Objectives  The objective is to study the tensor invariant method for determining the Earth's gravity field with satellite gravitational gradient data.

  Methods  The tensor invariant method does not depend on the acquisition of the spatial orientation information of the gradiometer, so it has a special advantage over the traditional methods in determining the earth gravity field. Numerical analyses are made for the linearization of tensor invariant observation equation, the processing of non-full tensor observation data, and the accuracy of gravity field recovery with the gradient data containing white noise.

  Results  The results show that the tensor invariant solution realizes the combine processing of the different tensor components. The tailored linearization effectively achieves the linearization of the tensor invariant observation model while the accuracy of gravity field model determined using tensor invariants is significantly higher than that of the single tensor component solution. Also, the choice of initial reference model exerts minor influence on the total iterative process.

  Conclusions  Due to the non-full tensor gradient observations, it is proposed to replace the low precision gradient component using the spherical harmonic synthesis of a priori gravity field model, which will not change the convergence and the accuracy of the solution even if the white noise exists in the observations because of the nadir-pointing characteristics of the gradiometer.