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Implicit Cooperative Positioning in Vehicular Networks

Gloria Soatti, Monica Nicoli, Nil Garcia, Benoit Denis, Ronald Raulefs, Henk Wymeersch

arXiv:1709.01282v1cs.NIstat.AP

TL;DR

Urban GNSS degradation and limits of explicit V2V ranging motivate a cooperative alternative. ICP uses V2V consensus to combine vehicles’ observations of passive features, and in a real urban scenario it improves location accuracy over stand-alone GNSS.

  • Problem

    Urban canyons can degrade or block GNSS, while cooperative positioning approaches often rely on explicit V2V ranging that is low-quality or incompatible with IEEE 802.11p.

    Source: §I · pp. 1–2

  • Method

    ICP has vehicles use onboard sensing to jointly localize passive features as shared noisy references, fusing feature information over V2V links with consensus-based message passing.

    Source: §I · p. 2, §IV · p. 5

  • Results

    In the real urban scenario, at 50% confidence, ICP location accuracy was 0.46 m with Rs = 50 m and 0.23 m with Rs = 100 m, versus 2.65 m for stand-alone GNSS.

    Source: B. Real urban scenario with… · p. 13

  • Takeaways & Limitations

    The reported urban results show ICP can improve GNSS-based vehicle positioning without relying on explicit V2V measurements.

    Source: §I · p. 2, §VIII · p. 13

    The framework assumes a linear measurement model and perfect data association; removing these assumptions is left for future research.

    Source: §VIII · p. 13

Abstract

from arXiv · show

Absolute positioning of vehicles is based on Global Navigation Satellite Systems (GNSS) combined with on-board sensors and high-resolution maps. In Cooperative Intelligent Transportation Systems (C-ITS), the positioning performance can be augmented by means of vehicular networks that enable vehicles to share location-related information. This paper presents an Implicit Cooperative Positioning (ICP) algorithm that exploits the Vehicle-to-Vehicle (V2V) connectivity in an innovative manner, avoiding the use of explicit V2V measurements such as ranging. In the ICP approach, vehicles jointly localize non-cooperative physical features (such as people, traffic lights or inactive cars) in the surrounding areas, and use them as common noisy reference points to refine their location estimates. Information on sensed features are fused through V2V links by a consensus procedure, nested within a message passing algorithm, to enhance the vehicle localization accuracy. As positioning does not rely on explicit ranging information between vehicles, the proposed ICP method is amenable to implementation with off-the-shelf vehicular communication hardware. The localization algorithm is validated in different traffic scenarios, including a crossroad area with heterogeneous conditions in terms of feature density and V2V connectivity, as well as a real urban area by using Simulation of Urban MObility (SUMO) for traffic data generation. Performance results show that the proposed ICP method can significantly improve the vehicle location accuracy compared to the stand-alone GNSS, especially in harsh environments, such as in urban canyons, where the GNSS signal is highly degraded or denied.

I. INTRODUCTION

GNSS degradation and limitations of explicit V2V ranging motivate ICP, which uses jointly sensed passive features as shared references to improve vehicle positioning. The system model combines vehicle GNSS fixes with vehicle-to-feature observations and V2V communication links.

I. INTRODUCTION

  • Existing cooperative positioning often requires explicit V2V ranges, specialized hardware, or infrastructure, while radio-based measurements may be low-quality or incompatible with IEEE 802.11p.GNSS availability is also limited in urban canyons, where signals can be degraded or blocked.Source: §I · pp. 1–2
  • ICP shares onboard sensing information over V2V links so vehicles jointly localize non-cooperative features as noisy references, without relying on explicit V2V measurements.The proposed distributed Gaussian message-passing framework uses consensus for feature estimation and includes a Kalman filter for vehicle dynamics based on GNSS.Source: §I · p. 2
  • The paper validates ICP in a simulated crossroad with varying connectivity and in a Bologna urban scenario using SUMO-generated traffic.The introduction reports the strongest gains in areas with many features and cooperative vehicles, where multipath and non-line-of-sight degrade GNSS.Source: §I · p. 2

