CN116359901A - 5G external radiation source radar low-altitude target positioning method based on particle filtering - Google Patents

5G external radiation source radar low-altitude target positioning method based on particle filtering Download PDF

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CN116359901A
CN116359901A CN202310279335.0A CN202310279335A CN116359901A CN 116359901 A CN116359901 A CN 116359901A CN 202310279335 A CN202310279335 A CN 202310279335A CN 116359901 A CN116359901 A CN 116359901A
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涂刚毅
武姿言
申鑫
徐文强
朱家宝
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Nanjing University of Information Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • G01S7/412—Identification of targets based on measurements of radar reflectivity based on a comparison between measured values and known or stored values
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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Abstract

The invention relates to the technical field of external radiation source radar positioning, in particular to a 5G external radiation source radar low-altitude target positioning method based on particle filtering, which comprises the following steps: s1, synchronizing signals between receiving stations and transmitting stations; s2, echo signal processing; s3, establishing a target state transition model and a measurement model; s4, initializing particles; s5, calculating pseudo-range errors between the target and the transceiver station; s6, updating the weight of the particles; s7, resampling particles; s8, extracting a target state. According to the invention, a time difference-based positioning method is adopted to obtain pseudo-range information, pseudo-range errors between a target and a 5G base station and a receiving station which participate in positioning are used as measurement values, the received echo signals are processed to obtain preliminary positioning and the pseudo-range information is used as priori information, a target state transition model and a measurement model are constructed, the position of the target to be measured is estimated through a particle filtering algorithm, the target positioning is finally realized, and the influence of clutter and interference on the target positioning in a low-altitude complex environment is reduced.

Description

一种基于粒子滤波的5G外辐射源雷达低空目标定位方法A particle filter-based low-altitude target location method for 5G external radiation source radar

技术领域technical field

本发明涉及外辐射源雷达定位技术领域，具体是一种基于粒子滤波的5G外辐射源雷达低空目标定位方法。The invention relates to the technical field of external radiation source radar positioning, in particular to a particle filter-based 5G external radiation source radar low-altitude target positioning method.

背景技术Background technique

近年来，无人机等低空目标的飞速发展给低空领域的安全带来一定威胁，对该类目标进行探测与定位是对低空领域进行监管与治理的关键环节。In recent years, the rapid development of low-altitude targets such as drones has brought certain threats to the safety of low-altitude areas. The detection and positioning of such targets is a key link in the supervision and governance of low-altitude areas.

外辐射源雷达是指自身不发射电磁波信号，而是利用第三方辐射源信号实现对目标的探测，相较于传统雷达，外辐射源雷达具有隐蔽性强、成本低、抗干扰能力强、环境友好、节省频谱资源等优势，逐渐成为目标探测的重要的感知手段之一。External radiation source radar means that it does not emit electromagnetic wave signals itself, but uses third-party radiation source signals to detect targets. Compared with traditional radars, external radiation source radar has strong concealment, low cost, strong anti-interference ability, and environmental protection. The advantages of friendliness and saving spectrum resources have gradually become one of the important sensing methods for target detection.

相比于传统调频信号等机会照射源，5G信号具有带宽更宽、载频更高等优点，同时5G基站的密集分布使得信号的覆盖范围更广，可实现多角度、全范围的目标照射，因而利用已有的5G基站设施实现对低空目标的探测和定位具有一定优势。Compared with traditional FM signals and other opportunistic radiation sources, 5G signals have the advantages of wider bandwidth and higher carrier frequency. At the same time, the dense distribution of 5G base stations makes the signal coverage wider and can achieve multi-angle and full-range target irradiation. Therefore, Using the existing 5G base station facilities to realize the detection and positioning of low-altitude targets has certain advantages.

粒子滤波是基于蒙特卡洛仿真的最优回归贝叶斯滤波算法，其核心是将所关心的状态矢量表示为一组有关权值的随机样本即粒子，在测量的基础上，通过调节粒子的权值大小和位置来获得服从实际分布的样本，并以样本均值作为系统状态估计值。粒子滤波器作为一种有效的非线性滤波算法，具有精度高、收敛快、无需对状态方程线性化处理等优点，且不受线性化误差和高斯环境的限制，适用于系统方程为非线性和噪声为非高斯的情况。Particle filter is an optimal regression Bayesian filter algorithm based on Monte Carlo simulation. Its core is to express the concerned state vector as a group of random samples of relevant weights, that is, particles. The size and position of the weights are used to obtain samples that obey the actual distribution, and the sample mean is used as the estimated value of the system state. As an effective nonlinear filtering algorithm, the particle filter has the advantages of high precision, fast convergence, no need to linearize the state equation, and is not limited by the linearization error and the Gaussian environment. It is suitable for systems whose equations are nonlinear and The case where the noise is non-Gaussian.

