SIGNAL PROCESSING REQUIREMENTS AND UNCERTAINTY MODELING

ISSUES IN COOPERATIVE VEHICULAR POSITIONING

Denis Gingras(1), Évangeline Pollard(1), Dominique Gruyer(2)

denis.gingras@usherbrooke.ca (1) Université de Sherbrooke, Québec, Canada, (2) LIVIC IFSTTAR France

ABSTRACT

Accurate and reliable vehicle localization is a key component to numerous applications, including active vehicle safety systems, real time estimation of traffic conditions, and high occupancy tolling. Up to now, most of the localization techniques rely on a given set of sensors embedded in a single vehicle. In this paper, we survey the issues considered in designing collaborative methods for localizing vehicles on roads using information coming from neighbor vehicles as well as from fixed infrastructures. We will in particular examine the signal processing issues and uncertainty modeling in estimating the relative ranges and angles of vehicles and the vehicles’ position from noisy measurements.

1. INTRODUCTION

1.1. Automotive context

Accurate and reliable vehicle localization is a key component of numerous automotive and Intelligent Transportation System (ITS) applications, including active vehicle safety systems, real time estimation of traffic conditions, and high occupancy tolling. Various safety critical vehicle applications in particular, such as collision avoidance, lane change management or emergency braking assistance systems, rely principally on the accurate knowledge of vehicles’ position within given vicinity.

Distributed algorithms [2], [3] have been of recent interest for collaborative localization. In this paper, we will review signal processing issues pertaining to the design of collaborative methods of localizing vehicles on roads, both using fixed infrastructure and in infrastructure-free environments.

1.2. Previous works on localization and positioning

Previous and current works on the information fusion problem for multiple vehicle cooperative navigation systems can be regrouped in three main broad categories: 1) military and aerospace, 2) mobile robotics and 3) wireless communication and sensor networks. In each case, we find commonalities, but also major differences with the automotive context. In the military case, localization of several targets are considered, often in a 3D unconstrained environments [7]. Costs are usually not an issue. Sensors reliability, robustness and quality as well as computing power are emphasized to achieve high performance at very

high speed. In mobile robotics, we typically consider sets of few closely located robotic plate-forms collaborating to achieve a given task in a constrained and often indoor environment. Those robots are moving at a relatively low speed. GPS (Global Positioning System) signals are usually not available and localization techniques rely on SLAM and dead-reckoning techniques [2]. In wireless sensor networks, communication based localization techniques are favored using either time-of-arrival, signal strength and triangulation or a combination thereof [3]. Sensors are usually fixed but at unknown locations. Energy consumption, bandwidth used and computing complexity are critical issues.

Localization in automotive applications deals with lots of high speed mobile plate-forms constrained to outdoor roads on a 2D surface. Sensors in automotive industry require the robustness and reliability of military applications, but at the very low-cost of consumer electronics. GPS signal is partly available, but high-end GPS receivers are not affordable for automotive applications. Design of navigation systems for automotive applications also suffer from the same constraints of energy consumption, bandwidth used and computing complexity as for the sensor networks, but to a lesser extend. Automotive applications can rely on heterogeneous sets of low-cost sensors embedded in clustered vehicles.

2. PROBLEM STATEMENT AND ISSUES

2.1. Single-vehicle localization architectures

Recursive filters are typically used for processing data coming from embedded sensors on a given vehicle. The Kalman filter is the most well-known, but relies on Gaussianity assumptions. Indeed, most of the existing works in the literature on localization assume that measurements are Gaussian. In real settings however, the distributions of interest are mixture distributions which are highly non-Gaussian in nature. Generalizations of Kalman Filtering, such as the Extended Kalman Filter (EKF) [4] had been proposed for non-Gaussian models. However, EKF solutions do not work well when the distributions are bimodal as in the case of mixture distributions, since Gaussians do not approximate bimodal distributions very well. Other types of recursive filters such as the Unscented Kalman filter (UKF) or particle filters have been proposed since to cope with this problem [5]. When the road geometry information is available from a digital map database, constrained data fusion schemes can also be used to improve the fusion accuracy.

Level of confidence for vehicle localization can be geometrically represented by ellipses, whose centre is the best estimation of the vehicle position and whose radius and orientation depend on the estimated covariance matrix of the estimate. The confidence ellipses are ideally an upper bound of the real current error (the difference between the real position and the estimated position). In practice, the real position is unknown and the positioning system is only able to calculate confidence ellipses.

2.2. Multi-vehicle cooperative architectures

In an automotive context, collaborative localization approaches investigates how positioning estimates of a cluster of moving vehicles can efficiently be computed in a distributed manner, robust to sensor/communication failures and uncertainty in the sensory or other sources of information. Based on new vehicular wireless communication capabilities, cooperative vehicle positioning approaches are emerging based on the concept of extended or “federated” filtering. Most mapping and localization problems have been solved for single vehicles so far. Those solutions do not account for extra positional information available from surrounding vehicles. Collaborating vehicles have the potential to perform positioning and localization more accurately and reliably than a single vehicle because on one hand, they can share complementary information (which aimed at improving accuracy), and on the other hand, they can share redundant information (which aimed at improving robustness and reliability). It also has been shown that collaborating vehicles have the potential to enhance the range of perception (extended environment map) to mitigate occlusion problems and to better assess collision risk between cooperating vehicles [6] (cf. Figure 1).

