PaperlayerView exact revision on arXiv

Source-linked AI summary

5G mmWave Cooperative Positioning and Mapping using Multi-Model PHD Filter and Map Fusion

Hyowon Kim, Karl Granström, Lin Gao, Giorgio Battistelli, Sunwoo Kim, Henk Wymeersch

arXiv:1908.09806v3eess.SP

TL;DR

The paper addresses 5G mmWave vehicle positioning and mapping under multipath, heterogeneous objects, imperfect detections, and limited fields of view. It proposes a multiple-model PHD filter with asynchronous map fusion for cooperative positioning and mapping, and reports that the approach handles mapping and vehicle-state-estimation challenges while map fusion significantly improves mapping performance.

  • Problem

    5G mmWave positioning must exploit multipath while handling imperfect detections, heterogeneous object measurements, and the mapping of object number, type, and state.

  • Method

    The method combines Rao-Blackwellized particle-filter PHD-SLAM with a multiple-model PHD filter and asynchronous map fusion.

  • Results

    The proposed PHD filter handles mapping and vehicle state-estimation challenges, while map fusion using other vehicles’ information significantly improves mapping performance.

  • Takeaways & Limitations

    Cooperative positioning and mapping can use multipath and shared map information to support vehicular positioning and environmental mapping.

Abstract

from arXiv · show

5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station and vehicles are equipped with large antenna arrays. However, radio-based positioning suffers from multipath signals generated by different types of objects in the physical environment. Multipath can be turned into a benefit, by building up a radio map (comprising the number of objects, object type, and object state) and using this map to exploit all available signal paths for positioning. We propose a new method for cooperative vehicle positioning and mapping of the radio environment, comprising a multiple-model probability hypothesis density filter and a map fusion routine, which is able to consider different types of objects and different fields of views. Simulation results demonstrate the performance of the proposed method.

I. INTRODUCTION

The paper addresses cooperative 5G mmWave positioning and mapping despite missed detections, false detections, unassociated multipath measurements, multiple measurement types, and limited vehicle fields of view. It proposes a multiple-model PHD-SLAM filter with asynchronous map fusion and demonstrates cooperative mapping in a two-vehicle simulation.

  • I. INTRODUCTION: 5G mmWave cooperative positioning and mapping must estimate vehicle states, map object number, type and position, and fuse map information among vehicles.Vehicle states include position, velocity, heading, and clock bias.
  • I. INTRODUCTION: The approach targets missed objects, clutter and channel-error false detections, short-lived objects, unassociated measurements, heterogeneous measurement types, and limited fields of view.Different measurement types motivate a separate model for each type, while limited observations prevent direct standard map fusion.
  • I. INTRODUCTION: The proposed method combines Rao-Blackwellized vehicle-map density representation, particle filtering for vehicle location, a multiple-model PHD filter for maps, and asynchronous arithmetic-average map fusion.The fusion weights account for different fields of view by decomposing map space into mutually disjoint subsets.
  • I. INTRODUCTION: The multiple-model PHD uses different measurement models rather than the mobility models commonly used in prior multiple-model tracking filters.The paper also derives a closed-form random-finite-set likelihood for updating the vehicle state.
  • I. INTRODUCTION: A Gaussian-mixture implementation is evaluated in a two-vehicle 5G mmWave scenario where all propagation paths are exploited and cooperative mapping speeds up the mapping process.The BS fuses maps asynchronously, processing one vehicle at a time so vehicles contribute to and access a global map.

II. RELATED WORKS

Prior work spans geometry-based, message-passing, and random-finite-set approaches to 5G SLAM, but leaves challenges in data association, unknown object cardinality, and fusion across limited fields of view.

  • Earlier methods may ignore small objects, while this paper handles both an unknown number of objects and unknown data association.
  • Message-passing SLAM filters generally omit data-association uncertainty, whereas this paper includes it.
  • RFS methods model uncertain object cardinality and states, but existing alternatives may require explicit data association or address mapping rather than the full SLAM problem.The paper positions its approach against MB and Poisson MB representations and prior mapping-only work.
  • Existing multiple-model methods motivate augmenting object states with object type, while this application does not require jump-Markov transitions between types.
  • Map fusion is difficult because vehicles maintain densities over different and limited fields of view, making direct GCI application unsuitable.A uniform nonzero initialization can fuse differing fields of view but becomes memory- and computation-intensive at large scale.
  • The paper adopts arithmetic averaging to take the union of involved densities, while noting that the fusion weight remains challenging to select.

