# Vehicular Localization Enhancement via Consensus
## 1 Introduction  
The realization of autonomous vehicular networks has been rendered achievable and imminent due to the recent advancements in various communication application areas, including fifth generation (5G) mobile communication and millimeter-wave (mmWave) technologies [1]. To ensure reliable operation of autonomous vehicles, precise and quick localization techniques are in demand. However, the inevitable occurrences of measurement and communication noises often digresses location estimates from the ground truth locations. Furthermore, the usage of Global Positioning System (GPS) has technical limitations since its signal power budget often fails to become sufficient enough to penetrate obstacles; unfavorable environments such as underground tunnels or indoors can lead to more inaccuracy [2]. Detection techniques where the vehicles cooperatively utilize each other's estimates to enhance the preciseness of the localization are therefore solicited [3]. Cooperative localization can be realized in centralized or distributed manners [4]. The centralized localization is implemented by employing a single computationally superior unit to estimate the locations of all vehicles within the network. Such an approach can be very efficient in various ways since most vehicles' loads on the computation and communication are significantly lifted. However, the centralized approach may not be robust to communication setbacks since the failure in the centralized management ends up with the eventual collapse of the entire system. In applications suchas V2X networks where a brief collision may result in major accidents, a robust and flexible approach is desirable. Furthermore, a centralized manner of the localization has limitations in scalability since the computational loads are devoted solely to a single unit. In such cases, the amount of computation scales directly to the number of the vehicles in the network. Considering the imminent implementation of large-scale vehicular networks, the limit in scalability renders the reliance to a single unit unsuitable. On the other hand, a distributed localization conducts the estimation independently and locally among neighboring vehicles. Since such approach does not require a central agent, it is less reliant to a single unit and easier to increase the network scale. A distributed implementation is therefore preferred in many circumstances, in particular, of mobile network configurations, such as V2X networks. To that end, distributed localization techniques with data-driven parameter estimation, such as maximum a posterior estimation [5; 6; 7; 8], Monte Carlo (MC) methods [9], maximum likelihood (ML) estimation [10], particle filters (PFs) [11], extended Kalman filters (EKFs) [12; 13], and sum-product algorithm over a wireless network (SPAWN) [14], have been developed. Factor graph models [15] and belief propagation (BP) algorithms are utilized in References [5; 6; 7; 8] to reduce communication and computation demands for synchronized cooperative localization. In Reference [9], a modified MC localization is utilized to estimate locations of robots with the robustness in indoor environments. ML estimation combined with numerical optimization techniques is used for localization without external localization units in Reference [10]. In Reference [11], the localization is achieved by combining results obtained from the PF technique and the GPS-based localization. In Reference [16], multi-node cooperative localization is developed based on dead reckoning and PF. With the data fusion of redundant data from multiple sensors, References [12; 13; 17] implement EKFs and PFs to cooperatively localize a large group of mobile robots and vehicles. In Reference [18], mmWave is utilized for the cooperative positioning while also taking advantage of radio-based multipath signals to build a map of available signal paths. A localization approach based on the SPAWN [14] and BP algorithms repetitively calculates the posterior distributions of messages to achieve localization with high accuracy.