We consider factor models used in the problems of residual statics and waveform correction. Such models lead to a system of linear equations, which allows us to perform a detailed analysis of the solutions obtained. In particular, it is possible to understand the problem of long- period statics and its connection with acquisition configuration. At the same time, it is shown how this problem can be solved at the algorithmic level with optimization of the used a priori information. The latter is especially relevant for the analysis of dynamic problems. In the study of linear systems two approaches are implemented: (i) an iterative process of consistently refining the factor estimates, and (ii) introducing heuristic conditions that ensure uniqueness and stability of the solution.