III. MODEL

The model describes cooperative vehicles communicating with a known base station and receiving multipath measurements generated by scattering points and reflecting surfaces. It represents source types and locations explicitly while accounting for missed detections, clutter, and transient sources.

  • Vehicles traverse a common environment, communicate with a known fixed base station, and have states containing position and clock bias.Vehicle dynamics use a known transition function with zero-mean Gaussian process noise of known covariance.
  • The environment contains scattering points with unknown 3D locations and reflecting surfaces represented by virtual anchors mirrored from the base station.
  • The received mmWave signal comprises a line-of-sight path and non-line-of-sight paths whose angles and arrival times have geometric meanings.The model uses transmit and receive array steering vectors, with AOA and TOA measured at the receiver and AOD at the transmitter.
  • Each source is represented by an unknown location and type, distinguishing the base station, virtual anchors, and scattering points.
  • The observation model incorporates missed detections within the field of view, Poisson clutter, and transient sources that appear and disappear from the map.
  • The vehicle is assumed to know the source-to-measurement function and clutter intensity used by the observation model.

D. Problem Formulation

The problem is to jointly track vehicle states and construct a common map of virtual anchors and scattering points. The proposed representation propagates conditional map PHDs over particle-based vehicle trajectories while distinguishing source types.

  • D. Problem Formulation: The objective is to track vehicle states and build a common environment map containing virtual anchors and scattering points.
  • A. Approach: The map is modeled as a multi-object Poisson process characterized by its probability hypothesis density rather than its full density.
  • A. Approach: The conditional map PHD includes a discrete source-type state so the filter can distinguish base stations, scattering points, and virtual anchors.
  • A. Approach: The Rao-Blackwellized representation uses particles for vehicle-state trajectories and maintains a conditional PHD for each particle.
  • A. Approach: The initial map assigns zero PHD to virtual anchors and scattering points while initializing the base-station component at its known location.
  • A. Approach: The recursive PHD filter is followed by a practical Gaussian-mixture implementation.
  • B. Basics on PHDs: An RFS density depends on cardinality and joint state distributions, but a PHD generally does not uniquely determine the full RFS density.
  • B. Basics on PHDs: For a Poisson point-process RFS, the intensity equals the PHD, whose integral over a region gives the expected number of objects there.

C. General Formulation

The formulation jointly represents vehicle-state uncertainty and type-specific environmental sources with multiple PHDs, using prediction and measurement updates. A Gaussian-mixture implementation introduces measurement-driven births and has complexity scaling with particles, models, mixture components, and measurements.

  • C. General Formulation: The filter alternates prediction from the motion model with measurement-set updates for the map and vehicle state.
  • 1) Prediction:: Each source type has its own PHD, while the known base-station location has no birth process.
  • 2) Measurement Update:: The update accounts for missed detections, detected measurements, clutter, and field-of-view-dependent detection probabilities.
  • 2) Measurement Update:: The method evaluates the PHD weight-update integral exactly under a Poisson point-process prior and point-object measurement model.
  • D. Gaussian Mixture Implementation: The practical implementation uses Gaussian mixtures for map prediction, map update, and vehicle-state update.
  • D. Gaussian Mixture Implementation: The implementation costs O(I × Nmodel × J × |Z|) per vehicle and time step, with special cases for SLAM, mapping, and localization.
  • 1) Map Prediction (10):: Birth components are indexed by measurements, assigned low baseline weights, and may be omitted when their likelihood is negligible or outside the field of view.
  • 1) Map Prediction (10):: Measurement-dependent births generate candidate sources of every type using inverse CKF transformations and source-location statistics.

2) Map Update (11):

The map update uses closed-form approximations and adaptive detection probabilities to update source PHDs, while accounting for missed detections and clutter. Vehicle states are then estimated from the particle distribution.

