Henk A. P. Blom

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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)
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)
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)
– For the problem of tracking closely spaced targets from possibly false and missing observations, the paper studies combinations of IMM and PDA where both the IMM step and the PDA step is performed jointly over all targets. The resulting filter algorithms are referred to as Joint IMM Coupled PDA (JIMM-CPDA) and track-coalescence-avoiding Joint IMM Coupled(More)