一种卫星影像RPC参数的HEIV估计方法

doi:10.19665/j.issn1001-2400.2020.02.015

摘要/Abstract

摘要：

由于卫星影像的定位精度主要受卫星影像有理多项式参数的估计精度影响,而现有算法中通常采用像点补偿或利用地面控制点改正的方法,未考虑设计矩阵元素的误差特性,存在系统误差剔除不完全、参数估计精度不高等问题。考虑到模型系统误差的影响,提出了一种异方差估计方法。首先建立了设计矩阵元素的随机模型,对系统特性进行更精准的描述;然后将设计矩阵元素的系统偏差考虑在内,采用马氏距离构建最小二乘模型,并使用广义特征值方法进行参数求解,从理论上降低了模型的系统误差。在天绘一号不同地形影像上的实验结果表明,新算法在影像纠正精度上较传统方法提升36倍以上,且精度一致性优良,对提高有理多项式参数估计和卫星影像定位精度具有重要意义。

关键词: 有理多项式参数, 异方差估计, 马氏距离, 广义特征值

Abstract:

The positioning accuracy of a satellite image is mainly affected by the estimation accuracy of the rational polynomial coefficients (RPCs). Image point compensation or ground control point correction methods are usually used in the existing algorithms. Because the error characteristics of the design matrix elements are not considered, there are problems such as incomplete systematic error elimination and low parameter estimation accuracy. Considering the influence of the model systematic error, a heteroscedastic estimation method is proposed in this paper. First, the random model of matrix elements is established in the algorithm to describe the system characteristics more accurately. Taking into account the system deviations of the design matrix elements, the least square model is constructed using the Mahalanobis distance as the metric, and parameters are solved using the generalized eigenvalue method. The systematic error can be reduced theoretically. Experiment on different terrain images of TH-1 shows that the image correction accuracy of the proposed method is improved by more than 36 times compared with the traditional method, and the precision consistency is superior, which is of great significance to improving the accuracy of RPC parameters estimation and satellite imagery positioning.

Key words: rational polynomial coefficients, heteroscedastic estimation, Mahalanobis distance, generalized eigenvalue

中图分类号:

P236

周瑜,胡莘,曹锴郎,周拥军,李云松. 一种卫星影像RPC参数的HEIV估计方法[J]. 西安电子科技大学学报, 2020, 47(2): 108-117.

ZHOU Yu,HU Xin,CAO Kailang,ZHOU Yongjun,LI Yunsong. Satellite image RPC parameters estimation method using the heteroscedastic errors-in-variables model[J]. Journal of Xidian University, 2020, 47(2): 108-117.

图/表 4

图1

图2

表1

3个区域条带影像有理多项式系数拟合精度对比"