Figure 1. Motivation and context of multi-vehicle cooperative

localization.

In route planning applications, collaborative architectures have also the potential to improve quality of navigation information and map matching.

3. SINGLE-VEHICLE FUSION AND LOCALIZATION ESTIMATION ALGORITHMS

Considerable research has been undertaken in the field of estimation theory applied to the automotive navigation

problem. However, most algorithms are designed for single platform. The most widely used positioning sensors in automotive applications are low-cost GPS receivers. However, standard low-cost GPS receivers can have errors over fifty or more meters, which is unacceptable for many of these applications. Therefore, other types of sensors are embedded in order to compensate GPS errors by using data fusion techniques. The basic principle behind data fusion is that more information about a phenomenon can be extracted and gathered from processing simultaneously measurements from a given set of sensors. A typical set of sensors within a vehicle may include GPS receiver, inertial, odometers, etc. Those are being used extensively to achieve a higher reliability in positioning and localization. As position determination of moving vehicles is subject to various types of uncertainty, the position determination problem is usually handled as a statistical filtering problem. One of the main problems is multipath interference [1], which is particularly prevalent in cities and “urban canyon” environments. In a multipath-rich environment, the received signals are no longer Gaussian in nature challenging the use of standard estimation techniques like the well-known Kalman filtering framework and its extensions. The principal idea behind GPS is to obtain three or more distance measurements from sources with known locations (e.g. satellites) and estimate the location based on trilateration. However, even if only one of the measurements is corrupted by multipath, the location errors can be significantly large. It has been well noted that redundancy in measurements is the key to tackle multipath. A state-space mathematical description is typically used. A local state vector representing one vehicle is defined with its associated covariance matrix. Iterative/recursive filter is then used for up-dating the position estimate (prediction/correction of the state vector) and its uncertainty covariance matrix. State recursive estimation is suitable for real-time applications. It has its roots in least squares estimation. It uses current localization estimates to give more accurate current and future estimates. To achieve this, all sensor outputs must be time-stamped, registered and provide uncertainty information (sensor covariance matrix, GPS Dilution Of Precision, Integrity).

4. COOPERATIVE FUSION AND LOCALIZATION ESTIMATION ALGORITHMS

FOR MULTIPLE VEHICLES

Cluster of vehicles, seen as multiple sources of information, can be considered in a higher level of fusion, where limited or unreliable local information gathered by a single vehicle necessitates collaboration. Position estimation of vehicles in ad-hoc vehicle networks are usually based on decentralized or federated recursive filtering. Distributed filters operate in a cooperative federated structure (also called decision fusion) for enhancing the accuracy of vehicle state estimation over unreliable sensors and wireless communication networks, subject to uncertain and limited measurements.

V to V Range

Wireless Access Point

Wireless Access Point

Single-vehicle based initialposition

estimate uncertainty

Collaborative positionEstimate uncertainty

Collision risk

Lane ambiguity

V to V Range

Wireless Access Point

Wireless Access Point

Single-vehicle based initialposition

estimate uncertainty

Collaborative positionEstimate uncertainty

Collision risk

Lane ambiguity

Figure 2. Propagation of uncertainties in position estimation. Each vehicle is using its own ego localization and data from 4

collaborative neighbor vehicles.

Filters rely on a variety of position measurements

obtained from on-board vehicle positioning system, from other cooperating vehicles in the vicinity, as well as from the immediate roadside environment via some given wireless communication protocol. Direct distance measurements between vehicles, between vehicles and stationary elements of the infrastructure can be used, if available, as additional/reference measurements. In collaborative architectures, we can hope resolving inconsistencies between measurements, such as due to malfunctioning sensors (ex. loss of GPS signal). High variability in signal characteristics and environmental conditions, such as those found in automotive applications, necessitates data fusion architectures that goes beyond single-vehicular plate-form. Collaborative localization can help reduce the variance in location accuracy among vehicles (nodes) within a cluster [4]. Intuitively, vehicles (nodes) in the same cluster may

help localize each other so as to enhance the overall average positioning accuracy / topology of the cluster and its vehicle members (cf. Figure 2). A typical collaborative positioning architecture should tackle the following tasks:

• Detect nearby vehicles in a given range; • Determine cluster topology and vehicle

membership; • Estimate absolute position estimates (local data

fusion) of each vehicle member; • Estimate inter-vehicular distances, heading

(relative positions) of member vehicles; • Compute confidence interval on estimates:

measures the accuracy/uncertainty of the local absolute/relative position estimates;

• Select relevant local estimates and uncertainty data for broadcasting to vehicle members (data positioning integrity);

• Add broadcasted data to local data fusion systems in order to perform global fusion and improve localization of individual vehicle members.

