This paper presents an efficient grasp pose estimation algorithm for robotic arm systems with a two-finger parallel gripper and a consumer-grade depth camera. Unlike traditional deep learning methods, which suffer from high data dependency and inefficiency with low-precision point clouds, the proposed approach uses ellipsoidal modeling to overcome these issues. The algorithm segments the target and then applies a three-stage optimization to refine the grasping path. Initial estimation fits an ellipsoid to determine principal axes, followed by nonlinear optimization for a six-degree-of-freedom grasp pose. Validation through simulations and experiments showed a target grasp success rate (TGSR) of over 83% under low noise, with only a 4.9% drop under high noise-representing a 68.0% and a 42.4% improvement over GPD and PointNetGPD, respectively. In real-world tests, success rates ranged from 95 to 100%, and the computational efficiency was improved by 56.3% compared to deep learning methods, proving its practicality for real-time applications. These results demonstrate stable and reliable grasping performance, even in noisy environments and with low-cost sensors.