随着近年来量子技术逐渐从学术研究发展到针对热点领域的工程探索与应用，基于量子纠缠的各类应用技术日益成熟。特别是将纠缠光量子的二阶关联特性应用于距离测量的量子测距技术，其理论测距精度可以突破散粒噪声极限，逼近海森堡极限，有利于实现更高精度的星间距离测量。但在实际应用中量子测距会受到杂散光、暗计数、探测器抖动误差、光学平台震动位移、待测目标相对运动等因素对测距精度的影响，导致测距精度难以提高，因此通过量子测距数据处理算法抑制上述干扰因素对测距精度的影响成为了实现高精度星间量子测距的关键所在。

本文基于纠缠光量子的二阶关联特性对应用于星间测距的量子测距技术开展了数据处理算法研究与实验验证，主要内容包括以下两个部分：

基于纠缠光量子的相对静止星间测距算法

量子测距技术具有较高的测量精度和灵敏度，也具备较高的抗干扰能力，但受限于设备性能、抖动、误差、分辨率等因素，实现量子测距需要将光电平台与软件相结合从而实现数据生成、处理和结果输出。本文搭建了以非线性晶体BBO和PPKTP为核心的小型纠缠源，结合位移系统、探测系统，组成了星间量子测距地面实验平台，为数据处理算法的设计采集了实验数据，并提供了验证条件。通过设计快速符合计数算法，降低了符合计数的时间复杂度，减少了二阶关联曲线生成所需的运算时间，提高了测距时效性，同时滤除被探测光子中的大部分杂散光子和无效纠缠光子，提高了信噪比。为实现高精度差分测距，抑制设备震动和内部光路微小变化对测距精度的影响，提出了基于DFT频域相位差加权算法，并以快速符合计数算法和基于DFT频域相位差加权算法为基础，设计了相对静止星间量子测距数据处理算法。将数据处理算法结合地面实验平台进行测距实验，实现了对自由空间中静态目标100 μm 量级的量子测距精度。

基于纠缠光量子的相对运动星间测距算法

针对目前基于量子纠缠的星间测距及其数据处理算法多应用于相对静止卫星间的距离测量，难以对一维相对运动卫星进行距离测量的问题，本文通过分析一维相对运动对符合计数和二阶关联曲线的影响，说明了相对静止星间测距算法在动态量子测距领域的不适用性。针对相对运动星间量子测距，提出了以动态光子匹配为核心的相对运动星间量子测距数据处理算法。将算法结合星间量子测距软件仿真平台对一维相对运动卫星进行模拟量子测距，抑制了卫星相对运动导致的纠缠光子对被探测时间差不定和二阶关联曲线累计轮廓扩展形变对动态目标测距精度的影响。测距结果验证了算法可行性，证明该算法可以实现对相对运动速度范围1000m/s内的匀速、匀加速、正弦运动的目标卫星星间距离的准确测量，测距精度达到毫米量级。该算法将量子测距的应用范围由静态目标扩展至一维运动的动态目标，尤其适用于卫星组网、卫星对接等存在相对运动的星间测距场景。

With the development of quantum technology from academic research to engineering exploration and application in hot fields in recent years, various applications based on quantum entangled light have become increasingly mature. Especially, the second-order correlation property of quantum entangled light is applied to quantum ranging technology of distance measurement. Its theoretical ranging accuracy can break through the limit of shot noise and approach the Heisenberg limit, which is conducive to achieving more accurate star-to-star distance measurement. However, in practical applications, quantum ranging will be affected by factors such as stray light, dark count, detector jitter error, optical platform vibration displacement, and relative motion of the target to be measured, which makes it difficult to improve the ranging accuracy. Therefore, through Quantum ranging data processing algorithm to suppress the impact of the above interference factors on ranging accuracy has become the key to realize high-precision inter-satellite quantum ranging.

 

In this paper, based on the second-order correlation characteristics of quantum entangled light, the data processing algorithm research and experimental verification of the quantum ranging technology applied to inter-satellite ranging are carried out. The main contents include the following two parts:

 

Relatively stationary inter-satellite ranging algorithm based on entangled optical quanta

Quantum ranging technology has high measurement accuracy and sensitivity, as well as high anti-interference capability, but limited by equipment performance, jitter, error, resolution and other factors, the realization of quantum ranging requires the combination of optoelectronic platform and software to realize data generation, processing and result output. In this paper, a small entanglement source with nonlinear crystals BBO and PPKTP as the core, combined with displacement system and detection system, has been built to form an quantum entanglement-based inter-satellite ranging ground experiment platform, which provides experimental data and verification conditions for the design of data processing algorithms. By designing a fast match counting algorithm, the time complexity of match counting is reduced, the operation time required for second-order correlation curve generation is reduced, the ranging timeliness is improved, and most of the spurious and invalid entangled photons in the detected photons are filtered out to improve the signal-to-noise ratio. In order to achieve high precision differential ranging and suppress the influence of equipment vibration and small changes in the internal optical path on the ranging accuracy, a DFT-based frequency domain phase difference weighting algorithm is proposed, and a relative quiescent inter-satellite quantum ranging data processing algorithm is designed based on the fast conformal counting algorithm and the DFT-based frequency domain phase difference weighting algorithm. The data processing algorithm is combined with the ground-based experimental platform for ranging experiments, and the quantum ranging accuracy of 100 μm for static targets in free space is achieved.

 

Relative motion inter-satellite ranging algorithm based on entangled optical quanta

To address the problem that the current quantum entanglement-based inter-satellite ranging and its data processing algorithms are mostly applied to distance measurement between relatively stationary satellites, and it is difficult to perform distance measurement for one-dimensional relatively moving satellites, this paper illustrates the inapplicability of static ranging algorithms in the field of dynamic ranging by analyzing the effects of one-dimensional relative motion on conformal counting and second-order correlation curves. For relative motion inter-satellite quantum ranging, a relative motion inter-satellite quantum ranging data processing algorithm with dynamic photon matching as the core is proposed. The algorithm is combined with an inter-satellite quantum ranging software simulation platform to simulate quantum ranging on a one-dimensional relative motion satellite, and the effects of the relative motion of the satellite on the dynamic target ranging accuracy caused by the entangled photons on the detected time difference and the cumulative profile expansion deformation of the second-order correlation curve are suppressed. The ranging results verify the feasibility of the algorithm, and demonstrate that the algorithm can achieve accurate measurement of inter-satellite distance between targets with uniform, uniformly accelerated, sinusoidal motion in the relative motion velocity range of 1000 m/s, and the ranging accuracy reaches millimeter level. The algorithm extends the application scope of quantum ranging from static targets to dynamic targets with one-dimensional motion, and is especially suitable for inter-satellite ranging scenarios with relative motion such as satellite networking and satellite docking.

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