As a key technological platform in critical fields including environmental monitoring, astronomical observation, industrial automation, and aerospace, the electro-optical tracking system faces increasingly stringent requirements for tracking accuracy as its application scenarios broaden. The system drive the azimuth-pitch dual-axis platform in real time through tracking control technology, reducing the angular deviation between the target captured by the image sensor and the optical axis center to achieve precise tracking. However, traditional tracking methods have inherent limitations. Sensor data fusion in equivalent feedforward control introduces lag errors, and image and attitude sensors can only provide azimuth and pitch angle data, leading to strong nonlinear issues for the Kalman filtering algorithm. Moreover, existing improved Kalman filter algorithms have computationally complex predictions and insufficient real-time performance, making them unsuitable for high-speed target tracking. To address the errors and delays caused by nonlinear models in the tracking system, a Kalman filter method based on a hybrid coordinate system was proposed.

By integrating the pulse laser ranging system with the electro-optical tracking platform (Fig.10), the distance, azimuth, and pitch angle data of a uniform linear-motion target were acquired in real time within the spherical coordinate system. These data were then converted into three-dimensional coordinates in the Cartesian coordinate system using a nonlinear spatial geometric transformation (equation (18)). Additionally, a linear state equation (equation (17)) was established based on the uniform linear-motion model. The standard Kalman filtering algorithm was used to predict the target’s motion trajectory in the Cartesian coordinate system. Finally, the prediction results were converted back to the spherical coordinate system via an inverse transformation to output the angle commands. This method avoided the direct processing of nonlinear models by the Kalman filtering through the coordinate system transformation mechanism (Fig.6) and leveraged the linear characteristics of the model in the Cartesian coordinate system to meet the algorithm’s requirements.

Simulation and experimental results demonstrated that the hybrid coordinate system method significantly improved prediction accuracy. In the uniform linear motion simulation (Fig.7, Fig.8), this hybrid coordinate system method followed the actual trajectory more closely than the traditional spherical coordinate model, with particularly noticeable error improvements in regions of abrupt angular velocity changes around sampling point 100 (Fig.9). Straight-line motion tracking experiments with an unmanned aerial vehicle (Fig.11) further confirmed that the root mean square error of azimuth axis prediction decreased from 2.13 mrad to 1.88 mrad, and that of the pitch axis prediction decreased from 2.89 mrad to 2.44 mrad (Fig.12, FIg.13), with an average error reduction of 13.65%.

The hybrid coordinate system effectively addresses the prediction error issues caused by nonlinearity in the electro-optical tracking system by combining spherical coordinate system measurements with the Cartesian coordinate system modeling . Both simulations and experiments indicate that this method reduces the root mean square error of trajectory prediction by an average of 13.65%, thereby improving the tracking accuracy for uniform straight-line motion targets. The hybrid coordinate system provides a reference solution for high-precision target tracking in electro-optical tracking systems.