  • 2) Map Update (11):: The update uses two approximations: one for detection probability and one for a closed-form Bayes update.
  • 2) Map Update (11):: Measurement-generated births are assigned unit detection probability and are not updated with their corresponding measurements.
  • 2) Map Update (11):: Existing targets use an adaptive detection probability obtained from the expected detection probability over each Gaussian component.
  • 2) Map Update (11):: PHD filtering is sensitive to missed detections and false alarms because the multi-object density is approximated as a Poisson random finite set.
  • 2) Map Update (11):: Retaining sources under missed detections requires low detection probabilities, increasing sensitivity to clutter.
  • 2) Map Update (11):: The estimated vehicle state is the particle sample mean, and its location is extracted from the estimated state.

V. GLOBAL PROCESSING: MAP FUSION

The fusion routine combines asynchronously communicated vehicle and base-station maps while respecting limited fields of view and differing information regions. It uses AA fusion with component matching and region-specific weights to preserve information outside shared views.

  • V. GLOBAL PROCESSING: MAP FUSION: Vehicles communicate asynchronously with the base station, sending an average PHD and accumulated field-of-view information.
  • V. GLOBAL PROCESSING: MAP FUSION: For common sources, equal weights are used; sources known only to one agent retain that agent’s contribution.
  • V. GLOBAL PROCESSING: MAP FUSION: AA fusion is selected because GCI is difficult to combine with sensors having limited fields of view.
  • V. GLOBAL PROCESSING: MAP FUSION: The fusion separates sources known by both agents, only the vehicle, or only the base station, because direct fusion is possible only for common information.
  • V. GLOBAL PROCESSING: MAP FUSION: AA fusion applies independently to the three source sets, using separate fusion weights that reflect each map’s information contribution.
  • V. GLOBAL PROCESSING: MAP FUSION: Mahalanobis distances and binary proximity matrices identify corresponding Gaussian components and determine approximate information decompositions.
  • V. GLOBAL PROCESSING: MAP FUSION: Unmatched sources outside the vehicle field of view are retained, whereas unmatched in-view sources are downweighted because they may be false alarms.

C. Downlink Transmission

The base station sends the fused map back to vehicles, which overwrite their local maps; this is computationally simple but reduces diversity across particle maps. The simulation uses a circular-road environment with one base station, four vehicles, and four source points.

  • C. Downlink Transmission: The base station sends its fused map to a vehicle, which overwrites the vehicle’s map with the received map.
  • C. Downlink Transmission: This downlink creates a common map containing information collected from other vehicles between communications.
  • C. Downlink Transmission: Using the fused map for every particle reduces map diversity but provides a low-complexity solution.
  • C. Downlink Transmission: The simulated environment is a circular road with one base station, four vehicles, and four source points.
  • C. Downlink Transmission: Two vehicles observe the same objects after exploring overlapping areas around time k ≈ 40.

VI. NUMERICAL RESULTS

The numerical evaluation uses a 3D vehicular scenario with a base station, vehicles, virtual anchors, and scattering points to assess the proposed positioning and mapping method. Simulations use fixed noise, visibility, detection, fusion, particle, and Monte Carlo settings.

  • Simulation scenario: The representative 3D scenario contains a base station, two moving vehicles, four virtual anchors, and four scattering points on a circular road.Virtual anchors are always visible, while scattering points are visible only within a 50 m field of view.
  • Scope: The authors note that actual localization and mapping performance depends on the chosen scenario.The scenario details are reported as available in reference [43].
  • Simulation settings: The simulation runs for K = 40 time steps with a 0.5 s interval, using specified process-noise and Gaussian vehicle-state priors.The priors use 0.3 m location standard deviations and 0.3 rad heading standard deviation.
  • Filter configuration: Measurements use detection probability pD = 0.9 within the field of view, clutter intensity based on λ = 1, and maximum sensing range Rmax = 200 m.The Gaussian implementation uses pruning threshold T = 10^-4, merging threshold U = 49, and Jmax = 50.
  • Fusion and evaluation: Asynchronous map fusion has each vehicle communicate with the base station every four time steps, with vehicles starting at times 10 and 12.Each vehicle state uses I = 2000 particles, and results average Nmc = 20 Monte Carlo runs.

