Instantaneous State InSAR: Smoothness Doublet and Ambiguity Resolution

Instantaneous state InSAR (ISI) enables epoch-wise parameterization, estimation and prediction for the dynamic motion of individual scatterers in near real-time displacement monitoring. Yet, it introduces a coupling problem: the state prediction (time-update) and the integer ambiguity resolution of double difference phase (measurement-update) depend on each other in a recursive loop. An inaccurate prediction can lead to an incorrect integer ambiguity number, that subsequently contaminates the state estimate and degrades every subsequent prediction. We analyze this coupling within the ISI framework and propose a two-step approach to address the problem. First, we represent the smoothness doublet of the time-update, i.e., the standard deviation and decorrelation time of the instantaneous velocity, with two physically interpretable metrics: the fractal dimension and the maximum absolute average velocity, and derive empirical relations between them, so that for a particular case study, the smoothness constraint can be introduced from prior physical expectations rather than by trial and error. Second, for the measurement-update, we propose a probabilistic ambiguity-resolution strategy that evaluates a small set of candidate integer ambiguities and assigns each a likelihood derived from the predicted-residual distribution.