Accurate estimation of railway track geometry degradation and reliable prediction of remaining useful life (RUL) are essential for cost-effective infrastructure management. This paper presents a self-contained Kalman filtering framework that integrates unsupervised tamping detection and Settling-aware post-tamping state management, jointly addressing state estimation, short-term forecasting, and RUL prediction for longitudinal level and twist parameters using only historical onboard monitoring (OBM) and measurement train (MT) data, without requiring traffic load, environmental, or maintenance metadata. The framework comprises four integrated stages: (i) source-specific outlier detection exploiting the distinct noise characteristics of OBM and MT instruments; (ii) unsupervised tamping detection through adaptive jump analysis on monthly representative values; (iii) a damped Kalman filter with adaptive noise modelling and spatial fusion of neighboring positions, augmented by a Settling-aware state management mechanism that detects the rapid post-tamping consolidation phase and injects physically informed velocity priors to prevent filter lag; and (iv) a RUL prediction module that propagates the final Kalman state forward under damped dynamics until the predicted geometry violates the Alert Limit (AL) or Immediate Action Limit (IAL) defined by EN 13848-5. The complete pipeline is evaluated on 50 consecutive track positions spanning a 50-metre segment of Sudostbahn line 870 (Switzerland), using 6 MT and 33 OBM observations per position collected over five years (2016-2021). Results demonstrate accurate estimation through both degradation and maintenance phases, with six-month forecast confidence bands. The multi-position RUL analysis classifies 98% of positions as safe beyond a 2-year horizon and identifies the remaining positions with finite RUL values, enabling spatially targeted maintenance prioritization.