# Real-Time Geo-Localization for Land Vehicles Using LIV-SLAM and Referenced Satellite Imagery
## 1 Introduction  
Autonomous navigation has drawn significant attention over the past years for its potential application in unmanned system. SLAM enables localization and mapping in GNSS-denied environments, making it a crucial and widely adopted technology for autonomous navigation across various applications [1,2]. Over the years, SLAM has undergone significant advancements, transitioning from pure vision-based approaches to more robust multi-sensor fusion methods that integrate LiDAR, inertial measurement units (IMU), and cameras to enhance localization accuracy and robustness. The most cutting-edge and advanced LIV-SLAM systems [3, 4, 5, 6] exploit the depth accuracy of LiDAR, the motion constraints of IMU, and the feature richness of vision sensors to achieve high-precision and reliable localization and mapping in complex, real-world environments. Despite the significant improvements achieved by the recent works, SLAM still faces several challenges. One major issue is the accumulation of errors over long-distance operation, leading to localization drift and map distortion. Additionally, global optimization for correcting accumulated errors in SLAM systems depends heavily on loop closure detection [7, 8, 9, 10]. However, in many real-world scenarios, loop closures may be absent or challenging to detect. Motivated by the limits of current methods and practical demands, we proposed a real-time geo-localizing navigation method for land vehicles that relies only on a LIV-SLAM and a referenced image. Our method is designed to function without GPS or loop closure. Instead, it estimates the global position by aligning the real-time constructed map to a referenced image with an efficient cross modal matching algorithm. This paper makes three main contributions:  
(1) A fast and robust cross-modal matching algorithm is proposed for the real-time geo-localization for land vehicles. The matching algorithm is designed to address the distortion caused by cross-modal, downward-view projection and cross-temporal scene variations, as shown in Figure 1. Figure 1a,b demonstrate cross-modal distortion, where the grayscale appearance of the same object varies significantly across modalities. Figure 1c,d depict projecting distortion, in which the object's appearance changes due to geometric transformation. Figure 1e,f show scene variations resulting from temporal discrepancies between the projection image and the referenced image. Notably, all projection images contain invalid regions, typically visualized as black areas, which may introduce ambiguity and reduce the robustness of the matching process. We exploit Dense Structure Principal Direction (DSPD) [11] to capture gradient-orientation-based texture patterns, which remains consistent for cross-domain images. Figure 1: Examples of cross-modal distortion and local scene changes. **(a,b)** Example of grayscale distortion; **(c,d)** Example of projection distortion; **(e,f)** Example of scene change. Furthermore, the similarity measurement is optimized, and the searching efficiency is significantly improved with a fast correlation in the frequency domain. The comparison in the ablation experiments demonstrates that the proposed cross-modal matching algorithm achieved the best result in both accuracy and efficiency. A detailed comparative evaluation of different matching algorithms is presented in Section 4.3.1, which clearly shows the superior performance of our method in terms of matching precision and computational speed. (2) This paper proposes an adaptive Kalman filter based on motion compensation (MC) and an Observation-Aware Gain Scaling (OAGS) mechanism. With motion compensation, the proposed AKF effectively eliminates prediction errors caused by observation delays and asynchronous updates. Ablation experiments demonstrate that MC effectively mitigates the adverse effects of observation delay, preventing degradation in fused localization accuracy, as detailed in the comparison of filters presented in Section 4.3.2.