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Article(id=1239167207431787241, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, articleNumber=null, orderNo=null, doi=10.12347/j.ycyk.20241218004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1734451200000, receivedDateStr=2024-12-18, revisedDate=1740672000000, revisedDateStr=2025-02-28, acceptedDate=null, acceptedDateStr=null, onlineDate=1773370084864, onlineDateStr=2026-03-13, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773370084864, onlineIssueDateStr=2026-03-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773370084864, creator=13701087609, updateTime=1773370084864, updator=13701087609, issue=Issue{id=1239167201161302658, tenantId=1146029695717560320, journalId=1238841944844054536, year='2025', volume='46', issue='2', pageStart='1', pageEnd='142', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773370083370, creator=13701087609, updateTime=1773370146323, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1239167465285014189, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1239167465285014190, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=79, endPage=85, ext={EN=ArticleExt(id=1239167207817663227, articleId=1239167207431787241, tenantId=1146029695717560320, journalId=1238841944844054536, language=EN, title=Estimation of Phase Calibration Results Based on Multi-Mode Feed System, columnId=1239133503154081962, journalTitle=Journal of Telemetry, Tracking and Command, columnName=TT & C Communication and Navigation, runingTitle=null, highlight=null, articleAbstract=

During the execution of precision measurement and control tasks by ground - based equipment, in order to accurately track the angular error demodulation signal, phase and slope correction of the tracking receiver are required, and the process of obtaining the correction value is called phase calibration. Ensuring the precise phase difference calibration of the sum and difference receiving channels is a key step to meet the self - tracking requirements of the target for the angle measurement subsystem. The traditional phase calibration method for multimode feed tracking systems faces challenges such as low efficiency, susceptibility to calibration equipment failures, and the impact of field setup environments, which not only limits the smooth progress of measurement and control tasks but may also have an adverse effect on the accuracy of target tracking. This paper aims to study and analyze existing calibration methods, deeply mine the existing calibration data, and introduce the method of multiple fitting analysis of mathematical statistics to predict the phase shift value, thereby effectively enhance emergency measurement and control capability of the measurement and control equipment in practice, ensuring the continuity and accuracy of task execution.

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在地面测控设备执行精密测控任务的过程中，为了准确地跟踪角误差解调信号，需要对跟踪接收机进行相位修正和斜率修正，获取修正值的过程称为校相。确保和差接收通道的精确相位差校准是满足测角分系统对目标自跟踪要求的关键步骤。多模馈源跟踪系统传统的校相方式面临效率低下、易受标校设备故障及野外架设环境影响等挑战，这不仅限制了测控任务的顺利进行，还可能对目标跟踪精度造成不利影响。本文旨在通过对现有标校方法进行研究分析，对现有标校数据进行深度挖掘，引入数理统计的多次拟合分析方法进行移相值预测，从而在实战中有效提升测控设备的应急测控能力，确保任务执行的连续性和准确性。

