Measurements in remote sensing geodesy have been well known to be of speckle noise nature. Although a number of despeckling algorithms have been proposed mainly based on the local weighted statistics in the engineering literature, there are relatively few studies on the statistical adjustment methods for processing the measurements contaminated with the speckle or multiplicative errors. We develop the least squares (LS)-based adjustment methods for the remote sensing measurements with multiplicative errors and trends, evaluate the accuracy of the parameter estimates, and derive the corresponding formulas to estimate the variance of the unit weight. Simulation examples are used to illustrate the developed theory and methods.

Although real-valued linear models, whether or not of full rank, have been thoroughly investigated and are well documented, very little is known about statistical and probabilistic aspects of a mixed integer linear model, which arose from space geodesy and serves as the standard starting model for precise positioning using the global positioning system (GPS). Voronoi cells play a fundamental role in the least squares estimation of the integer unknowns of the model. In this paper, we first develop a method to construct Voronoi cells and study how to fit figures of simple shape to a Voronoi cell, both from inside and outside. We then derive a number of new lower and upper bounds on the probability that the integers of the model are correctly estimated. Finally, we discuss the tests of two hypotheses on the integer mean.