Over-injection of time-correlated tropospheric constraints induces PPP height shifts: a Gauss–Markov remedy

Abstract External zenith total delay (ZTD) constraints improve precise point positioning (PPP) but are commonly treated as temporally independent epoch-wise pseudo-observations. Their errors exhibit substantial temporal correlation. Neglecting this correlation can over-inject constraint information and distort PPP height through its strong coupling with ZTD. This study uses ZTD derived from the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5) to quantify the resulting height effects. Treating the ZTD constraint errors as white noise overestimates their effective information content by a factor of about 65 relative to that implied by the residual autocorrelation, while the magnitude of the ZTD-to-height leakage coefficient reaches 1.74 in static mode and 1.93 in kinematic mode. To handle this temporal correlation, the constraint residuals are modeled as a combination of a diurnal cycle, a daily constant offset, and a time-correlated component described by a first-order Gauss–Markov process, with the constant offset and the Gauss–Markov process introduced as additional filter states. Results show that the proposed approach not only retains the convergence gain over the unconstrained solution but also substantially mitigates the constraint-induced height shifts. The magnitude of the ZTD-to-height leakage coefficient decreases to 0.08 in static mode and 0.11 in kinematic mode, the median absolute height difference from the unconstrained solution in static mode decreases from 9.4 to 0.4 mm, and the discrepancy between the filter-reported formal height uncertainty and the empirical height error is substantially reduced.