A main aspect of underwater passive navigation is how to identify the vehicle location on an existing gravity map.and several match-ing algorithms as ICCP and SITAN are the most prevalent methods that many scholars are using.In this paper,a novel algorithm that is different from matching algorithms for passive navigation is developed.The algorithm implements underwater passive navigation by directly estimating the inertial errors through Kalman falter algorithm,and the key part of this implementation is a Fourier series.based local geopotential model.Firstly,the pfinople of local geopotential model based on Fourier series is introduced in this paper,thus the discrete gravity anomalies data can be expressed analytically with respect to geographic coordinares to establish the observation equation required in the application of Kalman filter.Whereafter,the indicated gravity anomalies can be gotten by substituting the inertial posi-tions to existing gravity anomalies map.Finally,the classical extended Kalman filter is introduced with the differences between measured gravity and indicated gravity used as observations to optimally estimate the errors of the inertial navigation system(INS).This naviga-tion algorithm is tested on simulated data with encouraging results.Although this algorithm is developed for underwater navigation using gravity data,it iS equally applicable to other domains,for example vehicle navigation on magnetic or terrain data.