Importance Sampling Theory Research Articles

Construction of virtual test scenarios for intelligent car-pedestrian interaction

Aiming at the needs of intelligent car and pedestrian interaction testing under urban conditions, this paper proposes a scenario generation method that comprehensively considers the frequency of scenarios in the real world and the degree of challenge to human-vehicle interaction performance. First, according to the key features of intelligent car and pedestrian interaction, the original scene data of pedestrians crossing the road is extracted from the natural driving dataset; then, according to the needs of accelerated testing, a key scenario extraction method based on importance sampling theory is designed to extract and construct important scenarios for intelligent car-pedestrian interaction testing from the original scenes; finally, by comparing the data distribution of important scenarios with original scenarios, it is shown that this method can effectively screen out scenarios that may challenge safety performance during driving, thereby realizing accelerated testing, while taking into account the statistical characteristics of the test scenarios.

FROM OFFSHORE TO ONSHORE PROBABILISTIC TSUNAMI HAZARD ASSESSMENT WITH QUANTIFIED UNCERTAINTY: EFFICIENT MONTE CARLO TECHNIQUES

Offshore probabilistic tsunami hazard assessments (PTHAs) are increasingly available for earthquake generated tsunamis. They provide standardized representations of tsunami scenarios, their uncertain occurrence-rates, and models of the deep ocean waveforms. To quantify onshore hazards it is natural to combine this information with a site-specific inundation model, but this is computationally challenging to do accurately, especially if accounting for uncertainties in the offshore PTHA. This study reviews an efficient Monte Carlo method recently proposed to solve this problem. The efficiency comes from preferential sampling of scenarios that are likely important near the site of interest, using a user-defined importance measure derived from the offshore PTHA. The theory of importance sampling enables this to be done without biasing the final results. Techniques are presented to help design and test Monte Carlo schemes for a site of interest (before inundation modelling) and to quantify errors in the final results (after inundation modelling). The methods are illustrated with examples from studies in Tongatapu and Western Australia.

Off-road testing scenario design and library generation for intelligent vehicles

To realize the widespread application and continuous functional development of intelligent vehicles, test and evaluation of vehicle's functionality and Safety Performance in complex off-road scenarios are fundamental. Since traditional distance-based road tests cannot meet the evolving test requirements, a method to design the function-based off-road testing scenario library for intelligent vehicles(IV) is proposed in this paper. The testing scenario library is defined as a critical set of scenarios that can be used for IV tests. First, for the complex and diverse off-road scenarios, a hierarchical, structural model of the test scenario is built. Then, the critical test scenarios are selected adaptively according to the vehicle model to be tested. Next, those parameters representing the challenging test scenarios are selected. The selected parameters need to fit the natural distribution probability of scenarios. The critical test-scenario library is built combing these parameters with the structural model. Finally, the test scenarios that are most approximate to the natural driving scenario are determined with importance sampling theory. The test-scenario library built with this method can provide more critical test scenarios, and is widely applicable despite different vehicle models. Verified by simulation in the off-road interaction scenarios, test would be accelerated significantly with this method, about 800 times faster than testing in the natural road environment.

Accelerated Evaluation of Automated Vehicles Using Piecewise Mixture Models

The process to certify highly automated vehicles has not yet been defined by any country in the world. Currently, companies test automated vehicles on public roads, which is time-consuming and inefficient. We proposed the accelerated evaluation concept, which uses a modified statistics of the surrounding vehicles and the importance sampling theory to reduce the evaluation time by several orders of magnitude, while ensuring the evaluation results are statistically accurate. In this paper, we further improve the accelerated evaluation concept by using piecewise mixture distribution models, instead of single parametric distribution models. We developed and applied this idea to forward collision control system reacting to vehicles making cutin lane changes. The behavior of the cutin vehicles was modeled based on more than 403,581 lane changes collected by the University of Michigan Safety Pilot Model Deployment Program. Simulation results confirm that the accuracy and efficiency of the piecewise mixture distribution method outperformed single parametric distribution methods in accuracy and efficiency, and accelerated the evaluation process by almost four orders of magnitude.

Accelerated Evaluation of Automated Vehicles in Car-Following Maneuvers

The safety of automated vehicles (AVs) must be assured before their release and deployment. The current approach to evaluation relies primarily on 1) testing AVs on public roads or 2) track testing with scenarios defined in a test matrix. These two methods have completely opposing drawbacks: the former, while offering realistic scenarios, takes too much time to execute and the latter, though it can be completed in a short amount of time, has no clear correlation to safety benefits in the real world. To avoid the aforementioned problems, we propose accelerated evaluation, focusing on the car-following scenario. The stochastic human-controlled vehicle (HV) motions are modeled based on 1.3 million miles of naturalistic driving data collected by the University of Michigan Safety Pilot Model Deployment Program. The statistics of the HV behaviors are then modified to generate more intense interactions between HVs and AVs to accelerate the evaluation procedure. The importance sampling theory was used to ensure that the safety benefits of AVs are accurately assessed under accelerated tests. Crash, injury and conflict rates for a simulated AV are simulated to demonstrate the proposed approach. Results show that test duration is reduced by a factor of 300 to 100 000 compared with the non-accelerated (naturalistic) evaluation. In other words, the proposed techniques have great potential for accelerating the AV evaluation process.

