Correction method for pointing error of biaxial rotation system based on spherical crown function

Abstract

The invention discloses a correction method for a pointing error of a biaxial rotation system based on a spherical crown function. The method comprises the steps: error collection by selecting fixed stars or radio sources which are uniformly distributed all day long from a star catalogue for tracking observation, obtaining the theoretical and measurement positions of the fixed stars, subtracting the theoretical positions from the measurement positions, and obtaining error distribution; error model fitting by selecting an appropriate orthogonal spherical crown function model for the obtained error distribution, performing fitting, and calculating an error fitting coefficient; and error control compensation by putting the error model and a related fitting coefficient into a pointing controlsystem for compensation. The orthogonal spherical crown function model comprises a hemispherical harmonic function HSH, a Zernike spherical crown function ZSF and a longitudinal spherical crown function LSF. By adopting the method, the model is high in stability and is not easily influenced by measurement noise; the form of the model does not need to be determined according to the frame form of the telescope, and the correction precision is high.

Description

technical field [0001] The invention belongs to the field of precise positioning and pointing, and specifically relates to a pointing error correction of a dual-axis rotating system, including error collection, and a method for modeling and correcting distribution errors using spherical cap functions. Background technique [0002] "Double-axis rotation system" has many applications in practical engineering. For example, the azimuth rotation axis and the altitude rotation axis of the horizon-type optical (radio) telescope, photoelectric theodolite constitute a dual-axis rotation system, and the double swing on the CNC five-axis processing machine tool The milling head is also a typical two-axis rotary system. Due to machining accuracy, assembly error, etc., there will always be a certain difference between the pointing reading of the dual-axis rotating system and the ideal position, which is the pointing error. The pointing error has a great influence on the performance of t...

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Problems solved by technology

[0005] (2) Data compression: Use tables to record the positions and values ​​of all error measurements. This table method has a large amount of data, and there is no unified expression due to the difference in the number and distribution of test data, which is extremely inconvenient to use

[0007] (1) Spherical harmonic function model: The spherical harmonic function is a complete set of orthogonal functions on the entire spherical surface. Since the pointing range of the two-axis rotation system only covers a part of the spherical surface (spherical cap), the normal equation used when fitting the model parameters Large condition number, poor stability, susceptible to measurement noise

[0008] (2) Basic parameter model: Compared with the spherical harmonic function model, the calculation is relatively stable, but the form of the model needs to be determined according to the form of the telescope frame, and the number of parameter items considered is relatively small, which will affect the accuracy of the correction;

[0009] (3) Rack model: it is an extension of the basic parameter model, with high precision, but the disadvantage is that it is not as stable as the basic parameter model

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