# Vehicle Pose Estimation Method Based on Maximum Correntropy Square Root Unscented Kalman Filter
## 1 Introduction
This non-Gaussian characteristic can cause second-order statistical divergence, resulting in a significant decrease or even divergence in the positioning accuracy of the traditional Kalman filter and its derivative algorithms based on the minimum mean square error (MMSE) criterion [28; 29]. In response to the limitations of the aforementioned filtering algorithms, the Particle Filter SLAM (PF-SLAM) [30; 31] algorithm has been proposed. The PF-SLAM algorithm uses random sample data to approximate the posterior probability density function, so it requires a large amount of sample data to obtain acceptable estimation accuracy. This increases the computational complexity of the PF-SLAM algorithm. Furthermore, this also increases the difficulty of the algorithm in practical applications. In recent years, the Maximum Correntropy (MC) has been proven to solve the problem of low-pose estimation accuracy of traditional Kalman filtering and its derivative algorithms in non-Gaussian noise environments [32; 33; 34; 35]. [PERSON] et al. proposed vehicle state estimation algorithms based on the Maximum Correntropy Extended Kalman Filter (MC-EKF) [36] and the Maximum Correntropy Adaptive Extended Kalman Filter (MC-AEKF) [37]. The research results demonstrate that, under non-Gaussian noise environments (particularly heavy-tailed noise), MC-AEKF and MC-EKF exhibit stronger robustness and higher estimation accuracy compared to traditional AEKF/EKF. Subsequently, scholars have proposed the Maximum Correntropy Unscented Kalman Filter (MCUKF) [38] and an iterative Maximum Correntropy Unscented Kalman Filter algorithm [39]. These methods have demonstrated excellent performance in complex noise environments, though they were only validated through numerical simulations and not applied to practical problems. [PERSON] et al. introduced an MCUKF algorithm for loosely coupled positioning in an inertial navigation system (INS) and ultra-wideband (UWB) integration [40], which significantly outperforms traditional UKF methods in terms of positioning accuracy and robustness. [PERSON] et al. proposed a Maximum Correntropy Adaptive Unscented Kalman Filter (MC-AUKF) algorithm [41] for estimating vehicle states and key parameters. This algorithm demonstrates superior performance under non-Gaussian noise and effectively improves estimation accuracy. However, in highly non-Gaussian noise environments or during rapid motion scenarios, the iterative process of MC-AUKF may suffer from loss of positive definiteness in the covariance matrix due to rounding errors or ill-conditioning, leading to inconsistent state estimation and numerical instability in filtering. In contrast, the Square-Root Unscented Kalman Filter (SRUKF) significantly enhances numerical stability, computational efficiency, and robustness by introducing square-root decomposition, making it more suitable for robot-pose estimation in non-Gaussian noise environments. Based on the above research background, this paper combines the Maximum Correntropy with the square root unscented Kalman filter to propose the Maximum Correntropy Square Root Unscented Kalman Filter SLAM (MCSRUKF-SLAM) algorithm. The MCSRUKF-SLAM uses MC instead of MMSE, effectively solving the problem of low-pose estimation accuracy caused by non-Gaussian noise in the system. Furthermore, the MCSRUKF-SLAM algorithm adds the square root filter on the basis of the Unscented Kalman Filter. It ensures the positive definiteness of the covariance matrix and improves the stability of the filtering values by performing Cholesky decomposition on the covariance matrix. The rest of this paper is organized as follows: In Section 2, the SLAM problem is proposed, and then the SRUKF-SLAM algorithm is described. In Section 3, the MCSRUKF-SLAM for robot tracking is proposed. In Section 4, the robot system model is introduced, and then the simulation environment and parameters are given. In Section 5, the superiority of the proposed algorithm is verified by simulation and experiment. Finally, some conclusions are drawn in Section 6.