Continuous-discrete filtering (CDF) arises in many real-world problems such as ballistic projectile tracking, ballistic missile tracking, bearing-only tracking in 2D, angle-only tracking in 3D, and satellite orbit determination. We develop CDF algorithms using the extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF) with applications to the angle-only tracking in 3D. The modified spherical coordinates are used to represent the target state. Monte Carlo simulations are performed to compare the performance and computational complexity of the proposed filtering algorithms. Our results show that the CDF algorithms based on the EKF and UKF have the best state estimation accuracy and nearly the same computational cost.