Mapped Least Squares Support Vector Machine (MLS-SVM) And Its Application In Celestial Navigation

The objective of this paper is to develop support vector machine (SVM) methods, to extend application of SVM to image processing, and to improve performance and stability of star tracker. To realize these objectives, the researches are mainly carried out in algorithm and experiment aspects. The deep studies have been made to further extend application of SVM to pixel-level image processing and improve performance and stability of modern star tracker, which include: (a) mapped least squares support vector machine (MLS-SVM) theory and its application; (b) a novel star acquisition algorithm, extremal point algorithm; (c) an automatic dynamic visual magnitude threshold (DVMT) selection algorithm of guide star; (d) an automatic dynamic label visual magnitude threshold (DLVMT) optimization algorithm of guide star triplets; (e) a new star pattern recognition algorithm, B-vector algorithm. The studies are listed as follows in detail. (1) A novel version of regression SVM, MLS-SVM theory and its application, is proposed. It is shown that the solution of this optimization problem can be obtained easily once the inverse of a certain matrix is computed. This matrix, however, depends only on the input vectors, but not on the labels. Thus, if many learning problems with the same set of input vectors but different sets of labels have to be solved, it makes sense to compute the inverse of the matrix just once and then use it for computing all subsequent models. The computational requirements to train an regression SVM can be reduced to O(N2), just a matrix multiplication operation, and thus probably faster than known SVM training algorithms that have O(N2) work with loops. The characteristic of MLS-SVM and weighted MLS-SVM method are studied. The characteristic of MLS-SVM is investigated by analyzing the frequency responses of the MLS-SVM filters. The MLS-SVM decomposes an image into low frequency components and finest details at high frequencies, and the support values correspond to the high-frequency content. The analysis of the MLS-SVM with Gaussian kernel illustrates that the optimal configuration of the parameter σ2 exists and the regulation constant γis directly determined by the frequency content of the image. Prior information (e.g., local dominant orientation) are incorporated in a two dimension weighted function. Applications in image processing including image interpolation and edge detection, etc, are described. (2) An MLS-SVM based star acquisition method, extremal point approach, is proposed. The efficient star cluster grouping method is based on MLS-SVM with mixtures of radial basis function and polynomial kernels. By convolving star image with the second order directional derivative operators deduced from the MLS-SVM, the maximal extremum points (the possible center of stars) on the two-dimensional star image intensity surface are reliably determined, and then the star cluster grouping process in star acquisition procedure is significantly speeded up. For simulated star image, where the exact location of stars is known, the average sum of invert square distance between a declared star center and the nearest ideal star center, as the merit figure of star acquisition algorithms, is calculated under different noisy conditions, which is applied to optimize the MLS-SVM parameters. The experimental results demonstrate that the proposed approach is better than or near equal to the Motari's method in efficiency and merit when the noisy level is not too high. (3) A DVMT selection algorithm of guide star is proposed. With the creation of distribution function of the DVMT, the static VMT in the traditional visual magnitude filtering method is replaced by the DVMT. The experimental results demonstrate that the identified guide star catalog has fewer total numbers, smaller catalog size and better distribution uniformity. As a powerful method, it also flexibly meets different tasks. (4) A DLVMT selection method of on-board star triplet is proposed. By defining the label visual magnitude and the direction of the star triplet, the star triplet distribution is analyzed. The optimal star triplet database can be obtained by using the triplet filtering method with the DLVMT. The results demonstrate that the optimized triplet database has fewer total numbers, smaller database size and better distribution uniformity. (5) B-vector algorithm, an autonomous star pattern recognition algorithm, which is a sophistication of the search-less idea based on triangular index matching, is proposed. Once the measurement error of the angle separation between neighboring stars is removed out ahead of the matching process, and the E-vector star-triplet database and the corresponding B-vector are constructed, the determination of the admissible star triplets is a search-less process and the identification of validate stars is very fast. The experimental results demonstrate that the proposed algorithm is efficient and robust.