[0034] Specific implementation mode one, combination Figure 1 to Figure 3 In this embodiment, a star pattern recognition method for precision tracking telescopes includes two parts: the first frame recognition method and the continuous frame refresh method.
[0035] The spatial position corresponding to the midpoint of the photo and the initial corresponding fitting parameters obtained by the first frame recognition method are used as the input of the continuous frame refresh algorithm. Among them: the position corresponding to the midpoint of the first frame plus the change of the telescope in each frame relative to the position of the first frame is used as the parameter for the subsequent calculation of the ideal coordinates of the navigation star; the initial corresponding fitting parameters obtain the first fitting correspondence in the second frame , And then update the fitting of this relationship, output the fitting parameters and use it to obtain the corresponding relationship of the next frame.
[0036] In this embodiment, the first frame identification method adopts a table look-up method to speed up the triangle similarity speed. Taking the characteristic relationship as the angular distance as an example, the main steps of the method include:
[0037] 1. Number of observation stars (1 to N 1 ), and set its photo coordinates (a xi , A yi ) Into a photographic vector (a xi ·A, a yi ·A, -F). Calculate every two observation stars (i-th one, traverse 1 to N 1; The jth one, traverse i+1 to N 1 )'S angular distance: Where obs i Is the photographic vector of the i-th observation star. Store the angular distance calculation result as (R ij , I, j). In this way, the observation star pair with the same observation star composition is with Where j 0 ≠j 1;
[0038] 2. Number the navigation star (1 to N 2 ), and set its equatorial coordinates (Ra i , Dec i ) (All expressed in radians), transformed into the celestial sphere vector (cos(Ra i )·Cos(Dec i ), sin(Ra i )·Cos(Dec i ), sin(Dec i )). Use the celestial vector of the navigation star to calculate the angular distance of the navigation star, store it in the way described in the number of the observation star, change the order according to the magnitude of the angular distance, and store it as a navigation star list;
[0039] 3. Scale the angular distance of each observing star pair to a certain error, look up the navigation star table, and get the range index of each observing star in the navigation star table after scaling the diagonal distance.
[0040] 4. Investigate each group of star pairs to be tested. If the following two conditions are met, the comparison is successful.
[0041] According to the two groups of navigation star pairs involved in the two scope indexes, there is a common navigation star, then this common navigation star and its combined star are regarded as a set of candidate navigation star pairs, and its form is one of the following: (R A, B , A, B) and (R A, C , A, C) share A, (R A, B , A, B) and (R B, C , B, C) share B, (R A, C , A, C) and (R B, C , B, C) share C, and save the group of observed star pairs at this time.
[0042] In a certain group of candidate navigation stars, the angular distances composed of different navigation stars (for example, (B, C), (A, C), (A, B) in sequence) (calculated or look-up table), this implementation will try to use Table look-up method) The angular distances of different observation stars in the group of observation star pairs saved in the condition of step 4 are within the range of error scaling.
[0043] 5. Use this group of three observation stars and navigation stars to do linear fitting (the expression is as follows) to obtain fitting parameters.
[0044]
[0045] among them, Linear fitting for the observed meridian (fitting parameter: P 0 ~P 5 ) Obtained fitting coordinates, using fitting parameters (P 0 ~P 5 ) To get the midpoint (x c , Y c ) Corresponding spatial position (cRa, cDec).
[0046] 6. Use the spatial position (cRa, cDec) corresponding to the center point to calculate the ideal coordinates (ζ i , Η i ),
[0047] 7. Parameter fitting obtains the coordinates of the observation star and the ideal coordinates of the navigation star, and obtains the fitting parameter set (ie C 0 ~C 5 ). Its expression is as follows:
[0048]
[0049] 8. Check whether the parameter group meets the ideal coordinate parameter relationship:
[0050] C 1 +C 5 =C 2 -C 4 =0. If it is satisfied, it is used as output, and the navigation star corresponding to the observation star is searched for with this parameter group.
[0051] 9. If it is not satisfied, continue with steps 4 to 8 until all the star pairs to be measured are traversed.
[0052] 10. If all the star pairs to be measured do not meet the conditions, the error will be magnified; after step 11, the navigation star list will be searched again.
[0053] In this embodiment, due to the enlargement of the error, the range of the navigation star catalog found for each group of observation star pairs to be measured is increased: each range can be divided into three parts (a~b), (b~c), (c ~ D), where (b ~ c) is the range that has been compared; (a ~ b) and (c ~ d) are the new ranges added due to error amplification, that is, Δε=ba=dc. When the error is amplified each time, the parts (b~c) of the two star pairs to be measured will not be compared again. In addition, it should be noted that due to the amplification of the error, the calibration error in the original condition will also be enlarged.
[0054] The continuous frame refresh method in this embodiment is based on the above-mentioned fitting parameters, the law of slow changes during the process of changing the telescope pointing, and the parameter refresh method is used to avoid accumulated errors. The main steps of the method include:
[0055] A. The spatial position corresponding to the image center point obtained in the first frame is combined with the change of telescope pointing read from the telescope encoder to obtain the spatial position corresponding to the image center point of the current frame. This position will be used for the calculation of the ideal coordinates of the navigation star in this frame.
