We investigate a height estimation method for non-cooperative aerial targets without feature information during take-off phase. The observation process of the flight target can be divided into two distinct phases: small-angle and large-angle phases. Two height estimation methods are proposed based on geometric optics modeling. In the small-angle phase, scene features are utilized to estimate the height via optimizing the iterative solution of the camera focal length. In the large-angle phase, the height is calculated based on known camera parameters and geometric relationships in the absence of reference objects. Experimental results demonstrate that the proposed method achieves high precision and reliability, with average height estimation errors of 0.246 m and 0.108 m for the small-angle and large-angle phases, respectively. This study not only provides a novel technical approach for state estimation of flying targets during the take-off phase but also offers theoretical support for flight fault analysis and safety evaluation.

Aiming at the issues of unknown camera parameters and possible pitch deviations in the initial take-off phase of non-cooperative targets, we propose a parameter estimation method based on a measurable reference object. By utilizing the pixel dimensions of the reference object, the camera focal length is precisely estimated. The camera inclination angles and target altitude are calculated by analyzing pixel coordinate variations between the target and reference object. During the target's ascent phase, when there is a lack of reference benchmarks within the field of view, the camera focal length and initial height estimated in the small-angle observation phase are used as known quantities. By modeling the actual motion state of the target, the accuracy of altitude estimation is further optimized. This method effectively addresses the challenges posed by unknown camera parameters and target deviations in the initial take-off phase, providing a high-precision solution for state estimation of non-cooperative targets during take-off.

In our experiment, the height estimation methods for non-cooperative flight targets were precisely validated. The results show that, in the small-angle phase [Fig.7(a)], the maximum difference between the estimated height and the true value measured by the laser rangefinder was 2.77 m, with an average difference of 0.246 m. Regarding camera inclination angles, the maximum difference was 0.23°, with the average difference of 0.11° compared with the values measured by the inclinometer. These data indicate that the height estimation method has high accuracy in the small inclination angle phase.

In the large-angle phase [Fig. 7(b)], at calculation frame 7, despite clear power pole visibility, the estimated flight height deviated by 21.85 m from the true value, while the camera inclination angle differed by 7.51°. The cause of this outlier has been analyzed in detail in Section 2.3. Excluding this anomalous data point, the maximum height estimation deviation decreased to 1.4 m, averaging 0.108 m. Meanwhile, the maximum difference between the estimated camera inclination angle and the true value is reduced to 0.59°, and the average difference is 0.258°. The experiment proves that the height estimation method can also meet the accuracy requirements in the large-angle phase. Overall, the experimental results from both the small and large inclination angle phases demonstrate the high accuracy of the two proposed height estimation methods. These methods offer essential theoretical support and precise data for relevant task analysis.

This research addresses non-cooperative flight target altitude estimation during take-off without feature information, presenting two geometric optical modeling-based methods. Field flight validation experiments confirmed the methods’ effectiveness. During the small-angle phase, the average difference between estimated altitude and laser rangefinder measurement value is 0.246 m, while average difference between estimated camera inclination angle and inclinometer reading is 0.11°. The large-angle phase showed average differences of 0.108 m in altitude estimation and 0.258° in camera inclination angle estimation. These results demonstrate the methods’ high precision for non-cooperative flight target state estimation during take-off. This research advances non-cooperative target position estimation theory while supporting flight failure analysis and safety assessment. Current estimation errors primarily stem from imaging distortion and feature extraction inaccuracies. Future research will focus on developing self-calibration and feature extraction algorithms to enhance method applicability across diverse practical scenarios.