Jan Erik Stellet

Estimating the Process Noise Variance for Vehicle Motion Models

Vehicle motion models are employed in driver assistance systems for tracking and prediction tasks. For probabilistic decision making and uncertainty propagation, the predictions inaccuracy is taken into account in the form of process noise. This work estimates Gaussian process noise models from measured vehicle trajectories using the expectation maximisation (EM) algorithm. The method is exemplified and the results evaluated for three commonly used motion models based on a large-scale dataset. A novel closed-form adaptation of the algorithm to a covariance matrix with Kronecker product structure, as in models for translational motion, is presented. The findings suggest that the longitudinal prediction errors feature a non-Gaussian distribution but a reasonable approximation is given by the estimated model.

Localization accuracy estimation with application to perception design

Landmark-based localization in dynamic environments poses high demands on the perception system of a mobile robot. The pose estimate generally has to fulfill specific accuracy requirements which might be necessitated by dependent systems, such as behavior planning. Thus, in this contribution we focus on the model-based derivation of perception requirements, i.e. detectable landmark types and minimum detection rates, to enable global localization with a specified upper bound on uncertainty. To this end, we utilize stochastic geometry to accurately capture and explicitly consider characteristics of the dynamic environment (e.g. occlusions), and the perception system (e.g. missed detections). From this point our contributions are twofold: i) We propose an analytical model of upper bounds on localization uncertainty. For continuous pose tracking, the Kalman filter equations for intermittent observations are considered and ii) perception requirements, i.e. minimum detection rates, based on specified upper bounds on pose estimation uncertainty are derived. Monte Carlo simulations are used to demonstrate the performance of the proposed methods.

Uncertainty propagation in criticality measures for driver assistance

Active safety systems employ surround environment perception in order to detect critical driving situations. Assessing the threat level, e.g. the risk of an imminent collision, is usually based on criticality measures which are calculated from the sensor measurements. However, these metrics are subject to uncertainty. Probabilistic modelling of the uncertainty allows for more informed decision making and the derivation of sensor requirements. This work derives closed-form expressions for probability distributions of criticality measures under both state estimation and prediction uncertainty. The analysis is founded on uncertainty propagation in non-linear motion models. Finding the distribution of model-based criticality metrics is then performed using closed-form expressions for the collision probability and error propagation in implicit functions. All results are illustrated and verified in Monte-Carlo simulations.

Fahrbahnreibwertschätzung mit optimaler linearer Parametrierung

Zusammenfassung Modellbasierte Verfahren zur Fahrdynamikregelung beruhen auf einer Beschreibung des Reifen-Fahrbahn-Kraftschlusspotenzials. Dieser Beitrag beschreibt eine neue Methode zur schlupfbasierten Fahrbahnreibwertschätzung unter besonderer Berücksichtigung der on-line Anwendung. Hierzu wird eine optimale lineare Parametrierung des Burckhardt-Reifenmodells untersucht. Gegenüber bisherigen Arbeiten erzielt das vorgeschlagene Modell eine verbesserte Approximation. Des Weiteren werden Parameterschätzverfahren für das Modell diskutiert und in einer Gesamtfahrzeugsimulation evaluiert.

Analytical derivation of performance bounds of autonomous emergency brake systems

Autonomous emergency brake (AEB) systems have to decide on brake interventions based on an uncertain and incomplete perception of the environment. This paper analyses theoretical limitations in AEB systems caused by noisy sensor measurements and uncertain prediction models. Such performance bounds can be used to derive sensor accuracy constraints, to identify challenging scenarios or to develop objective metrics. In contrast to most previous studies, this work focusses on analytical derivations. To this end, the Cramér-Rao bound of the best attainable state estimation covariance is derived from a model of sensor measurement errors. This state- and time-dependent covariance is then propagated to an AEB decision making logic that is based on a criticality measure. Additional inherent prediction uncertainty in this risk assessment is taken into account. The effectiveness of the AEB subject to uncertainties is compared to the deterministic baseline case in terms of the brake activation time and the collision energy reduction.

Statistical Modelling of Object Detection in Stereo Vision-Based Driver Assistance

In this work, a statistical analysis of object detection for stereo vision-based driver assistance systems is presented. Analytic modelling has not been attempted previously due to the complexity of dense disparity maps and state-of-the-art algorithms. To approach this problem, a simplified algorithm for object detection in stereo images which allows studying error propagation is considered. In order to model the input densities, vehicle contours are approximated by Gaussian Mixture Models and distance dependent measurement noise is taken into account. Theoretical results are verified with Monte Carlo methods and real-world image sequences. Using the proposed model, a prediction on the uncertainty in object location and optimal threshold selection can be obtained.

Model-Based Derivation of Perception Accuracy Requirements for Vehicle Localization in Urban Environments

In this contribution, we address the model-based derivation of perception requirements based on upper bounds on vehicle localization uncertainty for urban driver assistance (UDA) and urban automated driving (UAD). We show that a probabilistic model for the estimation of map-relative localization accuracy can be obtained and utilized for proper parametrization of a perception system. Therefore, the paper at hand entails two main contributions: i) Proposal of a probabilistic model for localization accuracy in closed form under the assumption of a generic measurement model with Gaussian noise and a stochastic landmark distribution, ii) Presentation of a framework for model-based derivation of perception requirements which permit desired localization performance. To exemplify the application of our method, sensor parameters for a stereo vision system (e.g. stereo base-width) are determined and verified via comprehensive simulation experiments. This is conducted in the context of an urban automated lane keeping system under explicit consideration of non-existent or occluded lane markings and curb stones.

Performance bounds on change detection with application to manoeuvre recognition for advanced driver assistance systems

Recognising the intended manoeuvres of other traffic participants is a crucial task for situation interpretation in driver assistance and autonomous driving. While many works propose algorithms for (computationally feasible) inference, much less attention is paid to finding analytic upper performance bounds for these problems. This work studies the statistical properties of the optimal detector in a binary change detection problem, i.e. the Generalised Likelihood Ratio test. With analytic models of the best attainable receiver operating characteristic, the influence of system design parameters can be investigated without the need for empirical evaluation. Moreover, these bounds can be used to derive objective performance metrics.

Performance evaluation and statistical analysis of algorithms for ego-motion estimation

This contribution investigates algorithms for egomotion estimation from environmental features. Various formulations for solving the underlying procrustes problem exist. It is analytically shown that in the 2-D case this can be performed more efficiently compared to common implementations based on matrix decompositions. Furthermore, analytic error propagation is performed to second order which reveals a multiplicative estimator bias. A novel bias-corrected solution is proposed and evaluated in Monte Carlo simulations. Propagation of the derived error model to a representation used in the recursive trajectory reconstruction is presented and verified.