On One Solution of the Numerical Problem Differentiation in Calculation Vertical Speed of Aircraft

V. Panferov, Russian Air Force Military Educational, Y. Gagarin, S. Panferov, А.М. Hayutin, N. A. Trenin
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Abstract

To ensure safety and improve the efficiency of flight missions, reliable information about the altitude and speed parameters of the aircraft (AC) is required. Therefore, improving the algorithm for calculating the vertical speed used as part of the algorithmic support for air signal systems (ASS) is a very urgent task. Purpose of the study. The problem of calculating the vertical speed of an aircraft in the ASS is considered. Materials and methods. The analysis of literature data on the use of numerical differentiation procedures to solve this problem is carried out, it is noted that the methods used are based on different ideas and approaches. It is indicated that two-point algorithms are significantly worse than multi-point algorithms in terms of the achieved accuracy, howe¬ver, they are characterized by significant simplicity and speed. Various versions of multipoint algorithms are used, differing in complexity, the amount of information used, and the accuracy achieved. The features of the regularizing algorithms, which are essentially filters of a low-frequency useful signal, suppressing the high-frequency component of the error in measuring the altitude signal or, what is the same, atmospheric pressure, are noted. The data on systems with hardware differentiation of the height signal are given. Results. A fairly simple four-point algorithm for numerical differen¬tiation is proposed and substantiated. Due to the averaging of both the measurement results themselves and the estimates of the derivatives, significant filtering of noise is realized, which is an important advantage of the algorithm. For greater accuracy in estimating the vertical speed, it is envisa¬ged to include a preliminary filtering algorithm in the experimental data processing scheme. The filtering algorithm is found from the solution of the optimization problem; it is shown that this algorithm is structurally similar to the filtering algorithms constructed according to the well-known approaches of R. Kalman. The results of computational experiments on the study of the features and characteristics of the proposed algorithms are presented, illustrating their advantages, performance and the possibility of further use in ASS. It is shown that preliminary filtering significantly increases the accuracy of the vertical velocity estimation. Conclusion. The developed algorithms can be used to improve the algorithmic support of the ASS.
飞机垂直速度计算中数值问题微分的一种解
为了确保飞行任务的安全和提高飞行任务的效率,需要可靠的飞机高度和速度参数信息。因此,改进用于空中信号系统(ASS)算法支持的垂直速度计算算法是一项非常紧迫的任务。研究目的:研究了飞行器在空中垂直飞行速度的计算问题。材料和方法。对文献数据的分析利用数值微分程序来解决这一问题,需要注意的是,所使用的方法是基于不同的思想和途径。结果表明,两点算法在精度上明显低于多点算法,但在简单性和速度上明显优于多点算法。使用了各种版本的多点算法,其复杂性、所使用的信息量和所达到的精度各不相同。注意到正则化算法的特点,它本质上是低频有用信号的滤波器,抑制测量高度信号或相同的大气压力时误差的高频成分。给出了高度信号硬件微分系统的数据。结果。提出并验证了一种较为简单的四点数值微分算法。由于测量结果本身和导数估计的平均,实现了对噪声的显著滤除,这是该算法的一个重要优点。为了更准确地估计垂直速度,设想在实验数据处理方案中包括一个初步滤波算法。从优化问题的解中找到滤波算法;结果表明,该算法在结构上与根据著名的卡尔曼方法构造的滤波算法相似。通过计算实验对所提算法的特点和特点进行了研究,说明了所提算法的优点、性能和在自动导航系统中进一步应用的可能性。结果表明,初步滤波显著提高了垂直速度估计的精度。结论。所开发的算法可用于提高自动识别系统的算法支持度。
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