Objectives  Simultaneous and integrated strain tensor estimation from geodetic and satellite deformation measurements(SISTEM) is a popular method in this field due to its advantage of no-need for the interpolation of global navigation satellite system(GNSS) observations. However, the performance of the SISTEM method is greatly limited due to theinaccurate determination of the prior variance.

  Methods  Va-riance component estimation(VCE) algorithm is introduced to improve the SISTEM method.The strain model (SM) is used to establish the linear relationship between three-dimensional surface deformation of the target point and those of the neighborhood point.Different from the SISTEM method that only employs the InSAR observations of the target point when constructing the function model, the proposed method not only employs the InSAR observations of the target point, but also exploits an amount of nearest InSAR observations around it.This can improve the reliability of the SISTEM method in the region of lacking GNSS observations. In order to meet the requirement of VCE that the number of all types of observations are roughly equal, the number of both types of InSAR observations (i.e., ascending and descending) are approximately 3 times as that of GNSS observations.

  Results  Compared with those of the SISTEM method, the root mean square error(RMSE)from the proposed method achieve an improvement of 56.3%, 41.9% and 41.8% in east west(EW), south north(NS), up down(UD) components, respectively.In addition, the average weights of the interferometric synthetic aperture radar(InSAR) and GNSS observations derived from the proposed method is closer to the theoretical value than those from the SISTEM method. The real data experiments were then carried out by using the data acquired from the area near Kilauea Volcano on the island of Hawaii, US, including 29 GNSS observations and two pairs of ALOS PALSAR images in 2007. As expected, the accuracies of the proposed method are also improved by 31.4%, 18.6% and 22.8% in EW, NS, UD components, respectively, compared with those of the SISTEM method.

  Conclusions  It is found that the proposed method has better resistance to spatial decorrelation in the regions without sufficient GNSS data since more InSAR observations were used to form the observation equation.In addition, the results from the proposed method are less affected by local abrupt deformation.