Improved Local Linear Regression Estimator and Its Application to Estimation for Radar Altimeter Sea State Bias
JIANG Maofei①②③ XU Ke①② LIU Yalong④ WANG Lei①②
①(Key Laboratory of Microwave Remote Sensing, Chinese Academy of Sciences, Beijing 100190, China) ②(National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China) ③(University of Chinese Academy of Sciences, Beijing 100049, China) ④(Yantai Marine Environmental Monitoring Center Station, State Oceanic Administration, Yantai 264000, China)
在建立雷达高度计海况偏差(Sea State Bias, SSB)非参数模型时，通常会用到局部线性回归(Local Linear Regression, LLR)估计器，而传统的局部线性回归估计器涉及高维矩阵运算，当建模的数据量较大时，估计海况偏差需要大量的时间，从而使得非参数估计方法很难用于高维海况偏差模型。该文提出一种改进的局部线性回归(Improved Local Linear Regression, ILLR)估计器，可以避免传统的LLR估计器所需的高维矩阵运算，在不影响海况偏差估计结果的条件下，将局部线性回归估计器获取加权函数的时间复杂度由O(N2)降低为O(N)，从而大幅地降低估计海况偏差所需的时间，为实现高维非参数海况偏差模型的实时运算奠定了基础。
The Local Linear Regression (LLR) estimator is usually used when developing a nonparametric model for radar altimeter Sea State Bias (SSB). However, the conventional LLR estimator contains matrices with high dimension. When a large number of data are used to develop the SSB model, the SSB estimation costs too much time. Therefore, the nonparametric estimation method can hardly be used to develop high-dimensional SSB models. This paper presents an Improved LLR (ILLR) estimator, complexity from O(N2) to O(N) which can avoid high-dimensional matrix operations. The improved LLR estimator can greatly reduce the time for SSB estimation without affecting the estimated accuracy. So the improved LLR estimator can laid the foundation for high-dimensional SSB models.
蒋茂飞,许可,刘亚龙,王磊. 一种改进的局部线性回归估计器及其在雷达高度计海况偏差估计中的应用[J]. 电子与信息学报, 2016, 38(9): 2314-2320.
JIANG Maofei, XU Ke, LIU Yalong, WANG Lei. Improved Local Linear Regression Estimator and Its Application to Estimation for Radar Altimeter Sea State Bias. JEIT, 2016, 38(9): 2314-2320.
WANG L. Study on the data processing for high precision satellite radar altimeter[D]. [Ph.D. dissertation], National Space Science Center, Chinese Academy of Sciences, 2015.
WANG L, XU K, SHI L W, et al. A new range migration correction algorithm and its simulation for SAR altimeter[J]. Journal of Electronics & Information Technology, 2015, 37(11): 2713-2718. doi: 10.11999/JEIT150282.
LIU Y L. Calibration technology for HY-2 radar altimeter sea surface height[D]. [Ph.D. dissertation], Ocean University of China, 2014.
[4]
GASPAR P, OGOR F, LETRAON P Y, et al. Estimating the sea-state bias of the topex and poseidon altimeters from crossover differences[J]. Journal of Geophysical Research- Oceans, 1994, 99(C12): 24981-24994. doi: 10.1029/ 94JC01430.
[5]
PRANDI P, PHILIPPS S, PIGNOT V, et al. SARAL/AltiKa global statistical assessment and cross-calibration with Jason-2[J]. Marine Geodesy, 2015, 38(10): 297-312. doi: 10.1080/01490419.2014.995840.
[6]
TRAN N, VANDEMARK D, CHAPRON B, et al. New models for satellite altimeter sea state bias correction developed using global wave model data[J]. Journal of Geophysical Research-Oceans, 2006, 111(C9): 141-152. doi: 10.1029/2005JC003406.
[7]
BONNEFOND P, EXERTIER P, LAURAIN O, et al. SARAL/AltiKa absolute calibration from the multi-mission corsica facilities[J]. Marine Geodesy, 2015, 38(10): 171-192. doi: 10.1080/01490419.2015.1029656.
[8]
GASPAR P and FLOREANS J P. Estimation of the sea state bias in radar altimeter measurements of sea level: Results from a new nonparametric method[J]. Journal of Geophysical Research-Oceans, 1998, 103(C08): 15803-15814. doi: 10.1029/ 98JC01194.
[9]
CHELTON D B. The sea-state bias in altimeter estimates of sea-level from collinear analysis of topex Data[J]. Journal of Geophysical Research-Oceans, 1994, 99(C12): 24995-25008. doi: 10.1029/94JC02113.
[10]
GASPAR P, LABROUE S, OGOR F, et al. Improving nonparametric estimates of the sea state bias in radar altimeter measurements of sea level[J]. Journal of Atmospheric and Oceanic Technology, 2002, 19(10): 1690-1707. doi: 10.1175/ 1520-0426(2002)019<1690:INEOTS>2.0.CO;2.
[11]
WANG J X and XIAO Q X. Local polynomial estimation of time-dependent diffusion parameter for discretely observed SDE models[J]. Filomat, 2014, 28(4): 871-878. doi: 10.2298/ FIL1404871W.
[12]
SU L and ULLAH A. Local polynomial estimation of nonparametric simultaneous equations models[J]. Journal of Econometrics, 2008, 144(1): 193-218. doi: 10.1016/j.jeconom. 2008.01.002.
[13]
DETTMERING D, SCHWATKE C, and BOSCH W. Global calibration of SARAL/AltiKa using multi-mission sea surface height crossovers[J]. Marine Geodesy, 2015, 38(10): 206-218. doi: 10.1080/01490419.2014.988832.
[14]
PAIGE C C and SAUNDERS M A. LSQR: an algorithm for sparse linear-equations and sparse least-squares[J]. ACM Transactions on Mathematical Software, 1982, 8(1): 43-71. doi: 10.1145/355984.355989.
[15]
FONG D C L and SAUNDERS M. LSMR: An iterative algorithm for sparse least-squares problems[J]. SIAM Journal on Scientific Computing, 2010, 33(5): 2950-2971. doi: 10.1137 /10079687X.
[16]
TRAN N, VANDEMARK D, LABROUE S, et al. Sea state bias in altimeter sea level estimates determined by combining wave model and satellite data[J]. Journal of Geophysical Research-Oceans, 2010, 115(C03020): 1-7. doi: 10.1029/ 2009JC005534.
[17]
FENG H, YAO S, LI L Y, et al. Spline-based nonparametric estimation of the altimeter sea-state bias correction[J]. IEEE Geoscience and Remote Sensing Letters, 2010, 7(3): 577-581. doi: 10.1109/LGRS.2010.2041894.