[0056] B. Combine the ideal coordinates of the navigation star and the parameter group of the previous frame (for the second frame, this parameter group is the first frame parameter group, for other continuous frames, this parameter group is obtained by the continuous frame refresh method of the previous frame New parameter group) to find the corresponding relationship between the observation star and the navigation star.
[0057] C. According to the corresponding relationship found in step B, do two-point fitting (considering the worst case of the corresponding relationship found by the parameters of the previous frame). The fitting expression is as follows:
[0058]
[0059] The new fitting parameter set (i.e. C 0 ~C 3 ) And the corresponding relationship between the observation star and the navigation star derived from it are the updated parameters and output.
[0060] In this embodiment, although the time requirement of the first frame recognition algorithm is not urgent, the ordinary triangle matching algorithm calculates the three characteristic relationships determined by the three points (for example: angular distance, angle between two sides, etc.), and then group together The time required for the triangle is too long (for example, it takes 4.438s to calculate the correspondence between 39 observation stars and 39 navigation stars), and the data stored by the machine is too large (as in the above example, it takes Storage space). It is difficult to realize automatic error amplification algorithms in subsequent calculations. Modify the algorithm to be the observation star to be measured. For the method of searching the sorted navigation star catalog, the calculation time can be greatly shortened (as in the above example, it takes 0.016 s), and the stored data can also be reduced (as in the above example, the need Storage space).
[0061] In the algorithm implementation process, it is found that the selected comparison error is very important. When the error selection is too small, the algorithm cannot find a matching star pair; when the error selection is too large, a mismatch phenomenon will occur. Therefore, the algorithm introduces a method of step-by-step amplification of errors; and proposes a verification method based on the ideal coordinates of the navigation star, as follows:
[0062]
[0063] Satisfy: C 1 +C 5 =C 2 -C 4 =0.
[0064] Where (ζ i , Η i ) Represents the ideal coordinates of the navigator in the i-th matching pair (see below for details), (x i , Y i ) Represents the photo coordinates of the observation star in the i-th matching pair. And is the pixel size of the camera, and F is the focal length of the telescope system. This verification method ensures the accuracy of the algorithm.
[0065] The calculation method of the ideal coordinates of the navigation star is as follows:
[0066]
[0067] Where (Ra i , Dec i ) Is the right ascension and declination of each navigation star, (cRa, cDec) is the spatial position corresponding to the center of the photo in the current frame.
[0068] The first frame recognition method in this embodiment determines the spatial position corresponding to the center point of the initial image and the initial corresponding fitting parameters of the observation star and the guide star. The continuous frame refresh method continuously refreshes the fitting parameters between the ideal coordinates of the observation star and the guide star in each frame .
[0069] The first frame recognition method is a fast triangle matching algorithm, which uses the feature relationship of the star pair to be measured to scale the error, and the method of searching the navigation star table (such as the dichotomy table) instead of the traditional three stars combined into a triangle , And meet the error matching method one by one. This method greatly reduces the time complexity of calculation.
[0070] The observation star pair to be measured is two groups with the same observation star, and its performance and storage format are for example (R a, b , A, b) and (R a, c , A, c), where a is the same observation star, b and c are different stars in the group, R a, b Represents the characteristic relationship between a and b. In the algorithm implementation, the two observed stars and their characteristic relations are stored according to: The first star traverses all the observed stars with the variable i (ie: 1 to N 1 ), the second star traverses i+1 to N with variable j 1 Observing stars. In this way, the observation star pair to be tested only needs to consider the same situation as the first star in the two groups. This method reduces the loop range and shortens the calculation time.
[0071] The linear fitting method is used to find the spatial position corresponding to the point in the photo, instead of the telescope pointing to calculate the ideal coordinates of the navigator. This method reduces the accuracy requirements for the absolute pointing of the telescope.
[0072] Use the fitting parameter relationship between the ideal coordinates of the observation star and the navigation star to judge whether the group of matches is a mismatch. This method improves the accuracy of the algorithm.
[0073] When the zoom error of the observed star cannot get the correct matching result, the algorithm will expand the error to match until the matching is successful. This method reduces the experience requirement for error selection. While enlarging the error, the algorithm masks out the range in the navigation star catalog that has been searched for each group of observation star pairs; only compares the range in the newly added navigation star catalog after expanding the error. This method reduces the exponential increase in the calculation time after each loop amplification error.
[0074] In this embodiment, the continuous frame refreshing method is a fast and stable coordinate transformation method between the ideal coordinates of the observation star and the navigation star. Applying the observation star photo coordinates to the ideal coordinate transformation parameters of the navigator star, it is insensitive to the change of the telescope pointing to accurately find the correspondence between the observation star and the navigator star in the next frame. In the calculation of subsequent frames, the parameter relationship of the previous frame is used for matching, and the obtained matching pair is used to calculate the new fitting parameters; this parameter refresh method avoids cumulative errors.
[0075] The telescope pointing applied to calculate the ideal coordinates of the navigation star in subsequent frames is the calculated spatial position corresponding to the center of the photo plus the amount of change in the telescope pointing relative to the first frame in each subsequent frame. The relative information of telescope pointing required by this method is easy to obtain, which can greatly increase the calculation speed.
