# Sensor Fusion of GNSS and IMU Data for Robust Localization via Smoothed Error State Kalman Filter
###### Abstract  
High\(-\)precision and robust localization is critical for intelligent vehicle and transportation systems, while the sensor signal loss or variance could dramatically affect the localization performance. The vehicle localization problem in an environment with Global Navigation Satellite System (GNSS) signal errors is investigated in this study. The error state Kalman filtering (ESKF) and Rauch-Tung-Striebel (RTS) smoother are integrated using the data from Inertial Measurement Unit (IMU) and GNSS sensors. A segmented RTS smoothing algorithm is proposed in order to estimate the error state, which is typically close to zero and mostly linear, which allows more accurate linearization and improved state estimation accuracy. The proposed algorithm is evaluated using simulated GNSS signals with and without signal errors. The simulation results demonstrate its superior accuracy and stability for state estimation. The designed ESKF algorithm yielded an approximate 3% improvement in long straight line and turning scenarios compared to classical EKF algorithm. Additionally, the ESKF\(-\)RTS algorithm exhibited a 10% increase in the localization accuracy compared to the ESKF algorithm. In the double turning scenarios, the ESKF algorithm resulted in an improvement of about 50% in comparison to the EKF algorithm, while the ESKF\(-\)RTS algorithm improved by about 50% compared to the ESKF algorithm. These results indicated that the proposed ESKF\(-\)RTS algorithm is more robust and provides more accurate localization. error state Kalman; RTS smoothing; robust and accurate localization  
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discovered that the INS could only provide high \(-\)accuracy parameter estimation results for a short duration. During the satellite signal occlusion, the forward filtering algorithm alone thus cannot guarantee a robust localization. Applying the extended Kalman filter (EKF) to estimate the motion of vehicle systems is well desirable due to the system nonlinearity [13; 14; 15; 16]. The EKF linearizes the nonlinear model by approximating it with a first\(-\)order Taylor series around the state estimate and then estimates the state using the Kalman filter. [PERSON] [17] proposed utilizing the extended Kalman filter to merge data from inertial sensors with GNSS data in a loosely coupled mode to improve the accuracy of road network maps in determining lanes. The resulting lane determination success rate was an impressive 97.14%. However, the local linearization operation of this approach can introduce significant estimation errors. [PERSON] [18] introduced an Unscented Kalman filter algorithm that improves the estimation results, while its high complexity makes it unsuitable for most inertial guidance devices. [PERSON] [19] et al. pointed out through theoretical analysis and simulation verification that the UKF has poor filtering performance or even divergence in solving the high \(-\)dimensional (\(\geq\)20) nonlinear state estimation problem. For this reason, they used the spherical radial rule to approximate the state posterior distribution in the optimal framework, and then proposed the Cubature Kalman Filter (CKF), but the CKF has higher computational complexity and requires more sampling and operations, resulting in poor real \(-\)time performance, which is not suitable for some applications with high real \(-\)time performance requirements. The extended Kalman filter thus remains the mainstream state estimation algorithm, and developing a low \(-\)complexity filter with high accuracy is still challenging [20; 21]. To address this challenge, [PERSON] [22] presents a flexible design framework utilizing symbolic engines to represent and linearize system and measurement models. A robust fixed \(-\)lag smoothing approach is proposed in case there is a mismatch between the nominal model and the actual model [23; 24].