II. PROBLEM FORMULATION AND SYSTEM MODEL

  • Passive features such as people, traffic lights, and trees are sensed within a limited range and serve as common noisy references, with perfect measurement-to-feature association assumed.The features do not communicate or perform computations; vehicles communicate over a time-varying connected graph.Source: §II · p. 3
  • The model uses GNSS location fixes and vehicle-to-feature relative-location observations, focusing on RADAR measurements with both range and angle information.The framework can also include other classes of feature measurements.Source: §II · p. 3

III. CENTRALIZED ICP METHOD

The centralized ICP method estimates the joint vehicle-and-feature state from accumulated GNSS and vehicle-to-feature observations. Under the stated linear Gaussian models, this centralized estimate reduces to Kalman filtering.

III. CENTRALIZED ICP METHOD

  • The centralized MMSE estimate uses measurements through time t to infer the joint state of vehicles and features.Its posterior is formed from the measurement likelihood and state-transition model.Source: §III · p. 4
  • With Gaussian linear models, the centralized ICP estimate reduces to a Kalman filter for the vehicle and feature states.The formulation also specifies the prediction covariance and measurement-error covariance.Source: §III · p. 4
  • Fig. 2 illustrates how consensus on a jointly sensed feature through V2V links yields more accurate vehicle-location ellipses than stand-alone GNSS and V2F sensing.The caption represents the accuracies as 1-σ error ellipses.Source: Figure 2 · p. 4

IV. DISTRIBUTED ICP METHOD

The distributed ICP method replaces a centralized solution with Gaussian message passing (GMP) and consensus, because centralized computation scales cubically with vehicles and features. Vehicles cooperate through shared feature estimates rather than direct inter-vehicle measurements.

IV. DISTRIBUTED ICP METHOD

  • The centralized ICP solution is impractical at scale because it has a single point of failure and cubic computational complexity, motivating distributed GMP with consensus.The factor-graph view connects vehicle subgraphs through vehicle-to-feature measurements.Source: §IV · p. 4, Figure 3 · p. 5
  • Consensus-based GMP lets vehicles evaluate beliefs for passive features that cannot compute or communicate, using only neighboring-vehicle communication.Each vehicle must calculate both its own belief and feature beliefs.Source: §IV · pp. 4–5
  • In the illustrated case, three vehicles jointly estimate one feature and reach consensus on its location, with improved vehicle position accuracies reflected in their ellipses.The figure contrasts local beliefs based on GNSS and vehicle-to-feature measurements with the consensus feature estimate.Source: §IV · p. 5

A. Gaussian Message Passing Algorithm

The GMP algorithm factors the joint posterior over vehicle and feature states, then uses iterative message passing to approximate their marginal posteriors. Under Gaussian priors, linear models, and independent Gaussian noise, the messages remain Gaussian.

A. Gaussian Message Passing Algorithm

  • Conditional independence of measurements and static features allow the posterior to be factorized over vehicle and feature states, encoded as a factor graph for sum-product message passing.The factor graph represents each vehicle and feature state as a circle and each factor as a square.Source: A. Gaussian Message Passing Algorithm · p. 5
  • With Gaussian priors, linear state transitions and measurements, and independent Gaussian noise, all factor-graph messages are Gaussian and sum-product reduces to GMP.Particle-based approaches can be used when linearity and Gaussianity conditions do not hold, but generally incur significant computation and communication costs.Source: A. Gaussian Message Passing Algorithm · p. 5
  • Because the factor graph has cycles, GMP iterates to produce approximate marginal posteriors represented by vehicle and feature beliefs.The beliefs are updated over GMP iterations.Source: A. Gaussian Message Passing Algorithm · p. 5
  • GNSS contributes position-only information, while vehicle-feature measurements provide the likelihood messages used in message passing.The GNSS message has infinite variance in the velocity domain; the feature nodes are passive, so consensus is used to evaluate their beliefs.Source: A. Gaussian Message Passing Algorithm · pp. 5–6

B. Consensus-based Evaluation of the Feature Beliefs and Outgoing Messages

Since features are passive and cannot combine messages themselves, vehicles use average consensus within GMP to calculate feature beliefs and outgoing messages. The procedure exchanges information over V2V links and uses the consensus results to update beliefs at each GMP iteration.

