Autonomous driving of a personal mobility vehicle such as a wheelchair in a walking space is necessary in the future as a means of transportation for the elderly and the physically handicapped. To realize this, accurate pedestrian detection is indispensable. As existing 3D object detection methods are trained with a roadway dataset, they are widely used for object detection in roadways. These methods have two major issues in the detection of objects in walking spaces. The first issue is that they are largely affected by the difference of the LIDAR models. To eliminate this issue, we propose a 3D object detection method, CosPointPillars. CosPointPillars does not take the reflection intensities of LIDAR point cloud, which cause a sensor model dependency, as input. Furthermore, CosPointPillars utilizes a cosine estimation network (CEN) to retain the detection accuracy. The second issue is that networks trained with a roadway dataset cannot sufficiently detect pedestrians (who are major traffic participants in walking spaces) located within a short distance; this is because the roadway dataset hardly includes nearby pedestrians. To solve this issue, we generated a new walking space dataset called SimDataset, which includes nearby pedestrians as a training dataset in the simulations. An experiment on the KITTI showed that the CEN helps in pedestrian detection in sparse point clouds. Furthermore, an experiment on a real walking space showed that SimDataset is suitable for pedestrian detection in such cases.