Research on Reliability of Cumulative Navigation Error Propagation in Multi-Stage Underwater Delivery Missions

In multi-stage underwater delivery missions, when a mother platform releases a child platform, the estimation error of the mother's inertial navigation system (INS) is inherited as the initial position error of the child, leading to cumulative navigation error propagation across stages and affecting end-to-end mission reliability. To address this issue, a reliability modeling method for cumulative navigation error propagation is proposed, defining an error transfer coefficient for multi-stage missions and establishing closed-form expressions for the mission success probability of multi-stage delivery. Theoretical analysis reveals that the INS accuracy of the mother stage exerts a leverage effect on end-to-end reliability: given equal resources, improving the mother's accuracy yields significantly higher reliability gains than improving the child's accuracy. Moreover, there exists a critical value of the error transfer coefficient; when the coefficient falls below this critical value, inter-stage correction substantially improves reliability. Compared with traditional series reliability models, the proposed model overcomes the limitation of assuming independence of errors across stages, accurately characterizes the cross-stage coupling of errors, and achieves a mean absolute error below 5%. The model provides quantitative theoretical support for stage number design, platform selection, and mission reliability assessment of multi-stage underwater delivery systems.