Analysis of Inhomogeneous Random Sampling

Process estimation from randomly deployed samples in a multidimensional space with sample position errors is essential for various applications. This analyzes random sampling in R^d jointly accounting for finite-energy process properties (process spectrum and spatial correlation) and for sampling properties (inhomogeneous sample spatial distribution, sample availability, and non-ideal knowledge of sample positions). Based on process and sampling properties, the estimated process spectrum and the estimation accuracy are derived. Some properties expand the process spectrum while others modify the process without expansion. The process estimation accuracy is determined in a general case. The analysis is corroborated by verifying that previously known results can be obtained as special cases of the general one and by means of a case study accounting for various process and sample properties.