# Vehicular Localization Enhancement via Consensus
## 1 Introduction
A new distributed optimization technique based on alternating direction method of multipliers (ADMM) [19] is also developed to lift a large amount of the computational cost in cooperative localization by updating the solution by using only average values of probability distributions. However, considering the limited amount of computational resources available in a vehicle and the demand for the real-time update on the location, an enhanced protocol with improved localization accuracy is desired. To overcome these challenges, this work aims at a simple strategy of improving the accuracy of vehicular localization. The strategy is composed of two main steps--updates based on consensus and compensation. In the first half of the update phase, individual vehicles repeatedly, but not necessarily synchronously, exchange and update their location estimates in a consensus-based manner. The consensus-based protocol averages the local estimates by exchanging location data and measuring relative measurement with respect to each other. The iterative updates thus cause all neighboring vehicles to possess similar magnitudes and orientations of the localization error. Since the repetitive updates average out the local estimate errors, it is noticeable that the localization of the best-performing vehicle, called anchor, is bound to degrade. Such an observation is taken into advantage in the second half, the compensation phase, of the proposed strategy. In the compensation step, the homogenized measurement errors are significantly removed by counteracting the degradation of the location estimate of the best-performing vehicle among the neighboring vehicles. The entailed computations are maintained as simple as basic arithmetic operations and evaluation of \(L_{2}\) norm. In regard to the communication loads, the iterative data exchanges among the vehicles and the broadcast for the compensation step are involved. These loads can be minimized by communicating the information associated with a sufficient statistic that leads to the resulting estimate achieving Cramer-Rao lower bound (CRLB) [20]. The major contributions of the paper are summarized as:  
* An uncomplicated strategy to enhance localization performance in vehicular networks is constructed. The strategy involves the exchange of local data and the exploitation of a superior anchor vehicle within the vehicular network. Using local estimates of different qualities, the proposed strategy enhances the overall accuracy of all vehicles' localization to that of the anchor. The execution of the protocol does not involve a central manager, thus greatly improving the adaptability of the protocol to networks of different scales. * Mathematical formulations for the analyses of the different stages of the proposed strategy are made. Despite the computational simplicity, the analytically found optimal estimator efficiency is ultimately achieved in terms of CRLB. * Visual representations of the experiments based on 3 GPP TR 37.885 urban scenario specifications are provided and discussed. The effects of the execution of the proposed strategy are observed under diverse scenarios. Comparisons to centralized localization are also made in order to show the effectiveness of the distributed protocol for the intended environments. The remaining parts of the paper are organized as follows--Section 2 describes the system model. Section 3 develops a decentralized strategy of improving the localization performance along with performance analysis details. In Section 4, the utilization of the proposed strategy under a representative configuration is observed with discussion. The efficiency of the proposed strategy under various circumstances and implementation practices are addressed in Section 5. Section 6 concludes the paper.