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王向伟　1986年生，学士，工程师。

李敏剑　1984年生，硕士，工程师。

樊星　1982年生，学士，工程师。。

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王向伟　1986年生，学士，工程师。

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王向伟　1986年生，学士，工程师。

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李敏剑　1984年生，硕士，工程师。

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李敏剑　1984年生，硕士，工程师。

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樊星　1982年生，学士，工程师。。

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樊星　1982年生，学士，工程师。。

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An adaptive filter algorithm of exponentially-weighted miltiple attenuated memory[J]. Journal of Wuhan University of Technology, 2011, 33(11): 147-152., articleTitle=An adaptive filter algorithm of exponentially-weighted miltiple attenuated memory, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1239285163490857046, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, xref=null, ext=[AuthorCompanyExt(id=1239285163499245653, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, companyId=1239285163490857046, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=The Unit 63618 of PLA, Korla 841001, China), AuthorCompanyExt(id=1239285163511828567, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, companyId=1239285163490857046, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=中国人民解放军63618部队 库尔勒 841001)])], figs=[ArticleFig(id=1239285166791774410, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Fig. 1, caption=Principle block diagram of multi-mode feed tracking receiver, figureFileSmall=RtPEdAAI8fFO6I8azru4QA==, figureFileBig=OByi/xMkGBU3I1TzdLrMuw==, tableContent=null), ArticleFig(id=1239285166850494670, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=图1, caption=多模馈源跟踪接收机原理框图, figureFileSmall=RtPEdAAI8fFO6I8azru4QA==, figureFileBig=OByi/xMkGBU3I1TzdLrMuw==, tableContent=null), ArticleFig(id=1239285166951157973, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Fig. 2, caption=The original phase calibration data of a system, figureFileSmall=5jJulKYvmcI3/V400LA5AA==, figureFileBig=L21Qew/dwSPFjlQOK4QTcg==, tableContent=null), ArticleFig(id=1239285167022461146, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=图2, caption=某系统原始校相数据, figureFileSmall=5jJulKYvmcI3/V400LA5AA==, figureFileBig=L21Qew/dwSPFjlQOK4QTcg==, tableContent=null), ArticleFig(id=1239285167114735836, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Fig. 3, caption=The original phase calibration data processed by a system, figureFileSmall=oXz2rY8vJjTyXpOktH/tgg==, figureFileBig=7pD94rUVrQYJW8esLFxHoQ==, tableContent=null), ArticleFig(id=1239285167207010531, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=图3, caption=某系统处理后的原始校相数据, figureFileSmall=oXz2rY8vJjTyXpOktH/tgg==, figureFileBig=7pD94rUVrQYJW8esLFxHoQ==, tableContent=null), ArticleFig(id=1239285167282508004, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Fig. 4, caption=Fitting data and mean square error of data, figureFileSmall=H8mYXhvBqDzNKhMnpzhr4Q==, figureFileBig=qqsSKoTyLzUN14kFV/RsJQ==, tableContent=null), ArticleFig(id=1239285167374782695, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=图4, caption=拟合数据及数据均方误差, figureFileSmall=H8mYXhvBqDzNKhMnpzhr4Q==, figureFileBig=qqsSKoTyLzUN14kFV/RsJQ==, tableContent=null), ArticleFig(id=1239285167441891563, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Table 1, caption=

The minimum mean square error and the corresponding fitting order in 20 fittings

, figureFileSmall=null, figureFileBig=null, tableContent=
左旋方位左旋俯仰右旋方位右旋俯仰
拟合阶数k8777
误差最大值j2.072 75.682 51.745 06.174 1
), ArticleFig(id=1239285167521583345, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=表1, caption=

20次拟合中均方误差最小值和对应的拟合阶数

, figureFileSmall=null, figureFileBig=null, tableContent=
左旋方位左旋俯仰右旋方位右旋俯仰
拟合阶数k8777
误差最大值j2.072 75.682 51.745 06.174 1
), ArticleFig(id=1239285167613858038, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=EN, label=Table 2, caption=

The actual phase correction values of different point frequencies and the predicted phase correction values and cross coupling

, figureFileSmall=null, figureFileBig=null, tableContent=
点频(MHz)2 223.52 243.52 263.52 283.52 293.5
左旋方位实际(°)185.1107.451.387.023350.1
预估(°)186.3106.653.277.593348.6
误差(°) 1.2 -0.8 1.89 0.57 -1.5
交叉耦合 1/15 1/16 1/15 1/18 1/17
左旋俯仰实际(°)178.4103.541.891.52334.8
预估(°)179.9104.943.951.328335.6
误差(°) 1.5 1.4 2.06 -0.192 0.8
交叉耦合 1/17 1/18 1/16 1/16 1/18
右旋方位实际(°)155.880.862.12321.8299.4
预估(°)156.681.742.193322.6298.7
误差(°) 0.8 0.88 0.073 0.8 -0.7
交叉耦合 1/15 1/13 1/15 1/18 1/16
右旋俯仰实际(°)162.188.560.932334.9299.5
预估(°)161.388.2291.631335.7299.8
误差(°) -0.8 -0.331 0.699 0.8 0.3
交叉耦合 1/14 1/16 1/18 1/15 1/18
), ArticleFig(id=1239285167676772603, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167207431787241, language=CN, label=表2, caption=

