Multi-sensor System Simulation Based on RESTART Algorithm

Multi-sensor systems play a central role in modern advanced driver assistant systems. With the exponential growth of sensor systems technologies (e.g. denoising, filtering), erroneous sensor detection is rare but can also be caused by successive sensor reading and correlated between sensors (e.g. in a harsh weather condition). Since automotive systems are safety-critical, suitable descriptions of the safety of multisensor systems are required. Their reliability can be determined either with analytical methods or with simulations. In general, modeling with simulations has no constraints in comparison to analytical models and more potential to extend for a complex system. Nevertheless, simulation models can also lead to long run times when they observe infrequent events. Due to the low sensor error rate, it is almost impossible to simulate these sensor system models in practical run time. Therefore, the present study aims to check whether the rare event simulation method called the Repetitive Simulation Trials After Reaching Thresholds (RESTART) algorithm can make the problem feasible. We employ RESTART simulations to a proven multi-sensor system model, which is based on discretetime Markov chains and in consideration of dependencies between successive sensor errors and correlation between different sensors. Meanwhile, we compare the system failure probability results of RESTART simulations with the analytical method. Furthermore, in this study, we define a new parameter "acceleration factor" so that we can describe the acceleration of RESTART simulations. Based on this factor, we demonstrate the difference between system failure estimation of normal simulation results and related RESTART simulation, which can additionally validate RESTART simulation results. In conclusion, with different pairs of RESTART simulation parameters, we can approximately accelerate normal simulations ten to even a hundred and at the same time with acceptable accuracy of simulation results.