In Low Earth Orbit (LEO) augmentation scenarios, the substantial increase in visible satellites imposes a significant computational burden on the Fault Detection and Exclusion (FDE) at the receiver. Additionally, the random error model employed in Receiver Autonomous Integrity Monitoring (RAIM) and Advanced RAIM (ARAIM) is no longer applicable in such environments due to their complexity, resulting in overly conservative protection levels. This paper proposes a backward recursive FDE (BR-FDE) algorithm based on a three-dimensional mesh error random model. The algorithm utilizes the matrix inversion lemma to derive a general formula for multi-faults detection. It also presents a method for determining the weight matrix and calculating the integrity protection level using a three-dimensional grid, which incorporates the elevation, carrier-to-noise ratio (C/N0), and the Single Dilution of Precision (SDOP). Compared to the Multiple Hypothesis Solution Separation (MHSS) method, the proposed algorithm significantly reduces computational complexity in multi-satellite FDE scenarios. Compared to the positioning solutions from RAIM, Random Sample Consensus (RANSAC), and Factor Graph Optimization (FGO), the proposed algorithm achieves RMSE reductions of 23.88%, 24.09%, and 32.08%, respectively. Furthermore, it considerably enhances the protection levels, achieving a 44% and 43% improvement in horizontal and vertical protection levels, respectively, relative to RAIM.

Orbit determination in Earth–Moon space is challenged by dynamic-model mismatch and unstable GNSS observation conditions, especially under weak and intermittent signals. To address this issue, this paper proposes a GNSS single-point positioning (SPP)-aided orbit determination method based on adaptive sliding-window filtering. A tightly coupled framework is constructed by integrating orbital dynamics propagation with SPP pseudo-range observations, allowing propagation errors to be corrected in real time through measurement updates. To enhance adaptability under time-varying observation conditions, a dynamic sliding-window strategy is introduced, in which the observation-noise covariance is adjusted according to carrier-to-noise ratio ($C/N_0$) variations. Simulations for three representative Earth–Moon trajectories, including a near-rectilinear halo orbit (NRHO), a distant retrograde orbit (DRO), and a Halo orbit, show that the proposed method significantly outperforms the conventional tightly coupled solution. The three-dimensional RMS position error is reduced from 6.65 m to 1.27 m for NRHO, from 6.57 m to 1.27 m for DRO, and from 5.91 m to 1.44 m for Halo, corresponding to improvements of 80.9%, 80.4%, and 75.4%, respectively. Under a simulated 200-epoch GNSS interruption in the Halo case, the method also improves outage robustness and post-recovery performance, reducing the three-dimensional RMS error by 23.2% in the interruption-centered interval and by 26.1% over the full arc.

In the domains of the Internet of Things (IoT) and intelligent transportation, the importance of integrity monitoring has become increasingly prominent with the rapid development of autonomous driving. In complex environments, the redundancy of effective observations often fails to meet the stringent requirements of integrity monitoring. Moreover, due to the effects of multipath (MP) and non-line-of-sight (NLOS), receiver noise frequently deviates from the Gaussian distribution, thereby significantly degrading the performance of traditional global navigation satellite system (GNSS)/inertial navigation system (INS) integrated navigation algorithms. Capitalizing on the rapid deployment of Low Earth Orbit (LEO) satellite constellations, this article proposes a novel integrity monitoring algorithm for GNSS/LEO/INS tightly coupled (TC) systems within the KalmanNet framework. First, LEO satellites provide enhanced observational redundancy, thereby improving the reliability of integrity monitoring. Second, the proposed algorithm relaxes the Gaussian noise assumption and instead utilizes a masked convolutional neural network (CNN)–long short-term memory (LSTM)–attention (CLA) network to learn features from the observation data. Experimental results demonstrate that the proposed algorithm achieves root-mean-squared error (RMSE) reductions of 55.53%, 51.74%, 36.42%, and 29.50% compared to standard point positioning (SPP), TC IGG3, RLAKF, and BSRMCL algorithms, respectively.