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

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.