多站外辐射源雷达常用定位方法有DOA定位、TDOA定位以及FDOA定位等，直接使用这些方法在低信噪比的复杂低空环境下对目标进行定位会出现定位模糊。The commonly used positioning methods of multi-site radiation source radar include DOA positioning, TDOA positioning and FDOA positioning, etc. Directly using these methods to locate the target in a complex low-altitude environment with low signal-to-noise ratio will cause positioning ambiguity.

发明内容Contents of the invention

本发明的目的在于提供一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，以解决上述背景技术中提出的问题。The purpose of the present invention is to provide a particle filter-based 5G external radiation source radar low-altitude target positioning method to solve the problems raised in the above-mentioned background technology.

本发明的技术方案是：一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，包括以下步骤：The technical solution of the present invention is: a particle filter-based 5G external radiation source radar low-altitude target positioning method, comprising the following steps:

S1、收发站间信号同步：通过光纤信道实现所有参与定位的收发站间信号的高精度时间同步；S1. Signal synchronization between transceiver stations: realize high-precision time synchronization of signals between all transceiver stations participating in positioning through fiber optic channels;

S2、回波信号处理：外辐射源雷达系统信号接收端采用参考信道和监测信道分别接收直达波和目标回波信号，对接收信号进行处理得到直达波与目标回波时间差；S2. Echo signal processing: The signal receiving end of the external radiation source radar system uses the reference channel and the monitoring channel to receive the direct wave and target echo signals respectively, and processes the received signals to obtain the time difference between the direct wave and the target echo;

S3、目标状态转移模型与量测模型的建立：以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差Δρi,k为量测值，构造待测目标的状态转移模型与量测模型；S3. Establishment of target state transition model and measurement model: take the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error Δρ i,k between the target and the transceiver station at time k as the measured value, construct the target to be measured State transition model and measurement model;

S4、粒子初始化：构造由粒子状态与粒子权值组成的N个粒子的集合并进行粒子初始化；S4. Particle initialization: Construct a set of N particles composed of particle states and particle weights and perform particle initialization;

S5、目标与收发站间伪距误差的计算：采用到达时间差定位方法，由经回波信号处理得到的直达波与目标回波时间差计算收发站与待测目标间的伪距信息，结合目标估计位置计算伪距误差；S5. Calculation of the pseudo-range error between the target and the transceiver station: using the time difference of arrival positioning method, the pseudo-range information between the transceiver station and the target to be measured is calculated from the time difference between the direct wave and the target echo obtained by echo signal processing, and combined with target estimation Position calculation pseudo-range error;

S6、粒子权值更新：由获得的量测数据集对生成粒子的权值进行更新并计算经过归一化后的粒子权值；S6. Particle weight update: update the weight of generated particles from the obtained measurement data set and calculate the normalized particle weight;

S7、粒子重采样：用有效粒子数描述粒子的匮乏程度并与门限粒子数比较，若小于门限粒子数则对粒子进行重采样，否则结束循环；S7. Particle resampling: use the effective number of particles to describe the degree of scarcity of particles and compare it with the threshold number of particles. If it is less than the threshold number of particles, resample the particles, otherwise end the cycle;

S8、目标状态提取：从粒子集中提取目标状态，得到经定位优化后的低空目标位置。S8. Target state extraction: extract the target state from the particle concentration, and obtain the low-altitude target position after positioning optimization.

