile respectively.