Replicated Computations Results (RCR) Report for “Green Simulation: Reusing the Output of Repeated Experiments”

“Green Simulation: Reusing the Output of Repeated Experiments” by Feng and Staum describes methods based on likelihood ratio or importance sampling theory for reusing the outputs of simulation experiments at previous parameter settings to augment and improve (by reducing the estimator variance) simulation experiments at new parameter settings. The article presents empirical results for two realistic examples in the area of finance; Matlab code for these examples was made available by the authors. The examples were straightforward to run without extensive knowledge of Matlab, and both experiment and scenario parameters can be altered easily. All experiment results in the article were reproduced.

Importance Sampling for Reliability Evaluation With Stochastic Simulation Models

Importance sampling has been used to improve the efficiency of simulations where the simulation output is uniquely determined, given a fixed input. We extend the theory of importance sampling to estimate a system’s reliability with stochastic simulations. Thanks to the advance of computing power, stochastic simulation models are employed in many applications to represent a complex system behavior. A stochastic simulation model generates stochastic outputs at the same input. Given a budget constraint on total simulation replications, we develop a new approach, which we call stochastic importance sampling, which efficiently uses stochastic simulations with unknown output distribution. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of an estimator. Application to a computationally intensive aeroelastic wind turbine simulation demonstrates the benefits of the proposed approach. Supplementary materials for this article are available online.

Variance reduction of estimators arising from Metropolis–Hastings algorithms

The Metropolis---Hastings algorithm is one of the most basic and well-studied Markov chain Monte Carlo methods. It generates a Markov chain which has as limit distribution the target distribution by simulating observations from a different proposal distribution. A proposed value is accepted with some particular probability otherwise the previous value is repeated. As a consequence, the accepted values are repeated a positive number of times and thus any resulting ergodic mean is, in fact, a weighted average. It turns out that this weighted average is an importance sampling-type estimator with random weights. By the standard theory of importance sampling, replacement of these random weights by their (conditional) expectations leads to more efficient estimators. In this paper we study the estimator arising by replacing the random weights with certain estimators of their conditional expectations. We illustrate by simulations that it is often more efficient than the original estimator while in the case of the independence Metropolis---Hastings and for distributions with finite support we formally prove that it is even better than the "optimal" importance sampling estimator.

Adaptive Dynamic Clustered Particle Filtering for Mobile Robots Global Localization

This article presents an adaptive dynamic clustered particle filtering method for mobile robot global localization. The posterior distribution of robot pose in global localization is usually multimodal due to the symmetry of the environment and ambiguous detected features. Moreover, the multimodal distribution of the posterior varies as the robot moves and observations be obtained. Considering these characteristics, we use a set of clusters of particles to represent the posterior. These clusters are dynamically evolved corresponding to the varying posterior by merging the overlapping clusters and splitting the diffuse clusters or those whose particles gather to some sub-clusters inside. Further, in order to improve computational efficiency without sacrificing estimation accuracy, a mechanism for adapting the sample size of clusters is proposed. The theoretical lower bound of the number of particles needed to limit the estimation error is derived, based on the central limit theorem in multi-dimensional space and the statistic theory of Importance Sampling. Then, a method for tuning the sample size for each cluster according to the derived lower bound is presented. Experiment results show the effectiveness of the proposed method, which is sufficient to achieve robust tracking of robot's real pose and meanwhile significantly enhance the computational efficiency.

Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems

In this paper, we develop novel Bayesian detection methods that are applicable to both synchronous code-division multiple-access and multiple-input multiple-output communication systems. Markov chain Monte Carlo (MCMC) simulation techniques are used to obtain Bayesian estimates (soft information) of the transmitted symbols. Unlike previous reports that widely use statistical inference to estimate a posteriori probability (APP) values, we present alternative statistical methods that are developed by viewing the underlying problem as a multidimensional Monte Carlo integration. We show that this approach leads to results that are similar to those that would be obtained through a proper Rao-Blackwellization technique and thus conclude that our proposed methods are superior to those reported in the literature. We also note that when the channel signal-to-noise ratio is high, MCMC simulator experiences some very slow modes of convergence. Thus accurate estimation of APP values requires simulations of very long Markov chains, which may be infeasible in practice. We propose two solutions to this problem using the theory of importance sampling. Extensive computer simulations show that both solutions improve the system performance greatly. We also compare the proposed MCMC detection algorithms with the sphere decoding and minimum mean square error turbo detectors and show that the MCMC detectors have superior performance.

Importance Sampling for Polarization-Mode Dispersion: Techniques and Applications

The basic theory of importance sampling (IS) as relevant to polarization-mode dispersion (PMD) in optical fibers is discussed, and its application to Monte Carlo (MC) simulations of PMD-induced transmission impairments is demonstrated. The use of IS allows rare PMD events to be simulated much more efficiently than with standard MC methods. As a consequence, methods employing IS provide natural and effective tools to assess PMD-induced impairments and outages in optical transmission systems at realistic probability levels.

On the theory of importance sampling applied to the analysis of detection systems

Detection systems are designed to operate with optimal or nearly optimal probability of a wrong decision. Analytical solutions of the performance of these systems have been very difficult to obtain. Monte Carlo simulations are often the most tractable method of estimating performance. However, in systems with small probability of error, this technique requires very large amounts of computer time. A technique known as importance sampling substantially reduces the number of simulation trials needed, for a given accuracy, over the standard Monte Carlo method. The theory and application of the importance sampling method in Monte Carlo simulation is considered in a signal detection context. A general method of applying this technique to the optimal detection problem is given. Results show that in cases examined, the gain is approximately proportional to the inverse of the error probability. Applications of the proposed method are not limited to optimum detection systems; analysis, leading to a measure of the gain in using this biasing scheme, shows that in all optimal systems considered, less than 100 trials is needed to achieve estimates with 45% confidence, even for extremely small error probabilities. >