This paper presents a matrix formulation of factorial kriging, and its relationships with simple and ordinary kriging. Similar to other kriging methods, factorial kriging can be applied to both stationary and intrinsic stochastic processes, and is often used as a local operator. Therefore, the concepts of intrinsic random function and local stationarity are first briefly reviewed. Kriging is presented in a block matrix form in which the kriging solution is useful not only for understanding the relationships between simple and ordinary kriging methods, but also the relationships between interpolative kriging and factorial kriging. When used as a signal/noise-filtering method, factorial kriging is especially useful for multiscale modelling. Examples for general signal analysis and geophysical data signal filtering are given to illustrate the method..