(a)日本庄原平原地区有理多项式系数拟合精度													像素
方向	景号	直接最小二乘			L曲线岭估计最小二乘			截断SVD估计			HEIV模型
方向	景号	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy
前视	1	0.02837	0.00375	0.02861	0.00449	0.02759	0.02795	0.00880	0.00209	0.00905	0.00002	0.00019	0.00019
	2	0.00730	0.00215	0.00761	0.00606	0.02829	0.02893	0.02664	0.00411	0.02696	0.00002	0.00020	0.00020
	3	0.00781	0.00223	0.00812	0.00572	0.04021	0.04061	0.02880	0.01352	0.03181	0.00008	0.00029	0.00030
	4	1.87401	0.03449	1.87432	0.02933	0.01920	0.03506	0.03803	0.00491	0.03835	0.00034	0.00011	0.00035
		平均值		0.47967	平均值		0.03314	平均值		0.02654	平均值		0.00026
正视	1	0.03714	0.00486	0.03746	0.02411	0.04563	0.05160	0.01006	0.02527	0.02720	0.00032	0.00032	0.00045
	2	3.01080	0.04372	3.01112	0.06342	0.01737	0.06576	0.08235	0.00723	0.08267	0.00153	0.00011	0.00153
	3	0.09577	0.00780	0.09609	0.16654	0.06851	0.18008	0.01492	0.00973	0.01781	0.00090	0.00025	0.00094
	4	0.35450	0.01500	0.35482	0.08191	0.00613	0.08213	0.09250	0.00766	0.09282	0.00065	0.00013	0.00066
		平均值		0.87487	平均值		0.09489	平均值		0.05512	平均值		0.00090
后视	1	0.03525	0.00473	0.03557	0.03927	0.07163	0.08169	0.07382	0.00685	0.07414	0.00040	0.00042	0.00058
	2	1.72487	0.03309	1.72519	0.10662	0.07349	0.12949	0.01051	0.00817	0.01331	0.00065	0.00037	0.00075
	3	0.03361	0.00462	0.03393	0.03182	0.08978	0.09525	0.03540	0.00474	0.03572	0.00032	0.00071	0.00078
	4	0.18039	0.01070	0.18071	0.03134	0.01909	0.03669	0.06096	0.01967	0.06405	0.00012	0.00013	0.00018
		平均值		0.49385	平均值		0.08578	平均值		0.04680	平均值		0.00057
(b)中国吉林丘陵地区有理多项式系数拟合精度像素													像素
方向	景号	直接最小二乘			L曲线岭估计最小二乘			截断SVD估计			HEIV模型
方向	景号	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy
前视	1	0.00415	0.00152	0.00442	0.00404	0.01663	0.01711	0.01013	0.00238	0.01041	0.00008	0.00011	0.00014
	2	0.01275	0.00285	0.01307	0.01425	0.03199	0.03502	0.01302	0.00288	0.01333	0.00006	0.00020	0.00021
	3	0.01951	0.00352	0.01982	0.02524	0.01889	0.03152	0.01964	0.00353	0.01995	0.00013	0.00010	0.00017
	4	0.03273	0.00456	0.03305	0.03663	0.04789	0.06029	0.03486	0.00470	0.03517	0.00029	0.00037	0.00047
		平均值		0.01759	平均值		0.03599	平均值		0.01972	平均值		0.00025
正视	1	0.11044	0.00837	0.11076	0.01925	0.02865	0.03452	0.01369	0.00295	0.01400	0.00023	0.00022	0.00032
	2	0.00756	0.00219	0.00787	0.00755	0.01059	0.01301	0.00945	0.00245	0.00976	0.00013	0.00008	0.00015
	3	0.00887	0.00237	0.00918	0.00812	0.02347	0.02483	0.01106	0.00265	0.01137	0.00029	0.00016	0.00033
	4	0.10375	0.00812	0.10406	0.02587	0.01237	0.02867	0.05410	0.01853	0.05719	0.00042	0.00012	0.00044
		平均值		0.05797	平均值		0.02526	平均值		0.02308	平均值		0.00031
后视	1	0.05156	0.00572	0.05188	0.04508	0.02612	0.05210	0.04071	0.00508	0.04103	0.00043	0.00021	0.00048
	2	0.01646	0.00323	0.01677	0.01923	0.03401	0.03907	0.01638	0.00323	0.01669	0.00042	0.00020	0.00046
	3	0.17309	0.01048	0.17341	0.04422	0.02614	0.05137	0.19528	0.01114	0.19560	0.00089	0.00014	0.00090
	4	0.06384	0.00637	0.06415	0.01577	0.02514	0.02968	0.02415	0.00392	0.02446	0.00050	0.00017	0.00053
		平均值		0.07655	平均值		0.04305	平均值		0.06944	平均值		0.00059
(c)巴基斯坦克什米尔高山地地区有理多项式系数拟合精度													像素
方向	景号	直接最小二乘			L曲线岭估计最小二乘			截断SVD估计			HEIV模型
方向	景号	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy	m_y	m_x	m_xy
前视	1	0.00971	0.00226	0.00996	0.00913	0.02170	0.02354	0.01137	0.00244	0.01163	0.00019	0.00015	0.00025
	2	0.05972	0.00616	0.06004	0.03034	0.03978	0.05003	0.02968	0.00434	0.03000	0.00024	0.00031	0.00039
	3	0.00529	0.00172	0.00556	0.00420	0.01934	0.01979	0.00701	0.00198	0.00728	0.00004	0.00013	0.00014
		平均值		0.02519	平均值		0.03112	平均值		0.01630	平均值		0.00026
正视	1	0.05532	0.00593	0.05564	0.03460	0.02673	0.04372	0.03515	0.00472	0.03547	0.00041	0.00014	0.00043
	2	0.05569	0.00595	0.05601	0.01253	0.02466	0.02766	0.01354	0.00293	0.01386	0.00016	0.00018	0.00024
	3	0.00848	0.00218	0.00875	0.01062	0.01314	0.01690	0.03345	0.00432	0.03372	0.00006	0.00010	0.00012
		平均值		0.04013	平均值		0.02943	平均值		0.02768	平均值		0.00026
后视	1	0.02685	0.00413	0.02716	0.04126	0.05797	0.07115	0.02687	0.00413	0.02718	0.00019	0.00033	0.00039
	2	0.06295	0.00632	0.06327	0.07655	0.06646	0.10137	0.06175	0.00626	0.06206	0.00035	0.00050	0.00061
	3	0.13590	0.00799	0.13613	0.06082	0.39804	0.40266	0.07120	0.00578	0.07144	0.00111	0.00529	0.00540
		平均值		0.07552	平均值		0.19173	平均值		0.05356	平均值		0.00213

表1

表2

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(a)日本庄原平原地区有理多项式系数拟合时间						ms
方向	景号	直接最小二乘	L曲线岭估计最小二乘	截断SVD估计	HEIV模型
前视	1	839	768	513	3053
	2	575	448	411	2516
	3	579	489	414	2603
	4	579	494	420	2548
	平均值	643	550	440	2680
正视	1	621	512	416	2559
	2	592	603	429	2665
	3	564	569	419	2617
	4	562	479	417	2543
	平均值	585	541	420	2596
后视	1	583	486	474	2612
	2	580	509	440	2601
	3	575	550	477	2626
	4	602	489	439	2571
	平均值	585	509	458	2603
(b)中国吉林丘陵地区有理多项式系数拟合时间						ms
方向	景号	直接最小二乘	L曲线岭估计最小二乘	截断SVD估计	HEIV模型
前视	1	601	459	456	2558
	2	572	420	411	2422
	3	544	425	409	2415
	4	538	457	411	2555
	平均值	564	440	422	2488
正视	1	552	432	413	2460
	2	633	423	437	2461
	3	556	437	446	2473
	4	550	433	420	2452
	平均值	573	431	429	2462
后视	1	566	412	410	2517
	2	573	471	411	2451
	3	583	483	415	2496
	4	570	495	437	2440
	平均值	573	465	418	2476
(c)巴基斯坦克什米尔高山地地区有理多项式系数拟合时间						ms
方向	景号	直接最小二乘	L曲线岭估计最小二乘	截断SVD估计	HEIV模型
前视	1	634	586	490	2815
	2	575	482	422	2583
	3	581	449	435	2579
	平均值	597	506	449	2659
正视	1	617	495	416	2638
	2	575	487	413	2548
	3	640	468	425	2555
	平均值	611	483	418	2580
后视	1	595	529	414	2634
	2	589	528	411	2614
	3	731	1123	513	3472
	平均值	638	737	446	2907