The modern GNSS technique is one of the most effective geoscience and remote-sensing tool to observe crustal motions and quantify plate tectonics dynamics. Given multiple installed continuously operating GNSS observing stations, the multi-frame transformation is implemented to connect the timevarying GNSS coordinates by the traditional step-wise method. Compared with the step-wise treatment of each pair of frames, the proposed structured total least-squares method considers the combined estimation for all frames, guaranteeing unique and consistent results for the multi-frame symmetric transformation. Furthermore, we introduce the variance component as the nutshell and flexible indicator for land movement. The variance components can quantify the movement coordinate-wise, regional-wise, or frame-wise if the variance components are estimable as we analyze. The simulated experiment shows that the multi-frame symmetric transformation is statistically superior to the traditional stepwise treatment. For the application, the deformation caused by Tohoku earthquake that happened in 2011 in northeast Japan is analyzed.

In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision assessments. In this contribution, the Errors-in-Variables model equipped with Total Least Squares (TLS) estimation is proposed to address these issues. It fully considers random errors in both dependent and independent variables. An iterative algorithm is provided, and posterior accuracy estimates are provided to validate its effectiveness. Monte Carlo simulations demonstrate that TLS provides more accurate solutions than OLS, significantly improving the root mean square error by over 70%. Empirical experiments on datasets from Boston and Wuhan further confirm the superior performance of TLS, which consistently yields a higher coefficient of determination and a lower posterior variance factor, which shows its more substantial explanatory power for the data. Moreover, TLS shows comparable or slightly superior performance in terms of prediction accuracy. These results make it a compelling and practical method to enhance the HPM.

This paper explores the problem of symmetric transformation in the presence of outliers for photogrammetric and remote-sensing applications. We propose a point-wise robust objective for symmetric coordinate transformation by assuming the corresponding structure of the down-weighting matrix and choosing the squared Mahalanobis distance as the statistic to evaluate the down-weighting factors. Compared to the previous work, our method regards all the coordinates of one point as a whole. It is practical in principle since the displacement and correspondence relation are point-wise; it is statistically rigorous since the stochasticity of both frames is considered; it is flexible since the incorporated constraints enable all kinds of transformation. By utilizing the parameter partition technique, a more intelligent iteration manner is proposed for the implementation aspect, which specially suits globally distributed geoscience data. The developed method is vetted in the synthetic and real examples including geodetic datum conversion and point cloud registration. The algorithms have potential in many areas, including cross-source registration, image analysis, pattern recognition, surface modeling and remote-sensing image registration.