不同点频的实际校相值和与预估校相值及交叉耦合

, figureFileSmall=null, figureFileBig=null, tableContent=
点频(MHz)2 223.52 243.52 263.52 283.52 293.5
左旋方位实际(°)185.1107.451.387.023350.1
预估(°)186.3106.653.277.593348.6
误差(°) 1.2 -0.8 1.89 0.57 -1.5
交叉耦合 1/15 1/16 1/15 1/18 1/17
左旋俯仰实际(°)178.4103.541.891.52334.8
预估(°)179.9104.943.951.328335.6
误差(°) 1.5 1.4 2.06 -0.192 0.8
交叉耦合 1/17 1/18 1/16 1/16 1/18
右旋方位实际(°)155.880.862.12321.8299.4
预估(°)156.681.742.193322.6298.7
误差(°) 0.8 0.88 0.073 0.8 -0.7
交叉耦合 1/15 1/13 1/15 1/18 1/16
右旋俯仰实际(°)162.188.560.932334.9299.5
预估(°)161.388.2291.631335.7299.8
误差(°) -0.8 -0.331 0.699 0.8 0.3
交叉耦合 1/14 1/16 1/18 1/15 1/18
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基于多模馈源体制的校相结果预估
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王向伟 , 李敏剑 , 樊星
遥测遥控 | 测控通信与导航 2025,46(2): 79-85
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遥测遥控 | 测控通信与导航 2025, 46(2): 79-85
基于多模馈源体制的校相结果预估
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王向伟, 李敏剑, 樊星
作者信息
  • 中国人民解放军63618部队 库尔勒 841001

    • 王向伟　1986年生，学士，工程师。

    李敏剑　1984年生，硕士，工程师。

    樊星　1982年生，学士，工程师。。

Estimation of Phase Calibration Results Based on Multi-Mode Feed System
Xiangwei WANG, Minjian LI, Xing FAN
Affiliations
  • The Unit 63618 of PLA, Korla 841001, China
出版时间: 2025-03-15 doi: 10.12347/j.ycyk.20241218004
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摘要
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在地面测控设备执行精密测控任务的过程中，为了准确地跟踪角误差解调信号，需要对跟踪接收机进行相位修正和斜率修正，获取修正值的过程称为校相。确保和差接收通道的精确相位差校准是满足测角分系统对目标自跟踪要求的关键步骤。多模馈源跟踪系统传统的校相方式面临效率低下、易受标校设备故障及野外架设环境影响等挑战，这不仅限制了测控任务的顺利进行，还可能对目标跟踪精度造成不利影响。本文旨在通过对现有标校方法进行研究分析，对现有标校数据进行深度挖掘，引入数理统计的多次拟合分析方法进行移相值预测，从而在实战中有效提升测控设备的应急测控能力，确保任务执行的连续性和准确性。

多模馈源  /  测角分系统  /  校相  /  移相值

During the execution of precision measurement and control tasks by ground - based equipment, in order to accurately track the angular error demodulation signal, phase and slope correction of the tracking receiver are required, and the process of obtaining the correction value is called phase calibration. Ensuring the precise phase difference calibration of the sum and difference receiving channels is a key step to meet the self - tracking requirements of the target for the angle measurement subsystem. The traditional phase calibration method for multimode feed tracking systems faces challenges such as low efficiency, susceptibility to calibration equipment failures, and the impact of field setup environments, which not only limits the smooth progress of measurement and control tasks but may also have an adverse effect on the accuracy of target tracking. This paper aims to study and analyze existing calibration methods, deeply mine the existing calibration data, and introduce the method of multiple fitting analysis of mathematical statistics to predict the phase shift value, thereby effectively enhance emergency measurement and control capability of the measurement and control equipment in practice, ensuring the continuity and accuracy of task execution.

