## 1 Introduction  
Vehicle self-localization is an essential requirement for many of the safety applications envisioned for vehicular networks. However, to achieve a high degree of localization accuracy, computations that involve arrays of sensors and incorporate the physical characteristics of wireless communication channels may increase the complexity of the localization system. Accurate and efficient vehicle localization mechanisms are essential to the adoption of emerging location-based applications. Global Navigation Satellite Systems such as the Global Positioning System (GPS) have been widely used to provide localization for mobile nodes. However, it has been established that these systems may not always provide dependable position information, due mostly to signal deterioration in urban environments [1; 2]; contexts in which emerging vehicular applications increasingly require accurate localization. Research in localization accuracy is focused on the incorporation of additional data sources in the localization process in order to enhance the accuracy of a vehicle's GPS measurements. Example localization techniques are the fusion of data from other sensors [2], the use of anchor landmarks and maps [3], and cooperative positioning, the verification and correction of location data among neighbor nodes [4; 5]. However, deploying these methods may incur additional costs and increase the complexity of the localization scheme. Current localization schemes focus on modeling the localization error itself. This is translated to current literature being interested mainly in calculating the current location of vehicles. Little or no work considers time correlation between successive positioning errors in order to account for future positioning. The Kalman filter is a commonly used filtering technique for estimating vehicle positions, but it needs to be parameterized by the measurement noise, which is unknown and is usually modeled as a random variable with Gaussian distribution. Practical implementation of the Kalman Filter is often difficult due to the inability of getting a good estimate of the noise covariance matrices. Motivated by the above observations, we first investigate the existence of correlation between successive measurements, and determine the degree of correlation if it does exist. We proceed to present a mathematical model for positioning errors that takes into consideration the time correlation. Since vehicles exhibit a predictable and constrained behavior in terms of mobility, we anticipate that the future position of a vehicle will be correlated with its previous positions. Verifying this hypothesis via our proposed model can help improve the localization accuracy without incurring additional costs in terms of complexity. We propose to model the successive positioning errors as a \(p\) -order Gauss-Markov model, and investigate the order \(p\) in the \(p\) -order Gauss-Markov model over four datasets and verify the existence of time correlation. The proposed model can therefore be used as a prediction tool for other localization methods, and can be used for localization whenever the other methods fall short. The main benefit of this approach is that it produces vehicle positioning with a high level of accuracy with no need for fusion of additional data, making the localization process self-contained within the vehicle. By integrating our model into the Kalman filter, we show that therigorous modeling of positioning errors can assist in designing robust algorithms that predict the future locations of mobile node and improve the accuracy of localization. The contribution of this paper is three-fold; we establish the time correlation of successive location measurement errors, we define a \(p\)-order Gauss-Markov model that can be used for the prediction of future location while taking positioning error into account, and we use this model to enhance the accuracy of the prediction step in existing Kalman filter implementations with no need for data fusion.