## 1 Introduction  
The prediction of travel times is challenging because of the intrinsic uncertainty of travel on congested urban road networks as well as the uncertain influence of factors such as rainfall when probe vehicles travel on road networks. Uncertainty is produced by fluctuations in traffic and affected by traffic control (e.g., due to incidents, road works and road geometry), weather conditions (e.g., due to temperature, rain, snow and wind), stochastic arrivals and departures at signalized intersections [1], and the travel direction of traffic flows. The influence of different factors on travel time is often complicated and hard to predict. Understanding this influence is especially necessary when developing more accurate prediction algorithms. Traditionally, loop detectors have been used to collect traffic data reflecting traffic states and used to estimate or predict travel times [2; 3; 4; 5]. However,installing loop detectors everywhere in a city to collect comprehensive traffic information is not feasible, and maintaining installed devices is quite expensive. In contrast, probe vehicles as mobile traffic sensors equipped with GPS are being used to collect network-wide traffic data. Probe vehicles can collect information such as speed, timestamps, latitude and longitude coordinates, and azimuths, reflect the state of the urban traffic, and can play an important role in real-time or near real-time travel time prediction on a city road network. At present, several methods to estimate travel time use probe vehicle data. [PERSON] et al. [6] proposed a mathematical model to estimate travel time along the arcs and arrival times at nodes in a stochastic and dynamic network in real time, but ignored the sparse data problem. [PERSON] et al. [7] proposed a three-layer neural network model to estimate complete link travel time for individual probe vehicles traversing a link. This model was discussed and compared with an analytical estimation model developed by [PERSON] et al. [8]. Results showed that a neural network model had higher estimation precision on simulation data, Mean Absolute Percentage Error (MAPE) up to 3.97% under the condition of scenario 1. Those models however, were evaluated with data derived from vissim simulation model, not real GPS data reflecting traffic flows. [PERSON] [1] proposed a model to estimate arterial travel time by tracing a virtual probe vehicle along an OD (Origin-Destination) route with multiple intersections. The model works quite well with very low estimation error of 1.8%. [PERSON] et al. [9] presented a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observation data. The network model separated trip travel time into link travel time and intersection delays and integrated correlations between travel times on different network links in the model, based on a spatial moving average (SMA) structure. [PERSON] et al. [10] developed a methodology to estimate link travel time from OD trip data and demonstrated the feasibility of estimating network condition using large-scale geo-location data with partial information. This model estimated the travel time of a link or trip under the condition of the sufficient GPS data, whose MAPE is about from 21.52% to 29.305% corresponding to different model. The methods based on models, nevertheless, cannot efficiently infer link travel times under the condition of sparse data [7; 11; 12]. Due to the low frequency [13; 14] of probe vehicle data and the regional limitations of driving areas, trajectory information collected by probe vehicles cannot cover an entire urban road network. Thus, the data are sparse [7; 11] and, consequently, a solution for predicting link travel time using sparse data incorporating multi-factors is needed. In view of the data sparseness, we put forward a three-layer neural network model based on feature relationship between target link and adjacent link to estimate link travel time.