SWOT/KaRIn测高数据的联合沿轨-跨轨交叉点平差

doi:10.11947/j.AGCS.2026.20260122

测绘学报 ›› 2026, Vol. 55 ›› Issue (7): 1199-1211.doi: 10.11947/j.AGCS.2026.20260122

• 大地测量学与导航 • 上一篇

SWOT/KaRIn测高数据的联合沿轨-跨轨交叉点平差

刘新¹(), 押少帅¹(), 范鑫¹, 贾永君², 常晓涛³, 朱广彬³, 郭金运¹

^1.山东科技大学测绘与空间信息学院，山东　青岛　266590
^2.国家卫星海洋应用中心，北京　100081
^3.自然资源部国土卫星遥感应用中心，北京　100048

收稿日期:2026-04-02 修回日期:2026-07-08 发布日期:2026-08-18
通讯作者: 押少帅 E-mail:xinliu1969@126.com;13526663057@163.com
作者简介:刘新（1969—），女，博士，教授，研究方向为空间数据挖掘和机器学习。 E-mail：xinliu1969@126.com
基金资助:
国家自然科学基金(42430101; 42274006; 42374041)

Joint along-track and cross-track crossover adjustment of SWOT/KaRIn altimetry data

Xin Liu¹(), Shaoshuai Ya¹(), Xin Fan¹, Yongjun Jia², Xiaotao Chang³, Guangbin Zhu³, Jinyun Guo¹

^1.College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China
^2.National Satellite Ocean Application Service, Beijing 100081, China
^3.Land Satellite Remote Sensing Application Center, Ministry of Natural Resources, Beijing 100048, China

Received:2026-04-02 Revised:2026-07-08 Published:2026-08-18
Contact: Shaoshuai Ya E-mail:xinliu1969@126.com;13526663057@163.com
About author:Liu Xin (1969—), female, PhD, professor, majors in spatial data mining and machine learning. E-mail: xinliu1969@126.com
Supported by:
The National Natural Science Foundation of China(42430101; 42274006; 42374041)

摘要/Abstract

摘要：

本文提出一种SWOT/KaRIn测高数据联合沿轨-跨轨交叉点平差方法，以提高SWOT海面高数据质量。该方法采用混合多项式模型对沿轨方向与时间相关的误差进行改正，并利用线性模型对跨轨方向与地理相关的误差进行补偿。以日本周边海域（130°E—145°E，27°N—43°N）为试验区域，采用科学阶段SWOT/KaRIn L2级的海面高产品（L2_LR_SSH）第003周期的数据进行平差方法测试。利用沿轨傅里叶模型、沿轨混合多项式模型、沿轨混合多项式模型+跨轨傅里叶模型和沿轨混合多项式模型+跨轨线性模型4种方法对SWOT/KaRIn海面高数据进行了自交叉点平差解算。结果表明：当仅对沿轨方向进行交叉点平差时，沿轨混合多项式模型交叉点不符值精度要高于沿轨傅里叶模型；加入跨轨方向的平差后，沿轨混合多项式模型+跨轨线性模型的交叉点不符值标准差（STD）最小，在沿轨和跨轨方向分别为4.27和3.62 cm。为了评估该方法的普适性，采用Sentinel-6A和Jason-3海面高数据与SWOT海面高数据进行了互交叉点平差。结果表明，沿轨混合多项式模型+跨轨线性模型平差后互交叉点不符值的精度最优，而且该方法不等权的精度优于等权的精度。因此，联合沿轨-跨轨方向交叉点平差可以显著提高SWOT海面高的数据质量，为海洋重力场研究提供高质量的数据源。

关键词: 交叉点平差, 海面高, SWOT测高卫星, 交叉点不符值, 沿轨-跨轨

Abstract:

This study proposes a joint along-track and cross-track crossover adjustment method for SWOT/KaRIn altimetry data to enhance the quality of sea surface heights (SSHs). The approach employs a hybrid polynomial model to correct time-dependent errors along-track and a linear model to compensate for geographically correlated errors across-track. Validation was conducted in the sea region around Japan (130°E—145°E, 27°N—43°N) using scientific-phase Level 2 Ka-band Radar Interferometer low-rate SSH products (L2_LR_SSH) from cycle 003. Four adjustment schemes were tested: along-track Fourier model, along-track hybrid polynomial model, along-track hybrid polynomial model+cross-track Fourier model, and along-track hybrid polynomial model+cross-track linear model. Results indicate that, for along-track-only adjustment, along-track hybrid polynomial model yields higher accuracy in reducing crossover discrepancies compared to along-track Fourier model. Incorporating cross-track adjustment, along-track hybrid polynomial model+cross-track linear model achieves the lowest standard deviation (STD) of crossover discrepancies, measuring 4.27 cm along-track and 3.62 cm cross-track. To assess generalizability, external crossover adjustments were performed between SWOT and reference missions (Sentinel-6A and Jason-3). Along-track hybrid polynomial model+cross-track linear model consistently delivers optimal accuracy post-adjustment, with unequal weighting proving superior to equal weighting. These findings demonstrate that joint along-track and cross-track crossover adjustment significantly improves SWOT SSH data quality, providing a robust dataset for marine gravity field research.

Key words: crossover adjustment, sea surface height, SWOT altimetry satellite, crossover discrepancies, along-track and cross-track

中图分类号:

P228

刘新, 押少帅, 范鑫, 贾永君, 常晓涛, 朱广彬, 郭金运. SWOT/KaRIn测高数据的联合沿轨-跨轨交叉点平差[J]. 测绘学报, 2026, 55(7): 1199-1211.

Xin Liu, Shaoshuai Ya, Xin Fan, Yongjun Jia, Xiaotao Chang, Guangbin Zhu, Jinyun Guo. Joint along-track and cross-track crossover adjustment of SWOT/KaRIn altimetry data[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(7): 1199-1211.

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链接本文: http://xb.chinasmp.com/CN/10.11947/j.AGCS.2026.20260122

http://xb.chinasmp.com/CN/Y2026/V55/I7/1199

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测高卫星	轨道高度/km	轨道倾角/（°）	发布机构	测高任务	重复周期/d	观测时间	周期
Sentinel-6A	1 336	66	ESA	ERM	10	2023-08-26—2023-09-24	103～105
Jason-3	1 336	66	ESA	ERM	10	2023-08-28—2023-09-26	350～351
SWOT	890	77.6	NASA	ERM	21	2023-08-31—2023-09-21	003

交叉点个数	模型形式	k取值	模型参数个数
1	平均分配交叉点不符值	0	0
2～3	只选用误差模型线性部分	0	2
4～5	线性方程与一级傅里叶级数结合	1	4
6～8	线性方程与二级傅里叶级数结合	2	6
>8	线性方程与三级傅里叶级数结合	3	8

统计量	平差前	沿轨傅里叶模型	沿轨混合多项式模型	沿轨混合多项式模型+跨轨傅里叶模型	沿轨混合多项式模型+跨轨线性模型
Max	86.93	82.26	72.29	81.64	62.33
Min	－55.54	－53.31	－53.35	－55.75	－51.38
Mean	－1.15	－0.04	0.05	0.07	0.02
STD	8.47	6.32	6.08	6.57	4.27
RMS	8.55	6.32	6.08	6.57	4.27

范围绝对值/cm	平差前		沿轨傅里叶模型		沿轨混合多项式模型		沿轨混合多项式模型+跨轨傅里叶模型		沿轨混合多项式模型+跨轨线性模型
范围绝对值/cm	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）
<5	7 7312	55.73	99 756	71.91	10 0872	72.72	98 482	70.99	116 853	84.23
[5，10）	37 153	36.78	24 548	17.69	24 432	17.61	25 207	18.17	17 110	12.33
[10，20）	18 732	13.50	11 364	8.19	10 792	7.78	12 499	9.01	4 330	3.12
[20，30）	4448	3.21	2699	1.94	2384	1.72	2132	1.53	331	0.24
≥30	1072	0.77	350	0.25	237	0.17	397	0.28	93	0.06