优选的，S3包括设目标在第k时刻的状态为xk，则其状态转移模型可以表示为：xk＝fk(xk-1)+vk，Preferably, S3 includes assuming that the state of the target at the kth moment is x k , then its state transition model can be expressed as: x k =f k (x k-1 )+v k ,

其中，fk(.)表示第k时刻的状态转移函数，vk表示运动过程噪声；目标在第k时刻对应的量测模型表达式为：zk＝hk(xk)+wk，Among them, f k (.) represents the state transition function at the kth moment, v k represents the motion process noise; the measurement model expression corresponding to the target at the kth moment is: z k = h k (x k )+w k ,

其中，hk(.)表示第k时刻的量测函数，wk表示量测噪声，取k时刻目标Pu的位置坐标xk＝[xu,k,yu,k,zu,k]T为状态量，其中xu,k,yu,k,zu,k为第k时刻待测目标的空间坐标点；Among them, h k (.) represents the measurement function at the kth moment, w k represents the measurement noise, and the position coordinate x k of the target P u at the time k = [x u,k ,y u,k ,zu ,k ] T is the state quantity, where x u, k , y u, k , z u, k are the spatial coordinate points of the target to be measured at the kth moment;

取第k时刻参与定位的5G基站与接收站之间的伪距误差数据集

Figure BDA0004137584030000031
为量测值，其中Nsta为第k时刻参与定位的基站数量，Δρi,k为目标与第i组收发站之间的伪距误差；Take the pseudorange error data set between the 5G base station and the receiving station participating in the positioning at the kth moment
Figure BDA0004137584030000031
is the measurement value, where N sta is the number of base stations involved in positioning at the kth moment, and Δρi ,k is the pseudorange error between the target and the i-th group of transceiver stations;

从观测开始时刻到第k时刻为止，待测目标状态集合为X1:k＝{x1,x2,L,xk}，量测值集合为Zk＝{z1,z2,L,zk}。From the observation start time to the kth time, the target state set to be measured is X 1:k ={x 1 ,x 2 ,L,x k }, and the measurement value set is Z k ={z 1 ,z 2 ,L , z k }.

优选的，S4具体包括，构造含有N个粒子的集合并对其进行初始化

Figure BDA0004137584030000032
其中/>
Figure BDA0004137584030000033
表示第i个粒子在初始时刻的状态，/>
Figure BDA0004137584030000034
为该粒子此时的权值，表示如下：
Figure BDA0004137584030000035
Preferably, S4 specifically includes constructing a set containing N particles and initializing it
Figure BDA0004137584030000032
where />
Figure BDA0004137584030000033
Indicates the state of the i-th particle at the initial moment, />
Figure BDA0004137584030000034
is the weight of the particle at this time, expressed as follows:
Figure BDA0004137584030000035

优选的，S5包括在第k时刻，外辐射源雷达定位系统由参与定位的Nsta个5G基站和一个接收站组成，具体包括以下步骤：Preferably, S5 includes at the kth moment, the external radiation source radar positioning system is composed of N sta 5G base stations and a receiving station participating in the positioning, specifically including the following steps:

S51、以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差Δρi,k为量测值进行建模：设在第k时刻，参与定位的5G基站位置坐标分别为P1(x1,y1,z1),P2(x2,y2,z2),L,

Figure BDA0004137584030000041
其与目标间伪距分别为l1,k,l2,k,L,/>
Figure BDA0004137584030000042
接收站位置坐标为Pr(xr,yr,zr)，其与目标间伪距为lr,k，则参与定位的5G基站与接收站的伪距之和可表示为：ρi,k＝li,k+lr,k i＝1,2,L,Nsta；S51. Taking the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error Δρ i,k between the target and the transceiver station at time k as the measured value to model: set the position coordinates of the 5G base station participating in the positioning at the kth time Respectively P 1 (x 1 ,y 1 ,z 1 ), P 2 (x 2 ,y 2 ,z 2 ),L,
Figure BDA0004137584030000041
The pseudo-ranges between it and the target are l 1,k ,l 2,k ,L,/>
Figure BDA0004137584030000042
The position coordinates of the receiving station are P r (x r , y r , z r ), and the pseudo-range between it and the target is l r,k , then the sum of the pseudo-ranges between the 5G base station and the receiving station participating in the positioning can be expressed as: ρ i , k = l i, k + l r, k i = 1, 2, L, N sta ;