B. Consensus-based Evaluation of the Feature Beliefs and Outgoing Messages

  • The consensus procedure is nested within GMP because passive features cannot merge incoming messages or communicate, and vehicles must cooperate over V2V links to evaluate their beliefs.This cooperation can enable each vehicle to evaluate feature beliefs even when it has no measurement of a feature.Source: B. Consensus-based Evaluation of the… · p. 7
  • Average consensus lets vehicles cooperatively determine the first two moments of the product of feature measurement messages.Vehicles refine local estimates through information exchange with neighboring vehicles.Source: B. Consensus-based Evaluation of the… · p. 7
  • The consensus results provide the moments used to evaluate each feature's approximate marginal posterior and outgoing message at a GMP iteration.Once agreement is reached, each vehicle can evaluate the feature belief and message.Source: B. Consensus-based Evaluation of the… · p. 7

A. Fundamental limits

The fundamental-limit analysis derives a lower bound on cooperative localization accuracy under full sensing and communication view. It forms the joint vehicle-feature Fisher information matrix and uses its inverse to obtain a vehicle-position error bound.

A. Fundamental limits

  • The cooperative localization lower bound is reached only when all vehicles and features are in full sensing and communication view, meaning all-to-all connectivity.The analysis derives the joint-state Fisher information matrix and extracts the single-vehicle location submatrix of its inverse.Source: A. Fundamental limits · p. 8
  • For a simplified analysis, the vehicle and feature prior covariances are assumed specified and GNSS and vehicle-feature measurements are assumed identically distributed and independent within each subset.Under these assumptions, the Fisher information submatrices simplify.Source: A. Fundamental limits · p. 8
  • The inverse equivalent Fisher information matrix represents a lower bound on the mean square error matrix of vehicle position estimates.The bound is obtained by taking the Schur complement for vehicle states.Source: A. Fundamental limits · p. 8

B. Performance Scaling

The performance-scaling analysis describes limiting cases in which features act as anchors and vehicle-position uncertainty can vanish. With few features, good measurements and prior feature information are needed for good positioning.

B. Performance Scaling

  • When each feature is observed by infinitely many vehicles, its location becomes perfectly known and the features act as anchors.This is the stated accuracy reached when all features act as anchors.Source: B. Performance Scaling · p. 8
  • With many features, vehicle locations become certain even when features remain somewhat uncertain, because the features act as virtual anchors.The passage describes this as the case in which all vehicles’ locations become certain, provided there are many features.Source: B. Performance Scaling · p. 8
  • With fewer features, good measurements and prior feature information are required for good positioning; perfectly known feature locations define a limiting case.The paper notes that the performance reaches a limit when feature locations are perfectly known.Source: B. Performance Scaling · p. 8
  • When vehicle prior uncertainty is small, cooperation is not worthwhile because stand-alone positioning is already sufficiently accurate.The passage frames this as the limiting case of small vehicle prior uncertainty.Source: B. Performance Scaling · pp. 8–9

VI. IMPLEMENTATION ASPECTS

Implementation requires cooperative feature association and substantial V2V communication. The analysis assumes unique semantic feature labels, estimates communication demands, and describes adaptive stopping criteria.

A. Cooperative Data Association

  • The method assumes local sensors provide unique semantic labels for detected features, bypassing explicit treatment of data association and making its error a lower bound for a practical algorithm.The paper leaves the challenges of cooperative data association outside its scope.Source: A. Cooperative Data Association · p. 9

B. Communication Overhead

  • Consensus broadcasts dominate communication, with the number per vehicle scaling as O(NmpNcon).Each broadcast carries transmitter and feature beliefs and identifiers; the passage describes communication as significant.Source: B. Communication Overhead · p. 9
  • At 6 Mbit/s with 10 neighbors, 20 features, 100 belief bits, and Ts = 1 s, the example gives NmpNcon ≤ 300.The passage presents this as a reasonable number for the illustrated IEEE 802.11p case.Source: B. Communication Overhead · p. 9

Remark:

  • The numbers of message-passing and consensus iterations can be adapted by stopping each process when its stated convergence threshold is met.The passage gives separate convergence tests for message passing and consensus.Source: Remark · p. 9

C. Computational Complexity

The section evaluates computational cost, measurement timing, and crossroad performance. In the simulated canyon, ICP counters GNSS degradation, while accuracy and iteration behavior depend on vehicle and feature connectivity.

