Objective  The airborne electro-optical pods require high accuracy in viewing angle orientation when performing tasks such as autonomous target localization and simulating counter targets. Medium and large military airborne electro-optical pods often use high-performance measurement units, such as integrated sub-inertial guidance systems, to avoid the effects of errors caused by vibration to improve guidance accuracy. However, due to the limitation of size, weight, and power of the small and micro-unmanned airborne optoelectronic pods, their related measurement modules for viewing angle orientation are degraded in performance, and the viewing angle orientation accuracy is bound to decrease. In addition, the cost-effectiveness ratio is also an essential factor of modern unmanned combat. Therefore, how to select cost-effective components while ensuring overall accuracy is the primary problem when conducting the overall design of small and micro-unmanned airborne electro-optical pods. For this reason, an improved sparrow algorithm based on the simplex strategy is proposed in this paper to study the error distribution problem of small and micro-unmanned airborne electro-optical pod viewing angle from the perspective of multi-objective optimization, which provides a basis for engineering design and equipment selection.

  Methods  Firstly, the coordinate system is established according to the characteristics of the small and micro UAV photoelectric pod, and the viewing angle measurement model is derived by using the spatial homogeneous coordinate transformation method; Then the principal sources of errors are analyzed, the viewing angle error model is established, and error analysis is performed based on Monte Carlo simulation method; Finally, based on the viewing angle error model, the improved sparrow algorithm based on the simplex strategy proposed in this paper is used for error distribution, and compared with the average distribution method, the weighted distribution method, and the error distribution methods based on genetic algorithm and particle swarm algorithm.

  Results and Discussions   The improved sparrow algorithm based on simplex strategy proposed in this paper has certain advantages in solving the error allocation problem with multiple error parameters and complex error transmission process. Compared with the sparrow algorithm, genetic algorithm, and particle swarm algorithm, the improved algorithm has faster convergence and better optimization effect, overcomes the problem that the sparrow algorithm falls into local extremes, and has good global search ability (Fig.11). Compared with the traditional error distribution method, the error distribution margin of the optimal distribution scheme obtained by the improved algorithm can reach the magnitude of 10^-8 (Tab.5), which significantly improves the efficiency of the error distribution.

  Conclusions  In this paper, Monte Carlo simulation method is used to analyze the error of the viewing angle of the electro-optical pod, and an improved sparrow algorithm based on the simplex strategy is proposed for error distribution. The simulation results of error analysis show that the carrier yaw angle error and vibration yaw angle error have the greatest impact on the total error of the viewing angle, and the error transfer efficiency is slightly more than 100%, while the carrier roll angle error and vibration roll angle error have the least impact on the total error of the viewing angle, and the error transfer efficiency is only about 34%; The simulation results of error distribution show that the error distribution margin of the improved sparrow algorithm can reach the magnitude of 10-8, which significantly improves the distribution efficiency compared with the traditional error distribution method, and verifies the effectiveness of the improved sparrow algorithm based on the simplex strategy to solve the error distribution problem of the viewing angle of the electro-optical pod. However, the error distribution method based on the optimization algorithm is a kind of data fitting. When guiding practical engineering applications, it will be more instructive if the optimization range can be set with the design focus to determine the optimal error allocation scheme and use this scheme to guide the selection of crucial devices, which is also the subsequent research direction of this paper.