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.
Highlights
One of functions of the system of air signals (ASS) is the problem of calculation of vertical velocity of the aircraft. This problem is solved by method of numerical differentiation of signal of the barometric height determined by ASS
As it is represented to us, and some multipoint algorithms including procedures of averaging in the structure can be carried to regularizing algorithms
It representations is most characteristic of the algorithms of filtration developed with use of approach of Kallman [18, 23], only in this case the optimum value of coefficient of Kallman K is found from the solution of the following problem of optimization: M{ei2} M{(hiИ hiф )2} min, (13)
Summary
One of functions of the system of air signals (ASS) is the problem of calculation of vertical velocity of the aircraft. Where hi – measured signal value in i -ty moment (counting), hiФ – evaluation of the useful signal for i -th point in time (filter output), 1 and 2 – weight coefficients At such value hiФ the minimum of criterion (9) as the second derivative calculated in this point is equal is really reached 2 1 2 2 0. It representations is most characteristic of the algorithms of filtration developed with use of approach of Kallman [18, 23], only in this case the optimum value of coefficient of Kallman K is found from the solution of the following problem of optimization: M{ei2} M{(hiИ hiф )2} min,. The use of algorithms (8) and (11) makes it possible to obtain a completely efficient procedure for estimating the aircraft vertical speed
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