Christian Lundquist

A Gaussian mixture PHD filter for extended target tracking

In extended target tracking, targets potentially produce more than one measurement per time step. Multiple extended targets are therefore usually hard to track, due to the resulting complex data association. The main contribution of this paper is the implementation of a Probability Hypothesis Density (PHD) filter for tracking of multiple extended targets. A general modification of the PHD filter to handle extended targets has been presented recently by Mahler, and the novelty in this work lies in the realisation of a Gaussian mixture PHD filter for extended targets. Furthermore, we propose a method to easily partition the measurements into a number of subsets, each of which is supposed to contain measurements that all stem from the same source. The method is illustrated in simulation examples, and the advantage of the implemented extended target PHD filter is shown in a comparison with a standard PHD filter.

An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.

Road Intensity Based Mapping Using Radar Measurements With a Probability Hypothesis Density Filter

Mapping stationary objects is essential for autonomous vehicles and many autonomous functions in vehicles. In this contribution the probability hypothesis density (PHD) filter framework is applied to automotive imagery sensor data for constructing such a map, where the main advantages are that it avoids the detection, the data association and the track handling problems in conventional multiple-target tracking, and that it gives a parsimonious representation of the map in contrast to grid based methods. Two original contributions address the inherent complexity issues of the algorithm: First, a data clustering algorithm is suggested to group the components of the PHD into different clusters, which structures the description of the prior and considerably improves the measurement update in the PHD filter. Second, a merging step is proposed to simplify the map representation in the PHD filter. The algorithm is applied to multi-sensor radar data collected on public roads, and the resulting map is shown to well describe the environment as a human perceives it.

Back Driving Assistant for Passenger Cars with Trailer

This paper focuses on control strategies that are needed to stabilise a backing trailer and steer it into the desired direction. A model of the trailer and the car is used in order to calculate the desired steering wheel angle. An important constraint is that the driver should not be disturbed by the steering intervention. Measurements are done with a prototype car with an active front steering system. The results show that the drivers manage to fulfill the given driving task faster and with less steering wheel activity than without the assistant.

Marginalized adaptive particle filtering for nonlinear models with unknown time-varying noise parameters

Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback-Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.

Extended Target Tracking Using Polynomials With Applications to Road-Map Estimation

This paper presents an extended target tracking framework which uses polynomials in order to model extended objects in the scene of interest from imagery sensor data. State-space models are proposed for the extended objects which enables the use of Kalman filters in tracking. Different methodologies of designing measurement equations are investigated. A general target tracking algorithm that utilizes a specific data association method for the extended targets is presented. The overall algorithm must always use some form of prior information in order to detect and initialize extended tracks from the point tracks in the scene. This aspect of the problem is illustrated on a real life example of road-map estimation from automotive radar reports along with the results of the study.

Tracking stationary extended objects for road mapping using radar measurements

It is getting more common that premium cars are equipped with a forward looking radar and a forward looking camera. The data is often used to estimate the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary objects, that is typically not used. The present work shows how stationary objects, such as guard rails, can be modeled and tracked as extended objects using radar measurements. The problem is cast within a standard sensor fusion framework utilizing the Kalman filter. The approach has been evaluated on real data from highways and rural roads in Sweden.

Joint ego-motion and road geometry estimation

We provide a sensor fusion framework for solving the problem of joint ego-motion and road geometry estimation. More specifically we employ a sensor fusion framework to make systematic use of the measurements from a forward looking radar and camera, steering wheel angle sensor, wheel speed sensors and inertial sensors to compute good estimates of the road geometry and the motion of the ego vehicle on this road. In order to solve this problem we derive dynamical models for the ego vehicle, the road and the leading vehicles. The main difference to existing approaches is that we make use of a new dynamic model for the road. An extended Kalman filter is used to fuse data and to filter measurements from the camera in order to improve the road geometry estimate. The proposed solution has been tested and compared to existing algorithms for this problem, using measurements from authentic traffic environments on public roads in Sweden. The results clearly indicate that the proposed method provides better estimates.

Estimation of the Free Space in Front of a Moving Vehicle

There are more and more systems emerging making use of measurements from a forward looking radar and a forward looking camera. It is by now well known how to exploit this data in order to compute e ...

Road geometry estimation and vehicle tracking using a single track model

This paper is concerned with the, by now rather well studied, problem of integrated road geometry estimation and vehicle tracking. The main differences to the existing approaches are that we make use of an improved host vehicle model and a new dynamic model for the road. The problem is posed within a standard sensor fusion framework, allowing us to make good use of the available sensor information. The performance of the solution is evaluated using measurements from real and relevant traffic environments from public roads in Sweden. The experiments indicates that the gain in using the extended host vehicle model is most prominent when driving on country roads without any vehicles in front.