Multi-mode feed  /  Angle measurement and control subsystem  /  Phase calibration  /  Phase shift value
王向伟, 李敏剑, 樊星. 基于多模馈源体制的校相结果预估. 遥测遥控, 2025 , 46 (2) : 79 -85 . DOI: 10.12347/j.ycyk.20241218004
Xiangwei WANG, Minjian LI, Xing FAN. Estimation of Phase Calibration Results Based on Multi-Mode Feed System[J]. Journal of Telemetry, Tracking and Command, 2025 , 46 (2) : 79 -85 . DOI: 10.12347/j.ycyk.20241218004
正文
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0　引言
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在无线通信与卫星通信领域，确保信号传输的高效性与准确性是技术发展的核心目标之一。其中，天线系统的校准作为提升通信质量的关键步骤，其精度直接影响信号的覆盖范围、传输效率及系统整体的可靠性。而多模馈源体制下，天线系统需同时处理多种信号模式和环境影响，这对校相精度提出了更高要求。
多模馈源体制通过整合不同模式的馈源，如波导模式、缝隙模式等，实现了信号的多路径传输，有效应对了复杂电磁环境中的信号衰减问题。这种设计不仅提高了通信带宽，还增强了信号在远距离传输中的稳定性。然而，正是这些多样化的馈源模式，使得相位校准变得异常复杂。每个馈源模式都有其独特的相位响应特性，它们之间的相互作用会导致相位误差的累积，进而影响信号的质量和传输效率。
精准的相位校准[1-5]是确保信号高质量传输的前提。任何微小的相位误差都可能引发信号失真，降低通信系统的整体性能。因此，开发有效的校相结果预估方法对于提前识别潜在问题、优化系统设计、提升通信质量具有不可估量的价值。借助先进的数学建模和仿真工具模拟不同场景下的相位响应，从而实现对校相结果的精确预测和优化调整。
在校相方面，多模馈源体制比单通道单脉冲体制复杂。单通道单脉冲只需对一个点频进行校相，校相结果适用于所有点频，但多模馈源体制不同的点频对应不同的校相结果，在测控任务前需对已知点频进行校相。目前，多模馈源体制在多数测控设备中进行应用，但频繁的校相工作成为了任务准备的重点工作。
预先已知和预测校相结果，可避免因不确定的工作环境影响，导致无法进行精确的人工校相，进而造成设备无法对目标进行自跟踪或跟踪精度较差的情况。精确的校相预估有助于提前发现并解决潜在问题，确保天线系统在各种条件下均能维持最佳性能。在多变的通信环境中，动态调整校相策略，使系统更能适应环境变化，从而提升通信稳定性。
本文主要介绍了多模馈源体制的校相原理及常规校相方法，给出了通过分析不同点频间相位修正值的关系，实现对所有可用频点内任一点频的校相结果预估的方法，最后通过试验及实践验证了此方法的可靠性。
1　相位校准的方法原理
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对目标进行角度自动跟踪，要求天线主波束指向目标后，波束能连续跟随目标运动，保证天线轴始终指向运动目标的方向，以便自动连续地测出目标瞬时角坐标(方位角和俯仰角坐标)。实现角度自动跟踪的方法是：
当目标稍偏离天线轴的方向而出现跟踪误差时，天线系统自动产生一个相应的角误差信号，该误差信号可正确反映目标在什么方向偏离天线轴以及偏角的大小。信号经放大变换处理后，加于控制电机上，电机便自动驱使天线向减少误差信号的方向移动，直至天线轴重新对准目标，误差信号趋近于零为止。所以，角跟踪原理是利用误差信号本身来消除跟踪误差的。
而天线能够连续进行自跟踪需要对接收机置入准确的校相结果，接收机的原理框图如图1所示。左右旋和、差信号分别经场放(LNA)放大后，差信号Δ经过调制信号进行抑制载波调制，与和信号合路成一路信号。接收机将接收到的这路变频过的中频信号，经过解调，得到包含在信号中的方位、俯仰误差信息，并把方位、俯仰误差信息经滤波校正后传给伺服。伺服收到方位、俯仰误差信息后给天线驱动电机发送指令，驱动天线电机，使天线修正方位与俯仰角度，实现自跟踪的目的。
