ATM: Adaptive Temporal Kalman Filter-Based Solution Separation Method for Positioning and Integrity Monitoring

The Kalman filter is widely used in integrated navigation frameworks combining Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS). However, its assumption of Gaussian white noise is often violated in practice, as error sources such as satellite clock offsets and multipath effects show strong temporal correlations. This can affect both positioning accuracy and system integrity. To address this, we propose ATM: an Adaptive Temporal Kalman filter-based solution separation Method for positioning and integrity monitoring. Adaptive temporal Kalman filter mainly consists of Measurement Noise Modeling (MNM) and the Combination of State vector and Measurement vector (CSM). ATM models colored noise as a first-order adaptive Markov process, capturing temporal dependencies. The Kalman filter update is reformulated as a weighted least squares problem, enabling propagation to a new measurement vector and a refined measurement equation. This framework supports state solution separation in the positioning domain, improving fault detection and exclusion. Experiments on the public UrbanNav dataset show that ATM greatly improves positioning accuracy and reduces protection levels compared to baseline methods in medium and deep urban canyons. Specifically, horizontal positioning accuracy improves by 4.80% and 4.57%, while the Horizontal Protection Level (HPL) decreases by 13.32% and 18.32%, and the Vertical Protection Level (VPL) decreases by 18.51% and 26.74%1.