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This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation(More)
In theory, a good joint particle filter allows to approximate the exact Bayesian filter solution arbitrarily well. This has motivated a strong and successful development of single target tracking particle filters. Nevertheless, for tracking multiple closely spaced maneuvering targets, there is evidence in literature which seems to contradict the theoretical(More)
Switching Diffusion processes can be represented as pathwise unique solutions of SDE's in a hybrid state space that are driven by Brownian motion and Poisson random measure. This paper extends these SDE's to switching jump-diffusions, the jumps of which i) happen simultaneously with mode switching, and ii) depend on the mode after the switching. Jumps(More)
A mathematical model is presented for the evolution of situation awareness within the context of human performance modelling in accident risk assessment for ATM. Various aspects of situation awareness are defined within a group of agents, such as human operators and technical systems. Application of the model is illustrated for an accident risk assessment(More)
This paper extends the power hierarchy of dependability models developed by Malhotra and Trivedi (1994) and Muppala et al. (2000) to include Piecewise Deterministic Markov Processes (PDP) and PDP-related Petri Nets. PDPs are known as the largest class of continuous-time hybrid state Markov processes not involving diffusions. Since Petri Nets have proven to(More)
Technology allows aircraft to broadcast information about its own-ship position and velocity to surrounding aircraft, and to receive similar information from surrounding aircraft. This development has stimulated the rethinking of the overall concept for future Air Traffic Management (ATM), e.g., to transfer responsibility for conflict prevention from ground(More)
With increasing traffic there often are environmental and economical reasons to optimise Simultaneous Converging Instrument Approaches (SCIA) without sacrificing the high safety levels realised in air traffic. One of the well known safety issues of SCIA is the risk of a mid air collision due to a double missed approach. The aim of this paper is to show(More)
Air Traffic Management (ATM) involves interactions between multiple human operators, procedures and technical systems, all of which are highly distributed. This yields that providing safety is more than making sure that each of the ATM elements functions properly safe; it is the complex interaction between them that determines safety. The assessment of(More)
In theory, a good particle filter allows to approximate the exact Bayesian filter solution arbitrarily well. This has motivated a strong and successful development of particle filtering approaches towards target tracking. Literature also shows that successful multiple maneuvering target tracking seems to depend on the adoption of some suitable heuristics in(More)