图1中，Δ为差信号；Σ为和信号；ΔAZ为方位角误差；ΔEL为俯仰角误差；AGC为自动增益控制。
假设由馈源激励出的和信号u0(t)为
差信号u1(t)为
式中，b为和信号振幅；u为归一化误差信号斜率，；φ为在目标平面目标与x轴的夹角，φ=arctan(u2/u1)；ω为馈源接收信号的频率；θ为天线偏离目标角度；γ为合路前和、差信号的相位差。
利用和路信号的信号强度对差路信号进行幅度归一化控制，然后在和路信号准确跟踪的基础上，以和路信号的相位信息为基准，加上和差之间固定相位量的偏移，经过偏移的本地相位信息与差路信号同频同相，利用该信号实现对差信号的正交相干解调，获得方位和俯仰误差信号。其中，和差之间的相位偏移量需要通过校相提前获得。
设调制信号为k(t)(实际应用中常采用方波)，则合成后的信号输出为
式中，k为传输信道的电压增益；ω1为经过下变频后的信号频率。设参考源输出信号u3(t)=sin(ω1t)，则经过移相、正交移相后的信号为
式中，γ′为移相器的移相值。
相位检波器的实质就是参考信号与输入信号相乘，在滤除直流分量与高频分量后，检波器的输出信号分别为
式中，γ-γ′为和差通道相位差值。
相位校准的主要目的就是要调节移相器，令γ′=γ，从而使误差电压输出为最大，方位交叉耦合(ΔEL/ΔAZ)或俯仰交叉耦合(ΔEL/ΔAZ)为最小，以实现对目标的精确跟踪。
存在影响跟踪误差电压解调的相位、增益不一致性导致的交叉耦合，因而必须定期对跟踪系统的和差通道相位差进行校准。
2　目前存在的校相方法
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2.1　有塔标校
2.1.1　常规校相[6-9]
①校相时天线方位、俯仰指向塔上信标天线零点位置；
②将天线在方位上分别进行正向和负向拉偏，接收机移相器每改变一个度数，则记录方位电压值、俯仰电压值，根据数据画出度数对应误差电压的曲线；
③将天线在俯仰方向进行同样的操作，根据曲线分析出最佳校相值；
④同时调整接收机方位、俯仰增益使方位、俯仰ΔUa、ΔUe满足所设定值，最后拉偏方位、俯仰，进行交叉耦合检查。
2.1.2　快速自动校相
校相时天线方位、俯仰指向塔上信标天线零点位置。查询或设置接收机的方位、俯仰通道相位和增益初值，读取方位俯仰误差电压。天线方位或俯仰拉偏一定角度，再读取方位俯仰误差电压。根据公式计算出接收机的方位、俯仰通道相位和增益。最后拉偏方位、俯仰，进行交叉耦合检查。
2.1.3　优缺点
优点：
①可以通过塔上信标，对系统接收通道进行检查；
②可以针对某一频点进行精确校相，并对校相结果进行检验。
缺点：
①快速自动校相虽比常规校相节省时间，但仍需要人工进行标校塔架标；
②对于车载设备而言，野外条件较为局限，不具备标校塔条件；
③在信标机损坏的情况下无法完成校相工作；
④对于不同频点，校相结果差异较大，多个频点需要进行多次校相。
2.2　无塔校相
无塔化标校方法[10-12]主要有射电星校相、偏馈校相、近场校相等。其中射电星校相方法要求使用深空大口径高增益低噪声天线。偏馈校相方法利用偏馈校零变频器并结合传统校相方法，校相用时较长。近场校相需标校车和地面目标源配合。
快速机动的车载测控设备天线面口径一般不大，无法进行射电星标校；而偏馈校相和近场校相都与有塔校相类似，都需搭配其他设备(如信标机)，人工参与过多，工作的繁琐程度并未降低。
2.3　数理统计方法
文献[13-20]中的标校方法针对的是单通道单脉冲的校相结果，而对于多模馈源体制，不同的频点校相值相差较大，因此需考虑其他的校相估计方法。
目前上述校相方法已无法满足测控任务较为密集的需要，对不同频点间校相结果和校相原理的分析，可以采用曲线拟合的方法，通过已知频点的校相结果推算出所需频点的校相结果。
3　基于曲线拟合理论的校相预测
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3.1　数据分析及数据拟合的可行性
通过对某系统2.2 GHz~2.3 GHz每隔10 MHz校相结果进行定性分析，原始左右旋方位俯仰校相结果如图2所示。由于0°与360°为对应值，于是将超过360°的相应减去360°得到其对应值，处理后的左右旋方位俯仰校相结果如图3所示。
从图3中可看到校相结果与点频之间遵循一定的规律，可以用一条直线来近似描述，即相位差与点频之间存在线性关系，这为后续的拟合处理提供了理论基础。
