# Extended Particle-Aided Unscented Kalman Filter Based on Self-Driving Car Localization
## 1 Introduction  
In recent years, the self-driving car has become the hottest topic in the automotive industry [1; 2; 3; 4]. To make a self-driving car drive conveniently and safely, accurate identification of the vehicle's position is one of the most important parameters. Only if the self-driving car knows where it is can it execute the next decision. Localization is on the basic module of the perception module. Almost all the other data work on the basis of the location data. The most commonly used localization method is GPS [5]. However, GPS signals are affected by the quantity of satellites and by the multipath effect in an urban environment [6; 7; 8]. When GPS cannot obtain a sufficient quantity of satellites [9], an alternative approach to localization is needed. As high-definition (HD) maps have developed, it has become possible to localize the vehicle position based on map matching [10; 11]. However, not only does the HD map make a noise, but the sensors have a detect noise as well. A method is needed, therefore, to filter noise from different sources. The Kalman filter family is generally used to filter the noise of many sensors [12; 13; 14]. The Kalman filter is designed for processing Gaussian noise with a linear transition model and a linear measurement model. However, in the real world, most of the transitions and measurements are not linear. Therefore, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) were proposed [15; 16; 17; 18; 19; 20] to provide a methodology to handle nonlinear transitions and measurements. EKF and UKF still operate on a basic assumption of the Kalman filter, in that the noise always should be Gaussian. The particle filter (PF) is a Monte Carlo-based method that can handle any type of noise [21; 22; 23; 24; 25]. The more particles used, the more accurate PF can be. However, because the PF method involves calculating each particle's weight, the precision and computational burden must trade-off. In our previous work, we proposed the particle-aided unscented Kalman filter (PAUKF), which has more stable and precise performance compared to the PF using the unscented Kalman filter [26]. We constructed the PAUKF using the infrastructure two-dimensional information in previous research. The mean estimation error for the PAUKF is 1.08 m and its variance is 0.7147 m, which is more precise than the mean of 1.69 m and variance of 1.63 m obtained by GANGNAM for a similar noise environment. However, in the real world, there is rich 3D information gained from perception module sensors that use light detection and ranging (LiDAR), and radio detection and ranging (RADAR). The PAUKF algorithm only considers two-dimensional features; it cannot process features in three dimensions appropriately. The PAUKF algorithm needs extended capabilities to handle three-dimensional information. In this paper, we have improved the perception calculation method and extended the weight calculation scheme, by using a multivariable normal distribution in three dimensions. Compared to our previous research, the extended PAUKF improves the particle selection method. With an improved particle weighting scheme, the extended PAUKF extracts a more precise global location based on 3D features. We also found that the extended PAUKF provides feasibility to fuse multisource perception data into the PAUKF framework by weighting the particles. The simulation result shows that the extended PAUKF achieves better performance in a three-dimensional feature environment compared to the previous PAUKF. The extended PAUKF improves precision 73.81% compared to the initial PAUKF. The limitations of this algorithm are that the hyperparameters are not optimal even when tuned carefully, and that it does not consider the vehicle on the freeway on-ramps. These limitations should be mitigated in future research. Section 2 illustrates the extension of the basic PAUKF to incorporate three-dimensional features and the framework to fuse multisource perception data. Section 3 illustrates the simulation environment.