LiDAR-based place recognition schemes offer effective solutions for improving the localization of self-driving cars in GNSS-constrained environments. However, the presence of heterogeneous sensors introduces variations in point cloud measurements of the same environment during place recognition. In this paper, we propose an initial localization strategy for urban environments based on the commonalities of heterogeneous LiDAR. A novel point cloud descriptor is proposed for heterogeneous LiDAR, enhancing the ability to describe the environment by considering different vertical and horizontal viewpoints based on the spatial distribution characteristics of LiDAR point clouds. Through this descriptor, a robust initial localization solution is constructed, enabling accurate initial localization even when using descriptors from different LiDAR systems and incorporating environment a priori map information. Experimental evaluations using both public and self-built datasets confirm the superiority of the initial localization strategy based on heterogeneous LiDAR. The point cloud descriptor demonstrates improved performance compared to existing methods. Moreover, the place recognition strategy, applicable to both homogeneous and heterogeneous LiDAR, exhibits significantly lower error rates compared to traditional methods.