Time angle of arrival (AoA) and time difference of arrival (TDOA) are two widely used methods for solving dynamic signal source localization (DSSL) problems, where the position of a moving target is determined by measuring the angle and time difference of the signal's arrival, respectively. In robotic manipulator applications, accurate and real-time joint information is crucial for tasks such as trajectory tracking and visual servoing. However, signal propagation and acquisition are susceptible to noise interference, which poses challenges for real-time systems. To address this issue, a noise-immune zeroing neural dynamics (NIZND) model is proposed. The NIZND model is a brain-inspired algorithm that incorporates an integral term and an activation function into the traditional zeroing neural dynamics (ZND) model, designed to effectively mitigate noise interference during localization tasks. Theoretical analysis confirms that the proposed NIZND model exhibits global convergence and high precision under noisy conditions. Simulation experiments demonstrate the robustness and effectiveness of the NIZND model in comparison to traditional DSSL-solving schemes and in a trajectory tracking scheme for robotic manipulators. The NIZND model offers a promising solution to the challenge of accurate localization in noisy environments, ensuring both high precision and effective noise suppression. The experimental results highlight its superiority in real-time applications where noise interference is prevalent.