统计量	平差前	沿轨傅里叶模型	沿轨混合多项式模型	沿轨混合多项式模型+跨轨傅里叶模型	沿轨混合多项式模型+跨轨线性模型
Max	46.78	39.05	36.34	38.24	26.83
Min	－36.91	－33.72	－33.64	－40.64	－29.57
Mean	－0.98	－0.23	0.07	0.17	0.11
STD	8.20	6.34	6.13	6.35	3.62
RMS	8.26	6.35	6.13	6.35	3.62

SWOT/KaRIn测高数据的联合沿轨-跨轨交叉点平差

Joint along-track and cross-track crossover adjustment of SWOT/KaRIn altimetry data

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交叉点平差方法	交叉点数量	Max	Min	Mean	RMS	STD
平差前	16 202	48.36	－49.85	－3.78	9.69	8.92
沿轨傅里叶模型	16 202	47.69	－48.07	－1.92	7.71	7.47
沿轨混合多项式模型	16 202	43.76	－48.30	－1.04	7.48	7.25
等权沿轨混合多项式模型+跨轨线性模型	16 202	42.87	－49.07	－0.31	6.95	6.89
不等权沿轨混合多项式模型+跨轨线性模型	16 202	40.72	－47.93	－0.09	6.45	6.45

交叉点平差方法	交叉点数量	Max	Min	Mean	RMS	STD
平差前	16 072	49.18	－47.76	－4.42	10.42	9.44
沿轨傅里叶模型	16 072	44.88	－40.37	－2.23	8.42	8.12
沿轨混合多项式模型	16 072	48.31	－44.11	－2.17	8.20	7.91
等权沿轨混合多项式模型+跨轨线性模型	16 072	48.69	－41.94	－0.53	7.67	7.61
不等权沿轨混合多项式模型+跨轨线性模型	16 072	47.82	－40.31	－0.02	7.18	7.18

方向	Max	Min	Mean	RMS	STD
沿轨	49.22	－39.22	－0.36	7.75	7.75
跨轨	45.04	－33.26	－0.39	7.69	7.69

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范围绝对值/cm	平差前		沿轨傅里叶模型		沿轨混合多项式模型		沿轨混合多项式模型+跨轨傅里叶模型		沿轨混合多项式模型+跨轨线性模型
范围绝对值/cm	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）
<5	63 324	56.58	81 583	72.89	82 298	73.53	81 298	72.64	97 244	86.89
[5，10）	29 946	26.75	19 067	17.03	19 216	17.17	19 117	17.08	12 052	10.77
[10，20）	14 569	13.01	9055	8.09	8434	7.54	9325	8.33	2588	2.31
[20，30）	3423	3.05	2036	1.82	1853	1.65	1782	1.59	30	0.03
≥30	652	0.58	173	0.15	113	0.10	392	0.35	0	0

范围绝对值/cm	平差前		沿轨傅里叶模型		沿轨混合多项式模型		等权沿轨混合多项式模型+跨轨线性模型		不等权沿轨混合多项式模型+跨轨线性模型
范围绝对值/cm	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）
<5	7343	45.32	9402	58.00	9480	58.50	10 135	62.54	10 549	65.10
[5，10）	4899	30.23	4387	27.06	4449	27.45	4166	25.70	4039	24.92
[10，20）	3241	20.00	2031	12.53	1927	11.89	1627	10.04	1434	8.84
[20，30）	542	3.34	291	1.79	260	1.60	206	1.27	142	0.87
≥30	177	1.09	98	0.60	88	0.54	71	0.43	40	0.24

范围绝对值/cm	平差前		沿轨傅里叶模型		沿轨混合多项式模型		等权沿轨混合多项式模型+跨轨线性模型		不等权沿轨混合多项式模型+跨轨沿轨线性模型
范围绝对值/cm	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）
<5	6947	43.22	8851	55.07	8959	55.74	9668	60.15	10 078	62.70
[5，10）	4742	29.50	4473	27.83	4467	27.79	4145	25.79	3924	24.41
[10，20）	3350	20.84	2106	13.10	2107	13.10	1802	11.21	1732	10.77
[20，30）	773	4.80	534	3.32	429	2.66	379	2.35	290	1.80
≥30	260	1.61	108	0.67	110	0.68	78	0.48	48	0.29