This paper deals with the initial integrity evaluation of the navigation information provided by the multilayer GNSS and LEO-PNT constellation. Although, the global satellite navigation systems (GNSS) play indispensable role in almost all aspects of today’s society, their signals are prone to intentional or accidental interference. Therefore, low Earth orbit (LEO) constellations aiming at position, navigation, and timing (PNT) solution have recently been introduced as their extension. The LEO-PNT constellations are planned to contain hundreds of SVs with better interference resilience and geometric diversity. As a consequence, the multi-layer GNSS and LEO-PNT constellation was shown to offer more accurate PNT solution. In this paper, we focus on another important aspect of the multi-layer navigation information, which is its integrity assessment. In particular, we analyse possible dependencies between GNSS and LEO-PNT constellations and their impact on the integrity evaluated using the solution separation. The analysis is supported by the numerical simulations using GPS and LEO-PNT constellations with 32 and 441 satellites, respectively.

This paper deals with the resilient time provision based on an ensemble of clocks. In particular, the emphasis is laid on the combination of clock outputs and detecting possible faults. Two classes of fault detection methods, namely model-based and AI/ML-based, are discussed and analysed. In addition, a novel fault detection technique based on the solution separation principle is proposed and tailored for the area of the time provision. Selected fault detection methods are numerically evaluated using a model of an atomic clock ensemble.

Active fault diagnosis (AFD) of stochastic large-scale systems in multiple model framework involves two stages: offline and online. In the offline stage, an excitation input generator is designed based on a Bellman function. In the online stage, the generator is utilized together with an estimator of the model indices. A similar estimator is used in the offline stage for the Bellman function calculation using the value iteration technique. However, due to the high dimensions of information states of the associated perfect state information problem, the estimator in the offline stage must involve approximations. The paper provides the relations for the estimate calculation using the Bayesian recursive relations, proposes four algorithms, and studies effects of such approximations on the AFD decisions. In particular, the quality of the model index estimates is analyzed using a power network model.

The paper deals with the active fault diagnosis of large scale stochastic systems with faults modeled as mutually dependent Markov chains. The system is described by multiple models representing fault-free and faulty behavior of the system. The aim of the active fault detector in addition to detecting the faults is to excite the system to improve the detection quality. The algorithm consists of two stages: the off-line design of the Bellman function providing the optimal excitation and the on-line estimation, which generates the decisions and selects the optimal excitation according to the Bellman function. In particular, the paper focuses on the online estimation and proposes an algorithm in the hierarchical architecture. The local nodes estimate the continuous state of the subsystems, select the optimal excitations and send local likelihoods to the central node. The central node generates the decisions and submits the respective model probabilities to the local nodes. The performance of the proposed algorithm is validated using a simple numerical example.