﻿ 高度计测距精度对沿轨迹重力异常反演的影响
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Inference of Altimeter Accuracy on Along-track Gravity Anomaly Recovery
LI Yang, ZHANG Running
DFH Satellite Company Limited, Beijing 100094, China
First author: First author： LI Yang(1986—)，female，PhD candidate，majors in design of spacecraft and satellite altimetry.

E-mail： liyangcau@sina.com
Abstract: A correlation model between along-track gravity anomaly accuracy, spatial resolution and altimeter accuracy is proposed. This new model is based on along-track gravity anomaly recovery and resolution estimation. Firstly, an error propagation formula of along-track gravity anomaly is derived from the principle of satellite altimetry. Then the mathematics between the SNR (signal to noise ratio) and cross spectral coherence is deduced. The analytical correlation between altimeter accuracy and spatial resolution is finally obtained from the results above. Numerical simulation results show that along-track gravity anomaly accuracy is proportional to altimeter accuracy, while spatial resolution has a power relation with altimeter accuracy. e.g., with altimeter accuracy improving m times, gravity anomaly accuracy improves m times while spatial resolution improves m0.4644 times. This model is verified by real-world data.
Key words: satellite altimetry     radar altimeter accuracy     along-track gravity anomaly     spatial resolution
1 引 言

2 沿轨迹重力异常和空间分辨率的求解方法 2.1 求解沿轨迹重力异常的垂线偏差法

2.2 求解空间分辨率的交叉谱分析法

3 高度计测距精度对沿轨迹重力异常反演精度的影响

4 高度计测距精度对沿轨迹空间分辨率的影响

n1和n2互不相关，有N1N2*=N2N1*=0，式(6)变为P1(f)=P2(f)+S2(N1－N2)*+(N1－N2)S2*+2Pn(f)，得 交叉功率谱密度P12(f)=S1S2*=P2(f)+N1S2*－N2S2*，则 将式(7)代入式(8)得P12(f)2=P2(f)[P1(f)－2Pn(f)]+(N1S2*－N2S2*)(N1S2*－N2S2*)*。因n1、n2、s两两互不相关，有N1S2*=N1(S+N2)=0，N2S2*=N2(S*+N2*)=Pn(f)，则|P12(f)|2=P2(f)P1(f)－2Pn(f)+Pn2(f)，得一致性系数 式中，P1(f)=Ps(f)+SN1*+N1S*+Pn(f)=Ps(f)+Pn(f)，同理P2(f)=Ps(f)+Pn(f)，频率点f处的信噪比Q(f)=Ps(f)/Pn(f)，代入式(9)得一致性系数ρ(f)与Q(f)的关系为 式中，频率点f处信噪比Q(f)=Ps(f)/Pn(f)，其具体含义为：在频率点f附近很小的领域内，分别对信号和噪声的功率谱密度Ps(f)和Pn(f)进行积分，得出信号功率和噪声功率，两者相除得到在频率点f处的信噪比，由于在频率点f附近很小的领域内积分，信噪比可表示为Q(f)=Ps(f)/Pn(f)。由式(10)知，当ρ(f)=0.5时，Q(f)=2.414。

 图 1 沿轨迹重力异常精度和空间分辨率仿真框图 Fig. 1 Simulation scheme for accuracy and spatial resolution of along-track gravity anomaly

 图 2 沿轨迹重力异常精度随高度计测距精度的变化 Fig. 2 Accuracy of along-track gravity anomalies versus altimeter noise

 图 3 区域A功率谱密度和一致性系数 Fig. 3 Power spectral density and coherence versus frequency(1/wavelength) for area A
 图 4 区域B功率谱密度和一致性系数 Fig. 4 Power spectral density and coherence versus frequency(1/wavelength) for area B

 图 5 不同高度计测距精度下区域A的一致性系数 Fig. 5 Comparison of smoothed coherence between different altimeter noise for area A
 图 6 不同高度计测距精度下区域B的一致性系数 Fig. 6 Comparison of smoothed coherence between different altimeter noise for area B

 图 7 空间分辨率随高度计测距精度的变化 Fig. 7 Spatial resolution versus altimeter noise
6 结 论

(1) 根据求解沿轨迹重力异常的垂线偏差法，给出沿轨迹重力异常的误差传播方程，得出沿轨迹重力异常的反演精度与高度计测距精度成正比关系。

(2) 推导出交叉谱分析法中一致性系数与信噪比的解析关系，得出当一致性系数为0.5时信噪比为2.414的结论，为沿轨迹空间分辨率的估计提供了新的解决思路。

(3) 以上述结论为基础，建立了空间分辨率与高度计测距精度的关联性模型，表明空间分辨率与高度计测距精度成幂函数的关系，即高度计测距精度提高m倍，全球平均空间分辨率提高m0.4644倍。

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http://dx.doi.org/10.11947/j.AGCS.2015.20140022

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#### 文章信息

LI Yang, ZHANG Running

Inference of Altimeter Accuracy on Along-track Gravity Anomaly Recovery

Acta Geodaeticaet Cartographica Sinica, 2015, 44(4): 363-369.
http://dx.doi.org/10.11947/j.AGCS.2015.20140022