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Rectify and Align GPS Points to Parking Spots via Rank-1 Constraint

Jiaxing Deng, Junbiao Pang, Zhicheng Wang, Haitao Yu

TL;DR

The paper addresses the challenge of correcting drifted GPS coordinates for urban parking spots by introducing an unsupervised Rectify And Align (RAA) framework that enforces a rank-1 constraint $rank=1$ to jointly rectify and align two point sets. It leverages parking-spot geometry to sample candidate points on road segments and solves a convex, ADMM-based optimization that models sparse errors, translation, and rotation while enforcing a rank-1 structure on a concatenated point matrix. Experiments on Beijing data show sub-meter accuracy and high recall (e.g., 98.4% overall), outperforming traditional map-matching baselines (ED, CD, HA, WD) and proving robustness to random noise. The approach relies only static data and yields a general, unsupervised solution with publicly available data and code, with potential extensions to broader digital transportation applications.

Abstract

Parking spots are essential components, providing vital mobile resources for residents in a city. Accurate Global Positioning System (GPS) points of parking spots are the core data for subsequent applications,e.g., parking management, parking policy, and urban development. However, high-rise buildings tend to cause GPS points to drift from the actual locations of parking spots; besides, the standard lower-cost GPS equipment itself has a certain location error. Therefore, it is a non-trivial task to correct a few wrong GPS points from a large number of parking spots in an unsupervised approach. In this paper, motivated by the physical constraints of parking spots (i.e., parking spots are parallel to the sides of roads), we propose an unsupervised low-rank method to effectively rectify errors in GPS points and further align them to the parking spots in a unified framework. The proposed unconventional rectification and alignment method is simple and yet effective for any type of GPS point errors. Extensive experiments demonstrate the superiority of the proposed method to solve a practical problem. The data set and the code are publicly accessible at:https://github.com/pangjunbiao/ITS-Parking-spots-Dataset.

Rectify and Align GPS Points to Parking Spots via Rank-1 Constraint

TL;DR

The paper addresses the challenge of correcting drifted GPS coordinates for urban parking spots by introducing an unsupervised Rectify And Align (RAA) framework that enforces a rank-1 constraint to jointly rectify and align two point sets. It leverages parking-spot geometry to sample candidate points on road segments and solves a convex, ADMM-based optimization that models sparse errors, translation, and rotation while enforcing a rank-1 structure on a concatenated point matrix. Experiments on Beijing data show sub-meter accuracy and high recall (e.g., 98.4% overall), outperforming traditional map-matching baselines (ED, CD, HA, WD) and proving robustness to random noise. The approach relies only static data and yields a general, unsupervised solution with publicly available data and code, with potential extensions to broader digital transportation applications.

Abstract

Parking spots are essential components, providing vital mobile resources for residents in a city. Accurate Global Positioning System (GPS) points of parking spots are the core data for subsequent applications,e.g., parking management, parking policy, and urban development. However, high-rise buildings tend to cause GPS points to drift from the actual locations of parking spots; besides, the standard lower-cost GPS equipment itself has a certain location error. Therefore, it is a non-trivial task to correct a few wrong GPS points from a large number of parking spots in an unsupervised approach. In this paper, motivated by the physical constraints of parking spots (i.e., parking spots are parallel to the sides of roads), we propose an unsupervised low-rank method to effectively rectify errors in GPS points and further align them to the parking spots in a unified framework. The proposed unconventional rectification and alignment method is simple and yet effective for any type of GPS point errors. Extensive experiments demonstrate the superiority of the proposed method to solve a practical problem. The data set and the code are publicly accessible at:https://github.com/pangjunbiao/ITS-Parking-spots-Dataset.
Paper Structure (18 sections, 25 equations, 6 figures, 5 tables, 2 algorithms)

This paper contains 18 sections, 25 equations, 6 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. related work
  3. Map-matching
  4. Low-Rank Assumption
  5. OUR APPROACH
  6. Background of Parking Spots
  7. Problem Definition
  8. Rank-1 Alignment
  9. Iterative Convex Optimization
  10. Experimental Results and Analysis
  11. Real Data
  12. Evaluation metrics
  13. Methods in Comparison Study
  14. Qualitative Comparisons with The SOTA Methods
  15. Robustness of Our method
  16. ...and 3 more sections

Figures (6)

  • Figure 1: Representative examples of corrupted GPS points and the corresponding parking spots (best viewed in color).
  • Figure 2: The layout of three types parking spots.
  • Figure 3: Rank-1 constraint enables GPS point alignment by preserving dominant spatial patterns while maintaining structural integrity.
  • Figure 4: The parking spots in our dataset is projected onto a map. The boundary of the map is the longitude and latitude (116.3523566,39.86131312) to (116.6396339,39.96606271). The square blocks represent the parking spots we manually collected.
  • Figure 5: The manually collected GPS points of parking spots (in green) were rectified and aligned to the parking spots (in red) on a road segment, and the black points are the rectified and aligned GPS points for parking spots (best viewed in color).
  • ...and 1 more figures

Theorems & Definitions (2)

  • Definition 1: A road segment
  • Definition 2: The RAA of GPS points for parking spots