To tackle the computational cost and registration time challenges in traditional point cloud registration methods like ICP(iterative closest point) such as LIO-SAM (tightly-coupled lidar inertial odometry via smoothing and mapping) and newer models utilizing deep neural networks such as HRegNet(hierarchical registration network), a lightweight and real-time HKRNet (hierarchical kcpstack registration network) network model was proposed. The model was developed by thoroughly studying the HRegNet neural network point cloud registration framework. Initially, a combined filtering approach involving point cloud voxelization and Gaussian threshold downsampling was used to remove redundant points from ground radar scans, reducing the point count from around 130 000 to about 70 000. Subsequently, the computationally intense KNN (K-nearest neighbors) point cloud clustering algorithm within the HRegNet model was enhanced by optimizing it to a KD-Tree (K-dimensional tree) algorithm, resulting in a 25% improvement in processing speed while upholding accuracy. Lastly, to address high memory usage and low computational efficiency of the convolutional modules in the model, a lightweight convolutional module leveraging tensor decomposition and a hierarchical singular value decomposition algorithm was introduced. This leaded to a compressed model size of 86.1% of the original and a decrease of 61.2% in computational cost. The outcomes indicate that the HKRNet network, in comparison to the HRegNet network, can reduce registration time by 40% with minimal loss of accuracy, achieving a single registration time not exceeding 84ms, thus meeting real-time registration requirements.