B. Performance Metric

The evaluation measures vehicle-state estimation with MAE and RMSE and environment mapping with average GOSPA. Results compare prediction-only, LOS-only, local PHD, and fused PHD configurations across vehicle and map metrics.

  • Evaluation metrics: The evaluation computes MAE and RMSE for vehicle location, clock bias, and heading, and average GOSPA for environment mapping.The mapping metric is evaluated using source and estimated sets with specified GOSPA parameters.
  • Vehicle-state results: Prediction-only estimation loses accuracy over time, while the LOS-only case represents a best-case environment without objects and with a clear LOS path.The four cases also include the proposed local PHD filter and the proposed PHD filter with map fusion.
  • Vehicle-state results: The proposed PHD filter with map fusion performs much better than LOS-only processing, demonstrating the benefit of NLOS information even without known source association.The fused configuration is not reduced relative to local PHD filtering, although gains are marginal in this scenario.
  • Interpretation: Cooperative localization gains are limited here because vehicles localize well independently, virtual anchors are always visible, and scattering points have variable detection probability.The authors attribute the main potential cooperative gain to scattering points, which provide limited positional information in this scenario.
  • Virtual-anchor mapping: Downlink transmission provides little or no additional VA-map benefit because both vehicles always have all virtual anchors in their fields of view.Fig. 3 compares local map fusion with uplink transmission against the proposed configuration with downlink transmission.
  • Scattering-point mapping: Downlink map sharing reduces SP-map GOSPA faster because each vehicle benefits from the other vehicle’s measurements.The base-station SP map also improves faster because it uses information from all vehicles.
  • Conclusion: The paper concludes that multiple-model PHD filtering and map fusion address object number, type, position, and asynchronous map transmission in 5G mmWave vehicular networks.The reported results confirm handling of mapping and vehicle-state estimation challenges, while map information from other vehicles significantly improves mapping performance.

APPENDIX A GEOMETRIC RELATIONS

The geometric model relates channel measurements to vehicle states and object locations for line-of-sight paths, virtual anchors, and scattering points. Virtual anchors represent reflecting surfaces through mirrored base-station locations, while scattering-point relations form a special case of the geometry.

  • Measurement geometry: The observation model distinguishes three measurement cases according to the origin of the received signal.The vehicle state and map depend on the measurement origin.
  • Line-of-sight path: For a line-of-sight path, delay and angular measurements are related to the vehicle position, orientation, and clock bias.The direction of arrival is measured in the vehicle’s local frame, so vehicle orientation must be included.
  • Virtual anchors: A reflecting surface is represented by a virtual anchor obtained by mirroring the base station with respect to the surface.The specular incidence point is found where the line between the virtual anchor and vehicle intersects the reflecting surface.
  • Virtual anchors: The virtual-anchor geometry expresses channel delay and angles through the virtual-anchor location and vehicle state.The virtual anchor can also be expressed as a function of the incidence point.
  • Scattering points: For small scattering points, the relations are largely a special case of virtual-anchor geometry but include separate source-location expressions.The scattering-point equations specify delay, departure angles, and arrival angles using the scattering-point location.
  • Cubature propagation: The appendix then introduces cubature-point propagation for estimating source means and covariances from noisy measurements.The procedure factorizes measurement-noise covariance, forms cubature points, and evaluates propagated points through an inverse observation relation.

B. Simple Optimization Problem for Propagated Cubature Point

The propagated cubature point is estimated by minimizing a covariance-weighted observation residual because the nonlinear inverse observation relation generally lacks a closed-form solution. An iterative finite-difference optimization supplies the point used by the filter implementation.

  • Optimization formulation: The propagated cubature point is obtained by minimizing a covariance-weighted residual between the observation model and evaluated measurement cubature point.The optimization uses the source type, source location, vehicle state, and measurement-noise covariance.
  • Iterative solution: The optimization has no closed-form solution, so the optimum is determined iteratively.The update uses a design parameter η = 0.2 and initializes the iterate from geometric relations.
  • Iterative solution: A finite-difference Jacobian linearizes the observation relation, and iterations stop when the cost increases.The finite-difference step is set to 10^-3.
Loading 1908.09806v3…