Objective Optical measurement systems play an indispensable role in spaceflight measurement and flight testing due to their non-contact nature, high frame rates, and strong electromagnetic interference resistance. In complex operational scenarios such as rocket inter-stage separation, fairing jettison, or explosive disintegration at space launch sites, multiple targets often coexist. During such multi-target tracking, matching errors among different optical devices can easily occur, leading to the intersection of lines of sight (LOS) pointing to different physical entities. This results in distorted intersection trajectories and erroneous guidance information for command centers. Traditional "discriminate first, use later" modes rely heavily on equipment status codes, elevation thresholds, and target sorting, which not only waste valid measurement data but also fail to ensure data-to-entity consistency from a mechanistic perspective. Existing research directions, including image feature matching (computationally heavy and ineffective for distant weak targets), maximum likelihood estimation (MLE) dynamic association (ignoring systematic errors from target part differences), and offline skew line intersection methods, all have limitations in real-time applicability or robustness. To overcome these challenges, this study aims to develop a real-time optical target identity discrimination method based on the geometric constraints of common perpendiculars of skew lines. The goal is to establish a reverse "intersect first, discriminate later" architecture, enabling high-reliability intersection trajectory calculation and resolving real-time data association ambiguity in multi-target scenarios.

Methods The proposed method is grounded in the spatial forward intersection principle of two optical devices. Under ideal conditions, the LOS vectors from two stations should intersect at the target. However, in practice, influenced by angle measurement errors, atmospheric turbulence, and asynchronous tracking, the two LOS vectors form skew lines in three-dimensional Euclidean space. First, the direction vectors of the two LOS are defined using azimuth (A) and elevation (E) angles. The common perpendicular between the skew lines is then solved. The length of the common perpendicular segment, d representing the shortest distance between the two lines, is calculated via the formula d=\dfrac\left|\boldsymbolr \cdot\left(\boldsymbolu_1 \times \boldsymbolu_2\right)\right|\left|\boldsymbolu_1 \times \boldsymbolu_2\right| , where r is the vector connecting the two stations, and u₁, u₂ are the unit direction vectors of the LOS. To determine the optimal intersection position, a weighted midpoint M of the common perpendicular is derived, with weights adaptively balancing the measurement errors of the two devices based on their distances to the target (R₁, R₂) and dynamic angle measurement accuracies (\sigma_1, \sigma_2) . Since d varies with target distance, a relative intersection deviation angle \Delta \alpha is introduced for distance normalization. The deviation angles \Delta \alpha_1 and \Delta \alpha_2 for each station are computed using M as the reference point. A comprehensive dynamic error threshold \Delta \theta_\max is constructed, fusing dynamic angle measurement errors (e. g., servo jitter, calibration residuals) and target extraction position deviations (e. g., head/tail feature differences). The threshold is formulated as \Delta\theta_\max=\sqrtn^2\sigma^2+\left(\arctan\left(l/R\right)\right)^2 , where l is the extraction deviation length. The discrimination algorithm consists of three steps: 1) Data preprocessing: spatiotemporal synchronization, coordinate transformation, and statistical filtering to remove outliers; 2) Spatial intersection solving: computing the common perpendicular, weighted midpoint, and deviation angles; 3) Dynamic threshold comparison: if \left|\Delta \alpha_1\right| \leqslant \Delta \theta_1 \max and \left|\Delta \alpha_2\right| \leqslant \Delta \theta_2 \max , the target is identified as homonymous, and the intersection coordinates are output; otherwise, the data is discarded as a heteronymous target (e. g., debris or decoy).

Results and Discussions The proposed method was validated using actual measurement data from a space launch involving three optical devices (A, B, C). Comparative experiments were conducted against traditional intersection criteria. In terms of data utilization, the traditional method achieved 80. 69% for device pair A-B and 90. 34% for A-C. In contrast, the proposed method reached 100% utilization for both pairs, as it does not rely on restrictive pre-discrimination conditions and can process all valid intersection frames. For target identity discrimination, traditional methods could not discriminate homonymous from heteronymous targets, often producing false trajectories when different devices tracked different entities. The proposed method achieved a missed detection rate of 0. 24% (A-B) and 0. 31% (A-C), and a false alarm rate of 0. 11% (A-B) and 4. 78% (A-C). The slightly higher false alarm rate in A-C was attributed to specific separation dynamics where one device briefly lost track, yet the method still successfully identified and discarded anomalous data frames, preventing persistent false trajectory generation. The intersection time windows were significantly extended. For instance, in A-B, the traditional method covered only 11–128 seconds, while the proposed method covered 0–145 seconds continuously. In A-C, the traditional method covered 14–145 seconds, while the proposed method covered 0–73 seconds for target 1 and identified target 2 at 73 seconds, demonstrating superior multi-target handling. The dynamic threshold model proved robust across varying distances and angles. Analysis of different confidence coefficients showed that threshold redundancy could be tuned to balance missed detection and false alarm rates according to equipment performance and mission requirements. The method's computational efficiency was high, converting complex multi-dimensional matching into simple geometric threshold comparison, thus meeting real-time processing demands in engineering applications.

Conclusions This study proposed a real-time target identity discrimination method for optical intersection measurement based on the common perpendicular characteristics of skew lines. The main conclusions are: 1) The method is effective. By adopting a reverse "intersect first, discriminate later" architecture and leveraging spatial geometric constraints, it fundamentally resolves the issues of measurement data waste and false intersection of heteronymous targets that plague traditional methods. 2) The threshold is adaptive and robust. The derived intersection deviation angle model normalizes distance effects, and the comprehensive dynamic threshold—fusing angle measurement errors and target extraction deviations—adapts to varying operational conditions. Confidence coefficients can be reasonably set based on device performance. 3) The application is universal. The method requires no image features or equipment status codes, making it applicable to various optical measurement devices and complex scenarios involving long-distance, point targets, and strong interference. Future work will focus on extending the model to multi-sensor fusion (optical-radar, multi-optical); utilizing real-time discrimination results to guide mis-tracked devices; and integrating lightweight machine learning models to enhance processing capability for large-scale multi-target scenarios.