The attractiveness of cooperative positioning lies in

its independence from any major additional infrastructure other than the vehicular communication systems. Global fusion uses neighbor vehicles’ information to reduce its own vehicle's absolute and relative position errors. Putting together all available information from onboard and off-board systems in a collaborative system is quite a difficult task if the final goal is to maintain constant accuracy and reliability due to the high dynamic of the cluster. Required performances cannot be guaranteed for all cases. Collaborative positioning systems have to be able to autonomously qualify its outputs. Positioning integrity can be interpreted as the aptitude to detect and then eliminate aberrant measurements in order to estimate a position whose confidence (inaccuracy) are quantified. Confidence can be defined as the probability associated with the positioning assumption considered. Decentralized data fusion architectures for automotive applications have several advantages such as:

• To remove bottleneck and risk factors associated with centralized systems;

• To distribute processing and communication burdens across several vehicles;

• Data fusion which occurs at each vehicle is based on its own information source and from the information generated from surrounding vehicles;

• No vehicle forms a global data fusion of the total information at once;

• Global solution can be achieved if the decentralized fusion is in a broadcast mode and all vehicles can communicate their data with all others;

• Scalability of the whole system due to the removal of limitations on processing power and bandwidth;

• Robustness of the system when one node (vehicle) fails;

• Modularity, since each vehicle does not require total knowledge of the network topology.

For collaborative position estimation in practice,

each car measures the relative distance to a car moving nearby, communicates the measurements with other cars, and uses the received measurements for estimating its own position. In order to estimate the position even if the measurements are received with time-delay, we need to use time-delay tolerant data fusion algorithms or use time stamped data. For sharing relevant data, car-to-car wireless communication systems are used. Measurements sent from farther cars are received with larger time-delay. It follows that accuracy of the estimates of farther cars become less reliable. Furthermore, relevance of nearby vehicles decreases with distance, in particular for active safety applications. Hence, only states estimates of nearby cars are usually taken in priority to reduce uncertainty and reduce computing/communication efforts.

5. IMPLEMENTATION ISSUES

Road transportation is a very challenging information processing environment. It is highly dynamic and subject to outdoor harsh conditions. Vehicle topology and road environment are changing basically in the second and sub-second ranges. Uncertainty in temporal and spatial measurements critically affects positioning and localization estimation. Uncertainty in time stamping and synchronization affects directly the level of uncertainty in vehicles (nodes) location. Various sources of variability in signal characteristics affect the localization problem, such as Doppler shifts due to motion, gear shifting, acceleration in vehicles, variability in environmental and sensor conditions. Most algorithms exploit prior statistical information about sources of information. However, observed statistical characteristics can vary markedly depending on environmental conditions, such as road topology and conditions, vehicles distributions (traffic conditions), type of environment (urban/rural), climate etc. Heterogeneous sets of positioning sensors present in each vehicle, as well as variability in sensor characteristics and quality (e.g., gain calibration) are also contributing to the complexity of the problem. A key challenge is to develop collaborative algorithms that are robust to such uncertainty/variability in measurements and traffic conditions.

Basically, we deal with a problem of real time sensor fusion with spatially and temporally misaligned dissimilar sensors. Spatial–temporal registration model for intra and inter-vehicular sensors including radar, lidar, GPS, Inertial Navigation System (INS), and camera is required for sensor alignment. Sensor management is required to ensure sensor data is formatted and processed in a timely and accurate manner in order to improve estimation and prediction of given vehicles’ position. Some sensor self-diagnosis is also required at the single vehicle level because the accuracy of the vehicle-state estimation is too low otherwise to meet the requirements of collaborative positioning of multiple vehicles.

6. CONCLUSION

Some form of collaborative techniques is in general valuable and desirable to yield robust and reliable localization

performance, in particular in automotive applications, where harsh and variable environmental conditions prevail. One of the advantages of cooperative localization systems is that they do not require extensive or additional road infrastructures. Collective cluster position accuracy increases with vehicle density. Various collaborative architectures are possible (centralized or distributed). Trade off between computational and communication burdens is an important issue in collaborative approaches. Sensors properties and vehicle inter-distances influence the levels of uncertainty. Due to economic constraints of the automotive industry, low-cost embedded in-vehicle sensors have limited capabilities and qualities, which emphasize the need for collaboration. Keys are to combine minimum amount of information that yields desired performance (energy conservation), to minimize computational burden at each vehicle while minimizing communication burden across vehicles. Care must be taken also to avoid inconsistencies between sensors or vehicles outputs, which may compromise or annihilate performance gains obtained from collaboration.

7. ACKNOWLEDGEMENT

This work is part of COOPERCOM, a 3-year international research project (Canada-France). The authors would like to thank the National Science and Engineering Research Council (NSERC) of Canada and the Agence nationale de la recherche (ANR) in France for supporting the project.

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