Sequential Estimation of Terrestrial Reference Frame using Information Filter for a Singular System

At present, the solution of the International Terrestrial Reference Frame (ITRF) is computed through direct inversion of a single large-scale normal equation. The merits of performing the inversion by an alternative, sequential computational method include: (i) shorter computation time, and (ii) flexibility to incorporate empirical stochastic models for station motion and time-dependent noise processes. KALREF, an ITRF-like formulation implemented using the Kalman filter and a newly developed formulas for the RTS smoother, has been shown to be able to perform a significant portion of the computation sequentially in time. In this presentation, we present a sequential algorithm based on the "information filter", a well-documented variant of the Kalman filter. Unlike the standard Kalman filter, the information filter is able to handle under-constrained state variables and is hence particularly suitable for the "long-term solution" stage of ITRF, where the normal equation remains rank-deficient until an appropriate amount of data is collected ("stacked") over time. However, the ITRF "internal/intrinsic constraint" applied to the Helmert transformation parameters leads to a singularity in temporal dynamics, requiring some significant modifications in the filtering algorithm to avoid numerical degeneracy. We will present such developments in computational algorithms as well as evaluation of their numerical performances using actual data.