发表机构
School of Mechanical Engineering (FEM), University of Campinas (UNICAMP); Institute of Science and Technology (ICT), Federal University of São Paulo (UNIFESP); Department of Statistics, Institute of Mathematics, Statistics and Scientific Computing (IMECC), University of Campinas (UNICAMP)（坎皮纳斯大学机械工程学院; 圣保罗联邦大学科学技术研究所; 坎皮纳斯大学数学、统计与科学计算研究所统计学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出HIAR四元数模型处理不规则多光谱时间序列，通过卡尔曼滤波估计，在Sentinel-2数据上验证了其计算可行性，并能生成与森林边缘相关的持续性等描述符。
AI 中文摘要
我们提出了超复数不规则自回归（HIAR）模型，这是IAR/CIAR/BIAR族在四分量不规则时间观测上的四元数扩展。时间依赖性通过四元数参数的实数幂表示，并在状态空间形式下，以卡尔曼滤波的高斯创新似然为条件，基于所采用的协方差设定进行估计。在12,000次蒙特卡洛拟合中，平均绝对偏差随样本量增加而减小，在N=300时范围为0.0009至0.0023。我们将该模型应用于2020年至2023年间覆盖Mata de Santa Genebra ARIE的30,824个Sentinel-2像素序列。优化器在98.73%的拟合中报告了成功的数值终止；中位数||Φ̂||为0.6248，3,872个像素达到了高持续性操作阈值（||Φ̂||≥0.95），B8波段残差RMSE的中位数为5.1551个百分点。结果证明了HIAR的计算可行性及其生成多光谱持续性、向量动态、预测误差和可能与森林边缘相关的空间不连续性描述符的能力。
英文摘要
We propose the Hypercomplex Irregular Autoregressive (\HIAR) model, a quaternion extension of the \IAR/\CIAR/\BIAR{} family for four-component observations at irregular times. Temporal dependence is represented by a real power of a quaternion parameter and estimated in state-space form through the Gaussian innovation likelihood of the Kalman filter, conditional on the adopted covariance specifications. Across 12,000 Monte Carlo fits, mean absolute bias decreased with sample size and ranged from 0.0009 to 0.0023 at $N=300$. We applied the model to 30,824 Sentinel-2 pixel series covering the Mata de Santa Genebra ARIE from 2020 to 2023. The optimizer reported successful numerical termination in 98.73\% of the fits; the median $\|{\Phihat}\|$ was 0.6248, 3,872 pixels met the operational high-persistence threshold ($\|{\Phihat}\}\geq0.95$), and the median residual RMSE for band B8 was 5.1551 percentage points. The results demonstrate the computational feasibility of \HIAR{} and its ability to generate descriptors of multispectral persistence, vector dynamics, predictive error, and spatial discontinuities potentially associated with forest edges.
