Research on rational function model for Tianhui-2 bistatic imaging geometry

doi:10.11947/j.AGCS.2026.20260075

Abstract

Abstract:

This study investigates a three-equation rational function model (RFM) for the bistatic imaging geometry of the Tianhui-2 (TH-2) satellite system. We rigorously derive both forward and inverse RFM formulations and design the least-squares-based RFM parameter solution method. Departing from the conventional two-equation RFM, our formulation incorporates an interferometric phase equation, achieving a two-way precise mapping between image-space observations (azimuth coordinate, range coordinate, and interferometric phase) and geodetic coordinates (latitude, longitude, and height). Experimental validation is conducted using 6 independent TH-2 bistatic imaging InSAR datasets. The results the proposed three-equation RFM can accurately fit the strict imaging model. The geocoding experiments further verified the practicality of the model.

Key words: Tianhui-2, bistatic imaging, rational function model, interferometric phase

CLC Number:

P237

Xin Xiong, Guowang Jin, Jiahao Li, Hao Ye, Le Yang. Research on rational function model for Tianhui-2 bistatic imaging geometry[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(9): 1599-1611.

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http://xb.chinasmp.com/EN/Y2026/V55/I9/1599

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数据	区域	场景类型	获取时间	主图像采样间隔/（m×m）	主图像大小/（像素×像素）
1	廊坊地区	平地	2020-05-05	2.05×0.94	19 902×21 910
2	廊坊地区	平地	2024-08-01	2.00×0.94	18 098×21 642
3	郑州地区	半山地	2019-10-14	1.88×0.94	19 414×23 014
4	郑州地区	半山地	2024-03-01	1.74×0.94	20 767×20 890
5	丽江地区	山地	2024-09-12	1.52×0.94	21 044×18 760
6	丽江地区	山地	2024-09-12	1.52×0.94	28 340×18 760

格网大小	方位向RMSE/像素	方位向MAE/像素	距离向RMSE/像素	距离向MAE/像素	相位RMSE/rad	相位MAE/rad	计算耗时/s
10×10	2.426×10^-9	1.234×10^-8	1.446×10^-7	7.279×10^-7	5.809×10^-7	2.507×10^-6	0.009
15×15	2.451×10^-9	1.115×10^-8	1.418×10^-7	5.797×10^-7	5.299×10^-7	1.958×10^-6	0.015
20×20	2.451×10^-9	1.124×10^-8	1.454×10^-7	6.095×10^-7	5.902×10^-7	2.520×10^-6	0.024
25×25	2.626×10^-9	1.256×10^-8	1.505×10^-7	8.357×10^-7	6.183×10^-7	2.297×10^-6	0.035
30×30	2.790×10^-9	1.512×10^-8	1.590×10^-7	7.410×10^-7	6.613×10^-7	2.979×10^-6	0.050
35×35	2.874×10^-9	1.594×10^-8	1.577×10^-7	7.109×10^-7	6.811×10^-7	3.274×10^-6	0.064
40×40	2.959×10^-9	1.977×10^-8	1.615×10^-7	7.704×10^-7	6.914×10^-7	3.267×10^-6	0.082
45×45	2.984×10^-9	1.671×10^-8	1.685×10^-7	8.726×10^-7	7.117×10^-7	3.400×10^-6	0.104
50×50	3.030×10^-9	1.701×10^-8	1.662×10^-7	8.845×10^-7	7.236×10^-7	3.837×10^-6	0.128

格网大小	经度RMSE/（°）	经度MAE/（°）	纬度RMSE/（°）	纬度MAE/（°）	高程RMSE/m	高程MAE/m	计算耗时/s
10×10	2.421×10^-11	1.230×10^-10	1.094×10^-11	3.592×10^-11	1.941×10^-5	7.552×10^-5	0.013
15×15	2.273×10^-11	7.213×10^-11	1.203×10^-11	4.651×10^-11	1.926×10^-5	8.671×10^-5	0.016
20×20	2.604×10^-11	1.079×10^-10	1.298×10^-11	4.744×10^-11	1.962×10^-5	6.730×10^-5	0.025
25×25	2.725×10^-11	1.068×10^-10	1.384×10^-11	5.412×10^-11	2.164×10^-5	9.577×10^-5	0.038
30×30	2.919×10^-11	1.305×10^-10	1.458×10^-11	7.249×10^-11	2.303×10^-5	1.045×10^-4	0.052
35×35	2.971×10^-11	1.413×10^-10	1.481×10^-11	7.088×10^-11	2.351×10^-5	1.140×10^-4	0.069
40×40	3.002×10^-11	1.385×10^-10	1.471×10^-11	8.014×10^-11	2.381×10^-5	1.119×10^-4	0.088
45×45	3.109×10^-11	1.510×10^-10	1.523×10^-11	8.314×10^-11	2.437×10^-5	1.221×10^-4	0.111
50×50	3.135×10^-11	1.678×10^-10	1.550×10^-11	9.701×10^-11	2.483×10^-5	1.418×10^-4	0.141

方案	方位向RMSE/像素	距离向RMSE/像素	相位RMSE/rad	计算耗时/s
叠加平地相位	2.451×10^-9	1.418×10^-7	5.299×10^-7	0.015
不叠加平地相位	2.451×10^-9	1.418×10^-7	32.17	0.015

数据	场景类型	方位向RMSE/像素	距离向RMSE/像素	相位RMSE/rad	计算耗时/s
1	平地	3.727×10^-9	5.410×10^-8	2.581×10^-7	0.015
2	平地	3.132×10^-9	4.072×10^-8	1.955×10^-7	0.015
3	半山地	4.938×10^-10	6.883×10^-8	5.799×10^-7	0.016
4	半山地	3.521×10^-9	4.054×10^-8	3.247×10^-7	0.014
5	山地	3.306×10^-9	1.875×10^-7	7.991×10^-7	0.015
6	山地	5.288×10^-10	4.593×10^-7	1.022×10^-6	0.014