S52、构造待测目标的状态转移模型：基站与接收站间的距离分别为d1,d2,L,

Figure BDA0004137584030000043
待测目标位置坐标为Pu(xu,k,yu,k,zu,k)，由回波信号处理得到直达波与目标回波时间差分别为Δτ1,k,Δτ2,k,L,/>
Figure BDA0004137584030000044
光速用c表示，根据关系式Δτi,k×c＝ρi,k-di i＝1,2,L,Nsta，k时刻待测参与定位的5G基站与接收站之间的伪距之和可表示为：ρi,k＝Δτi,k×c+di i＝1,2,L,Nsta；S52. Construct the state transition model of the target to be measured: the distances between the base station and the receiving station are d 1 , d 2 , L,
Figure BDA0004137584030000043
The position coordinates of the target to be measured are P u (x u,k ,y u,k ,zu ,k ), and the time differences between the direct wave and the target echo obtained by echo signal processing are Δτ 1,k , Δτ 2,k , L, />
Figure BDA0004137584030000044
The speed of light is represented by c, according to the relationship Δτ i,k ×c=ρ i,k -d i i=1,2,L,N sta , the pseudo-range between the 5G base station and the receiving station to be measured at time k The sum can be expressed as: ρ i,k =Δτ i,k ×c+d i i=1,2,L,N sta ;

S53、构造待测目标的量测模型：由于量测噪声的存在，根据空间位置几何关系会得到多个可能的目标位置，对得到的所有可能目标位置坐标值取平均作为初始目标估计位置，则在目标估计位置

Figure BDA0004137584030000045
处参与定位的5G基站与接收站之间的伪距之和可以表示为：/>
Figure BDA0004137584030000046
S53. Construct the measurement model of the target to be measured: Due to the existence of measurement noise, multiple possible target positions will be obtained according to the spatial position geometric relationship, and the average of all possible target position coordinates obtained is used as the initial target estimated position, then at the estimated position of the target
Figure BDA0004137584030000045
The sum of the pseudo-ranges between the 5G base station and the receiving station participating in the positioning can be expressed as: />
Figure BDA0004137584030000046

则伪距误差可以表示为：

Figure BDA0004137584030000047
Then the pseudorange error can be expressed as:
Figure BDA0004137584030000047

S54、输出第k时刻的伪距误差量测集：最终得到第k时刻由多站测得的伪距误差量测集为：

Figure BDA0004137584030000048
S54. Output the pseudorange error measurement set at the kth moment: finally obtain the pseudorange error measurement set measured by multiple stations at the kth moment:
Figure BDA0004137584030000048

优选的，S6具体包括由获得的量测数据集

Figure BDA0004137584030000051
对生成粒子的权值进行更新，表示如下：/>
Figure BDA0004137584030000052
Preferably, S6 specifically includes the measurement data set obtained by
Figure BDA0004137584030000051
Update the weight of the generated particles, expressed as follows: />
Figure BDA0004137584030000052

其中，

Figure BDA0004137584030000053
为似然函数，/>
Figure BDA0004137584030000054
为重要密度函数，/>
Figure BDA0004137584030000055
为先验密度函数，若重要密度函数/>
Figure BDA0004137584030000056
与先验密度函数/>
Figure BDA0004137584030000057
相等，则粒子权值可以表示为：/>
Figure BDA0004137584030000058
in,
Figure BDA0004137584030000053
is the likelihood function, />
Figure BDA0004137584030000054
is the important density function, />
Figure BDA0004137584030000055
is the prior density function, if the important density function/>
Figure BDA0004137584030000056
with the prior density function />
Figure BDA0004137584030000057
equal, the particle weight can be expressed as: />
Figure BDA0004137584030000058

在低空环境下，假设各站与目标之间伪距误差彼此独立，则似然函数可以表示为：

Figure BDA0004137584030000059
那么，粒子权值可以表示为：
Figure BDA00041375840300000510
In the low-altitude environment, assuming that the pseudo-range errors between each station and the target are independent of each other, the likelihood function can be expressed as:
Figure BDA0004137584030000059
Then, the particle weight can be expressed as:
Figure BDA00041375840300000510

归一化后的粒子权值可以表示为：

Figure BDA00041375840300000511
The normalized particle weights can be expressed as:
Figure BDA00041375840300000511

优选的，S7包括使用有效粒子数作为一个指标对粒子的匮乏程度进行描述，其估计值可以表示为：

Figure BDA00041375840300000512
Preferably, S7 includes using the number of effective particles as an indicator to describe the degree of scarcity of particles, and its estimated value can be expressed as:
Figure BDA00041375840300000512

门限粒子数估计值可以表示为：

Figure BDA00041375840300000513
The threshold particle number estimate can be expressed as:
Figure BDA00041375840300000513

