Henk A. P. Blom

An efficient filter for abruptly changing systems

For a linear discrete time system with Markovian coefficients a new filtering algorithm is given, which is called the Interacting Multiple Model (IMM) algorithm. The mathematical support for this algorithm is outlined and a qualitative comparison with other known filtering algorithms is made. The main conclusion is that the ratio between performance and computational complexity is far better for the IMM algorithm.

Probabilistic data association avoiding track coalescence

For the problem of tracking multiple targets, the joint probabilistic data association (JPDA) approach has shown to be very effective in handling clutter and missed detections. The JPDA, however, tends to coalesce neighboring tracks and ignores the coupling between those tracks. Fitzgerald (1990) has shown that hypothesis pruning may be an effective way to prevent track coalescence. Unfortunately, this process leads to an undesired sensitivity to clutter and missed detections, and it does not support any coupling. To improve this situation, the paper follows a novel approach to combine the advantages of JPDA coupling, and hypothesis pruning into new algorithms. First, the problem of multiple target tracking is embedded into one filtering for a linear descriptor system with stochastic coefficients. Next, for this descriptor system, the exact Bayesian and new JPDA filters are derived. Finally, through Monte Carlo simulations, it is shown that these new PDA filters are able to handle coupling and are insensitive to track coalescence, clutter, and missed detections.

Piecewise deterministic Markov processes represented by dynamically coloured Petri nets

Piecewise deterministic Markov processes (PDPs) are known as the largest class of Markov processes virtually describing all continuous-time processes not involving diffusions. For PDPs, a substantial amount of powerful analysis and control results are available. As such, PDPs are attractive for use in modelling complex distributed systems. However, the specification of an appropriate PDP model for complex distributed systems that exist in practice is far from trivial. This difficulty already applies for the specification of a continuous-time Markov chain (CTMC). For a compositional specification of a CTMC model, Petri Nets have proven to be extremely useful. In order to realise a similar situation for PDP, this paper develops a novel type of Petri Net, named dynamically coloured Petri Net (DCPN), and proves that there exist into-mappings between PDPs and DCPNs.† †Part of this research has been performed within the project HYBRIDGE of the European Commission, contract number IST-2001-32460

Combining IMM and JPDA for tracking multiple maneuvering targets in clutter

The paper combines IMM and JPDA for tracking of multiple possibly maneuvering targets in case of clutter and possibly missed measurements while avoiding sensitivity to track coalescence. The effectiveness of the filter is illustrated through Monte Carlo simulations.

CONTRASTING SAFETY ASSESSMENTS OF A RUNWAY INCURSION SCENARIO: EVENT SEQUENCE ANALYSIS VERSUS MULTI-AGENT DYNAMIC RISK MODELLING

In the safety literature it has been argued, that in a complex socio-technical system safety cannot be well analysed by event sequence based approaches, but requires to capture the complex interactions and performance variability of the socio-technical system. In order to evaluate the quantitative and practical consequences of these arguments, this study compares two approaches to assess accident risk of an example safety critical sociotechnical system. It contrasts an event sequence based assessment with a multi-agent dynamic risk model (MA-DRM) based assessment, both of which are performed for a particular runway incursion scenario. The event sequence analysis uses the well-known event tree modelling formalism and the MA-DRM based approach combines agent based modelling, hybrid Petri nets and rare event Monte Carlo simulation. The comparison addresses qualitative and quantitative differences in the methods, attained risk levels, and in the prime factors influencing the safety of the operation. The assessments show considerable differences in the accident risk implications of the performance of human operators and technical systems in the runway incursion scenario. In contrast with the event sequence based results, the MA-DRM based results show that the accident risk is not manifest from the performance of and relations between individual human operators and technical systems. Instead, the safety risk emerges from the totality of the performance and interactions in the agent based model of the safety critical operation considered, which coincides very well with the argumentation in the safety literature.

SEQUENTIAL MONTE CARLO SIMULATION OF RARE EVENT PROBABILITY IN STOCHASTIC HYBRID SYSTEMS

Recently (Cerou et al., 2002) developed an elegant factorization of rare event probabilities appearing in diffusion processes and other strong Markov processes, and a sequential Monte Carlo simulation approach to estimate the factorized rare event probability. The paper extends this approach towards rarely switching diffusions, and demonstrates the effectiveness for a simple example.

Safety risk assessment by Monte Carlo simulation of complex safety critical operations

This paper gives an overview of performing safety risk assessment of a safety critical operation with support of Monte Carlo (MC) simulation. The approach is outlined for an air traffic example involving aircraft departing from a runway, which is occasionally crossed by taxiing aircraft. At the airport considered, a Runway Incursion Alert System (RIAS) is installed to warn the air traffic controller in case of impending runway incursions. The paper explains the key issues to be mastered in performing a MC simulation supported safety risk assessment of this kind of operation. To begin with, one has to develop an appropriate simulation model, and a sound way to speed up the MC simulation based on this model. Complementary, one has to validate the simulation model versus the real operation, and the simulation supported approach has to be embedded within the safety risk assessment of the total operation. For this application example MC simulation results are given and the way of feedback to the design of the operation is outlined.

Joint IMMPDA particle filter

For the problem of tracking multiple manoeu- vering targets in clutter and missing measurements the pa- per develops a Joint IMMPDA type of particle filter and compares this with other IMMJPDA based filters through Monte Carlo simulation for a simple example.

Petri-nets and hybrid-state Markov processes in a power-hierarchy of dependability models

Abstract 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 be extremely useful in developing Markov process models of complex practical processes, there is a clear need for a type of Petri Net that can play such role for developing PDP models. This paper defines such Petri Nets and shows their relation to PDPs and other Petri Nets.

Safety risk simulation of an airborne self separati on concept of operation

[Abstract] This paper evaluates through Monte Carlo (MC) simulation an airborne self separation concept which has been developed for use in en-route traffic conditions such as encountered over the Mediterranean area. For three different encounter scenarios, probabilities for violating minimum separation and for near-mid-air and mid-air events are estimated by applying powerful novel MC simulation approaches in rare event estimation. This provides great new insight in the efficacy of airborne conflict resolution management. The paper shows several quantitative risk estimates and presents an interpretation of these results in terms of safety. It shows that airborne self separation can be very effective, but also has its limitations for dense traffic conditio ns when conflict resolution is done in a sequential and un-coordinated way.