基于上述线性关系，采用曲线拟合技术，特别是最小二乘法，对收集到的相位差数据进行拟合。通过选择合适的拟合系数，能够获得一个描述相位差与点频之间关系的数学模型。这一模型不仅简化了相位差的计算过程，还允许在没有直接测量数据的情况下，预估任意点频的校相值，极大地提高了工作效率和准确性。
3.2　曲线拟合算法原理
对于N组标校数据，可采用如下的多项式拟合建立频率x和移相值f(x)的数学关系，即
为满足式(8)的插值函数，则f(x)的n+1个待定系数a0,a1,...an满足
从几何上看，上述多项式插值就是通过n+1个数据点(xi,f(xi))，i=1,2,••,n, 作一条多项式曲线y=f(x)。
拟合算法如下：
①取初始拟合长度为n∈(1,2,••,m)，针对初始的m个数据，依据最小二乘法按照式(9)拟合曲线获得f(x)；
②把已知数据中的频率值xn，代入拟合曲线f(x)与实测值来求拟合误差；
③借助下式使拟合均方误差最小化，找出拟合均方误差最小时所对应的拟合曲线阶数n和相应的待定系数a0,a1,••,an，将其用于移相值预测计算，即
④把需要的点频带入f(x)中，就能够计算出对应的校相值。
倘若针对N组数据构建一个统一的多项式数学模型，那么较低的多项式阶数会致使拟合误差较大，较高的多项式阶数会引发“过拟合”现象。
4　仿真试验
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4.1　拟合阶数的选取
对于图4中的校相数据，其频率与移相值之间的关系可由式(2)所描述的数学模型来确定。为防止出现“过拟合”或“拟合误差”较大的情况，在实际数据模拟中通过计算选取合适的拟合阶数。
左右旋方位、俯仰校相结果分别进行20次拟合，直至选取均方差最小值及其对应的拟合阶数，如表1所示。
从表1可看出：对左右旋方位、俯仰校相结果分别选取多项式阶数为8,7,7,7进行拟合，能满足误差最小、拟合曲线较平滑的要求。拟合数据曲线与均方误差曲线如图4所示。
4.2　仿真结果分析
通过式(8)可对频段内任一频点预估校相结果。随机选取五个点频的预估值与实际校相值进行统计，如表2所示。
从表2可以看出：这5组点频的实际校相值与预估校相值误差均在5°以下，将预估校相值装载至接收机后对标跟踪交叉耦合均小于设备指标1/7，满足日常跟踪需求。
在实际应用中，若未知信号频率，可在等待点通过频谱仪检测信号频率，对下变频器设置该频率，再通过该频率查询获得对应的校相结果，并将其装载至接收机，从而实现对目标信号的自跟踪。
5　结束语
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在多模馈源跟踪系统中，相位差的精确控制是实现高效跟踪与校准的关键。本文深入分析了多模馈源跟踪过程中相位差与对应频率的收敛轨迹特征，发现其曲线特征呈现线性关系。基于此发现，本文提出了一种利用曲线拟合理论对相位差与频率的收敛轨迹进行拟合处理的新方法，旨在无需搭建复杂信号源检查交叉耦合系统，为多模馈源跟踪系统提供一种高效、准确的相位校准解决方案。该方法不仅简化了校准流程，降低了成本，还显著提高了系统的应急响应能力和测控精度。
未来研究可进一步探索更高级的拟合算法，以及算法在更广泛频段内的适用性，以期在复杂多变的跟踪环境中算法保持更高的性能稳定性。随着大数据和人工智能技术的进一步发展，相信这一策略将会变得更加智能化、自适应化，为地面测控领域带来更多可能性。
文献
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2025年第46卷第2期
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doi: 10.12347/j.ycyk.20241218004
  • 接收时间：2024-12-18
  • 首发时间：2026-03-13
  • 出版时间：2025-03-15
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  • 收稿日期：2024-12-18
  • 修回日期：2025-02-28
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    中国人民解放军63618部队 库尔勒 841001
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