An innovative supervised learning structure for trajectory reconstruction of sparse LPR data

Abstract

The automatic license plate recognition (LPR) system has the advantages of strong continuity, high data accuracy, and large detection samples. The detection data can be used as quasi and full sample sampling of road network vehicles. However, the system has the disadvantage of sparse geographical location, so the data is difficult to be used effectively. In order to obtain the full sample vehicle travel trajectory on an urban road network, this paper investigates the sparse trajectory recovery problem based on LPR data. A trajectory reconstruction algorithm based on the Markov decision process (MDP) in road network space is proposed. The algorithm is divided into two stages, including off-line training and on-line prediction. In the off-line training stage, the LPR data is transformed into the trajectory set represented by the link edge sequence in the road network space. The MDP model is used to describe the vehicle driving behavior, and the design rules of the link reward function in the model are discussed. An unsupervised Bayesian inverse reinforcement learning algorithm is proposed to train the historical vehicle trajectory data and learn the model parameters. In the online prediction stage, the transfer probability between links is calculated according to the trained model. The negative logarithm of the transfer probability modified by the spatio-temporal coefficient is used as the edge weight to construct a directed graph. The shortest path search is used to obtain the path with the highest probability to restore the missing path. The proposed method is implemented on a realistic urban traffic network in Ningbo, China. The comparison with the baseline algorithms indicates that the proposed method has higher accuracy, especially when the coverage rate of the LPR device is low. When the coverage rate is more than 60%, the comprehensive accuracy of the proposed algorithm is more than 85%, and reliable path estimation results can be obtained.

Appendix

The probability of a path under a particular observation

Given an origin link $o$ and a destination link $d$, $P\left( {\left( {y^{1} ,y^{2} , \ldots ,y^{J} } \right){\mid }o,d} \right)$ denotes that a driver is observed by the detectors $(y^{1} ,y^{2} , \cdots ,y^{J} )$ during a trip from link $o$ to link $d$. Since the first detector observation $y^{0}$ is associated with a path in the link set ${\mathcal{L}}_{y} \left( {y^{1} } \right)$, $P\left( {\left( {y^{1} ,y^{2} , \ldots ,y^{J} } \right){\mid }o,d} \right)$ can be expressed as follows:

$$ P\left( {\left( {y^{1} ,y^{2} , \ldots ,y^{J} } \right)|o,d} \right) = \mathop \sum \limits_{{l \in {\mathcal{L}}_{Y} \left( {y^{1} } \right)}} P\left( {\left( {l,y^{2} , \ldots ,y^{J} } \right)|o,d} \right) $$

(A.1)

where $P\left( {\left( {l,y^{2} , \ldots ,y^{J} } \right){\mid }o,d} \right)$ is the probability that the first observed is link $l$, followed by the detectors $\left( {y^{2} , \cdots ,y^{J} } \right)$. We assume that actual choice is independent of historical choice. Eq. (A.1) can be further decomposed into:

$$ P\left( {\left( {l,y^{2} , \ldots ,y^{J} } \right)|o,d} \right) = P_{{y^{1} }} (l\left| {o,d} \right.,\varepsilon )P\left( {\left( {y^{2} , \ldots ,y^{J} } \right)|l,d} \right) $$

(A.2)

The term $P_{{y^{1} }} \left( {l\left| {o,d} \right.,\varepsilon } \right)$ is the expected probability observed at link $l$ arrival under the detection rate $\varepsilon$. $P\left( {\left( {y^{2} , \ldots ,y^{J} } \right){\mid }l,d} \right)$ is the probability to reproduce the remaining detector observation path, starting at link $l$. Substituting (A.2) into (A.1) can get the following recursive expression:

$$ P\left( {\left( {y^{1} ,y^{2} , \ldots ,y^{J} } \right)\left| {o,d} \right.} \right) = \mathop \sum \limits_{{l \in {\mathcal{L}}_{y} \left( {y^{1} } \right)}} P_{{y^{1} }} (l\left| {o,d} \right.,\varepsilon ) \cdot P\left( {\left( {y^{2} , \ldots ,y^{J} } \right)|l,d} \right) $$

(A.3)