This paper presents a method for detection and trajectory estimation of moving objects such as walking humans to achieve efficient indoor navigation of a mobile manipulator. Mobile manipulation requires interactions of the robot with objects such as humans and robots, which are usually in motion, thus it is important that a robot can detect moving humans and robots, estimate their trajectories for collision avoidance and path planning in order to improve safety and travel efficiency. We introduce our omni-directional mobile robotics system which is specially designed for efficient navigation in cluttered indoor environments with narrow passages. To achieve detection and trajectory estimation of moving objects while the robot base itself is also in motion, relative position information between the base and the world is necessary in our algorithm and it is obtained by a proposed robust fused odometry. Moving objects are detected with their 3D bounding boxes by integration of the fused odometry and a proposed algorithm using point cloud captured by Kinect. At the same time, velocities and trajectories of the moving objects are also estimated and can be used for path planning and moving obstacle avoidance. The overall system has been implemented on our robot base for real practice.