C. Computational Complexity

  • Ignoring data-association complexity, per-vehicle computation scales as O(NvNmp(NconNf + 8Nf)), versus O((Nv + Nf)^3) for centralized processing.The distributed consensus steps use vector additions, and each vehicle inverts Nf + 1 covariance matrices of dimension 2×2.Source: C. Computational Complexity · p. 9

D. Measurement Synchronization

  • Quasi-isochronous measurements are assumed because sensor refresh and awareness-message periods are below the typical Ts of about 1 s.The paper suggests detecting outdated measurements and leaves other synchronization schemes outside its scope.Source: D. Measurement Synchronization · p. 9

A. Simulated crossroad scenario with mixed rural/urban areas

  • In the canyon, ICP counters GNSS degradation; centralized and distributed ICP perform nearly identically, and high connectivity yields centimeter accuracy with 5 features and 12 vehicles.The figure compares ICP accuracy over time with stand-alone GNSS and an all-to-all connectivity lower bound.Source: Figure 4 · p. 10, A. Simulated crossroad scenario with… · p. 11
  • For a fixed feature count, more vehicles improve positioning accuracy; the simulated crossroad places vehicles through rural, canyon, and rural road sections.The experiment includes static features in the crossroad scenario.Source: A. Simulated crossroad scenario with… · pp. 10–11
  • Consensus iterations increase as vehicle connectivity changes, while message-passing iterations stay below 10 in the considered scenarios.Consensus iterations rise as the graph merges and splits; their count increases with vehicles and decreases with features.Source: Figure 6 · p. 11, A. Simulated crossroad scenario with… · p. 12

B. Real urban scenario with SUMO-simulated traffic

In the SUMO-simulated Bologna scenario, distributed ICP improves location accuracy over stand-alone GNSS, with lower reported error at the larger sensing range. The conclusion describes a fully distributed method for estimating common passive features, while identifying linear measurement and perfect data association as assumptions.

B. Real urban scenario with SUMO-simulated traffic

  • The Bologna evaluation uses SUMO-generated vehicle and pedestrian trajectories across a 1.2 km × 0.5 km urban area.The simulation includes 10 vehicle and 20 pedestrian trajectories; streets are associated with different GNSS signal qualities.Source: B. Real urban scenario with… · p. 12, Figure 7 · p. 12, Figure 8 · p. 12
  • At 50% confidence, location accuracy is 0.46 m for ICP at Rs = 50 m and 0.23 m at Rs = 100 m, versus 2.65 m for stand-alone GNSS.The comparison is reported for the Bologna scenario; Fig. 9 plots the location-error CDFs.Source: Figure 9 · p. 13, B. Real urban scenario with… · p. 13
  • All vehicles improve their position accuracy with ICP, but the amount varies with receiver type, local GNSS quality, and vehicle and feature positions.Fig. 10 shows the intersection between Viale Sabotino and Viale G. Vicini, with error ellipses evaluated over 100 independent observations.Source: B. Real urban scenario with… · p. 13, Figure 10 · p. 13

VIII. CONCLUSION

  • The proposed framework estimates common passive features in a fully distributed way to improve GNSS-based vehicle positioning.The conclusion describes distributed Gaussian message passing with consensus-based feature-position estimation.Source: §VIII · p. 13
  • The framework assumes linear measurement models and perfect data association; handling these issues is left for future research.The paper notes that nonlinear models and data association could be incorporated into the framework.Source: §VIII · p. 13

APPENDIX

The appendix enumerates limiting cases for the analytical bounds as vehicle or feature counts grow and measurement uncertainties approach zero.

APPENDIX

  • The listed limiting cases consider vehicle and feature counts tending to infinity, and V2F, feature-position-prior, or GNSS uncertainty tending to zero.The supplied appendix passages identify these conditions but do not state the resulting bound expressions.Source: APPENDIX · p. 14
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