Deflected Rectangular Information Granulation Method and Its Application in Satellite Attitude Time-Series Analysis

Objectives: Conventional axis-parallel rectangular information granules are widely adopted in granular computing for time-series representation. Nevertheless, such granules generate redundant covered regions when describing data clusters with oblique correlation distributions, which degrades the specificity of granular representation and further impairs time-series similarity measurement. Aiming at this drawback, this paper proposes a deflected rectangular information granulation method grounded on the principle of justifiable granularity. The proposed approach is further applied to similarity analysis of real satellite attitude angular-velocity time-series. It expects to improve the description fidelity for obliquely-distributed two-dimensional feature points (original time-series paired with its first-order difference), and provide a feasible granular-computing tool for satellite attitude data mining, periodic pattern comparison and auxiliary data-quality evaluation. Methods: First, raw one-dimensional time-series is transformed into two-dimensional feature samples constructed by original sequence values and their first-order differences. The overall main distribution direction of point-set is estimated via least-squares linear fitting to obtain the optimal deflection angle. Coordinate rotation is performed so that data clusters are aligned with rectangle boundaries. Under the principle of justifiable granularity which balances coverage and specificity, deflected rectangular information granules are optimized in the rotated coordinate system. Fuzzy C-means clustering is utilized for multi-granule segmentation over long time-series, and the optimal granule number is determined according to the sum of granule volumes. A grid-sampling approximation strategy is designed to calculate granule area and overlapping area, and a symmetric similarity metric is defined for pairwise time-series comparison. Validations are carried out on five public UCR time-series datasets, and real measured star-sensor angular-velocity data from an in-orbit satellite is adopted for practical application verification. Results: Comparative experiments on UCR datasets including Synthetic Control, CBF, Coffee, Olive Oil and Haptics demonstrate that the deflected rectangular granules produce more compact coverage. In total 80 % of test groups achieve larger granule-volume sum compared with traditional axis-parallel rectangular granulation. For samples from identical classes, similarity values calculated by the proposed method are higher; for samples of different classes, the obtained similarity values are lower, showing enhanced discriminative capability for time-series categories. In satellite-attitude experiments, 16-time windows corresponding to approximate orbital cycles are segmented from real X-axis angular-velocity observations. The similarity matrix computed by deflected rectangular granules successfully reveals the intra-orbit-cycle consistency and local disturbance differences of satellite attitude motion. High-similarity and low-similarity window pairs can be effectively distinguished through granular visualization. Conclusions: The proposed deflected rectangular information granulation breaks the axis-parallel limitation of classic rectangular granules, and improves the specificity of granular representation for obliquely-distributed two-dimensional time-series feature points. It achieves better performance on time-series similarity measurement. The method can characterize periodic changing patterns from satellite attitude time-series and support auxiliary analysis for space-borne measurement data. Future work will focus on extending this framework to high-dimensional deflected hyper-boxes and implementing joint multi-axis similarity evaluation for complete satellite attitude sequences.