针对小样本条件下多元时间序列之间的关联分析问题, 提出了一种小样本概率关联度模型。使用样本函数或样本统计量代替样本构造累积经验分布函数并计算概率关联系数。当比较序列样本容量n < 5, 使用样本顺序统计量的经验分布函数计算概率关联系数; 当比较序列样本容量n≥5, 使用Bootstrap方法重抽样扩充样本后再构造经验分布函数计算概率关联系数, 改进了概率关联度模型中关联系数的计算方法, 解决了小样本条件下这一类多元数据关联分析问题。证明了小样本概率关联度模型满足的基本性质, 给出了小样本概率关联分析的基本步骤, 仿真案例和实际应用验证了文中模型的正确性和有效性。

The most basic and direct method for simulation model validation is to compare the consistency of missile flight data and simulation data under the same input conditions. However, the existing dynamic data consistency analysis methods are mainly suitable for the case between 1-D missile flight data and 1-D simulation data, and do not conform to the consistency test of single sample flight data and multi-sample simulation data in equipment qualification/finalization test. To solve this problem, a simulation model validation method based on probabilistic relational analysis is proposed. The consistency of output data is measured from the two scales of probability relational coefficient and probability relational degree. The probability relational coefficient is determined by calculating the cumulative distribution probability value of real missile flight samples in the distribution function constructed by simulation data. The probability correlation degree is calculated by judging whether the probability relational coefficient satisfies the uniform distribution of[0 1]. The consistency analysis problem of a kind of dynamic data association is solved accordingly. The correlation theorem that the probability relational degree must satisfy and its property are proved. Meanwhile the operation steps of simulation model verification based on probability correlation analysis are given. This method can process all multi-dimensional simulation data at the same time, and integrate the random factors in the test process, so it can make full use of the test information under the condition of small sample flight test, and improve precision and the reliability of simulation model verification. The rationality and validity of this method are further verified by numerical tests and application examples.

The air-to-ground missile with strapdown seeker may have the problems, including small field of view(FOV), limited overload, and fall angle constraint. To solve the above mentioned problem, a phased guidance scheme is proposed. In this scheme, the attack trajectory is divided into the following six stages, including glided stage, fall angle constraint stage, target acquisition and adjustment stage, terminal guidance stage and blind zone stage. The glided stage is designed to increase range, the terminal fall angle is attained ahead of time at fall angle constraint stage. The aim of target acquisition and adjustment stage is to adjust the missile attitude, so that the target will fall within the FOV of the seeker. It creates good condition to capture the target for strapdown seeker. In the terminal stage, the guidance law of proportional navigation and attitude track are used to fit the needs of FOV constraint and attack accuracy. The simulation result shows that the project trajectory can solve the application of attacking moving targets for air-to-ground missile with strapdown seeker under multi constraints.

Under the missile speed is uncontrollable, a design method of multi-missile formation flight controller based on the sliding mode variable structure control theory and adaptive dynamic surface control theory is proposed. Firstly, according to the relative position of the leader and the follower in the inertial frame, the tracking error model for the relative position and the expected relative position between the leader and the follower is obtained, and the multi-missile formation control system in the inertial coordinate system is obtained. Secondly, in order to obtain the expression of the formation control system in the ballistic coordinate system, the acceleration of the missile in the ballistic coordinate system is converted to the inertial coordinate system. Combining with the tracking of the relative position and the desired relative position of the leader and the followers, we can obtain the simplified error model for the formation control system. Then the sliding mode variable structure control theory and the adaptive dynamic surface control theory are used to design the formation controllers for the leader and follower missiles respectively, and the stability of the present controller is analysed via the Lyapunov stability theory. Finally, the designed formation controllers are used for the leader and follower missiles to simulate the parameters. The results verify the feasibility and effectiveness of the present method.