若Neff＜Nth，则对粒子进行重采样，否则记录有效粒子集，令

Figure BDA0004137584030000061
If N eff <N th , resample the particles, otherwise record the effective particle set, let
Figure BDA0004137584030000061

优选的，S8包括由式

Figure BDA0004137584030000062
提取目标状态xk＝[xu,k,yu,k,zu,k]T，得到经定位优化后的低空目标位置Pu(xu,k,yu,k,zu,k)坐标，重复该过程直到目标轨迹结束。Preferably, S8 includes the formula
Figure BDA0004137584030000062
Extract the target state x k ＝[x u,k ,y u,k ,zu ,k ] T , and obtain the optimized low-altitude target position P u (x u,k ,y u,k ,zu ,k ) coordinates, repeat this process until the end of the target trajectory.

本发明通过改进在此提供一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，与现有技术相比，具有如下改进及优点：The present invention provides a particle filter-based 5G external radiation source radar low-altitude target positioning method through improvement. Compared with the prior art, it has the following improvements and advantages:

本发明采用基于时间差的定位方法得到伪距信息，以目标到参与定位的5G基站与接收站之间的伪距误差作为量测值，通过对接收到的回波信号进行处理得到初步定位以及伪距信息作为先验信息，构造目标状态转移模型与量测模型，通过粒子滤波算法对待测目标位置进行估计，最终实现目标定位，降低了低空复杂环境下杂波与干扰对目标定位的影响。The present invention adopts a positioning method based on time difference to obtain pseudo-range information, takes the pseudo-range error between the target and the 5G base station participating in positioning and the receiving station as the measurement value, and obtains preliminary positioning and pseudo-range information by processing the received echo signal. The range information is used as prior information to construct the target state transition model and measurement model, and the particle filter algorithm is used to estimate the position of the target to be measured, and finally achieve target positioning, which reduces the impact of clutter and interference on target positioning in low-altitude complex environments.

附图说明Description of drawings

下面结合附图和实施例对本发明作进一步解释：Below in conjunction with accompanying drawing and embodiment the present invention will be further explained:

图1是本发明的5G外辐射源雷达多站单目标定位示意图；Fig. 1 is a schematic diagram of 5G external radiation source radar multi-station single target positioning of the present invention;

图2是本发明的定位方法流程图；Fig. 2 is the flow chart of positioning method of the present invention;

图3是本发明的粒子滤波算法流程图。Fig. 3 is a flowchart of the particle filter algorithm of the present invention.

具体实施方式Detailed ways

下面对本发明进行详细说明，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The present invention will be described in detail below, and the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

本发明通过改进在此提供一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，本发明的技术方案是：The present invention provides a particle filter-based 5G external radiation source radar low-altitude target positioning method through improvement. The technical solution of the present invention is:

如图1-图3所示，一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，包括以下步骤：As shown in Figures 1-3, a particle filter-based 5G external radiation source radar low-altitude target positioning method includes the following steps:

S1、收发站间信号同步：通过光纤信道实现所有参与定位的收发站间信号的高精度时间同步；S1. Signal synchronization between transceiver stations: realize high-precision time synchronization of signals between all transceiver stations participating in positioning through fiber optic channels;

S2、回波信号处理：外辐射源雷达系统信号接收端采用参考信道和监测信道分别接收直达波和目标回波信号，对接收信号进行处理得到直达波与目标回波时间差；S2. Echo signal processing: The signal receiving end of the external radiation source radar system uses the reference channel and the monitoring channel to receive the direct wave and target echo signals respectively, and processes the received signals to obtain the time difference between the direct wave and the target echo;

S3、目标状态转移模型与量测模型的建立：以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差为Δρi,k量测值，构造待测目标的状态转移模型与量测模型，具体的，设目标在第k时刻的状态为xk，则其状态转移模型可以表示为：xk＝fk(xk-1)+vk，S3. Establishment of the target state transition model and measurement model: take the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error between the target and the transceiver station at time k is the measured value of Δρ i,k , and construct the target to be measured State transition model and measurement model. Specifically, assuming that the state of the target at the kth moment is x k , its state transition model can be expressed as: x k =f k (x k-1 )+v k ,

其中，fk(.)表示第k时刻的状态转移函数，vk表示运动过程噪声；目标在第k时刻对应的量测模型表达式为：zk＝hk(xk)+wk，Among them, f k (.) represents the state transition function at the kth moment, v k represents the motion process noise; the measurement model expression corresponding to the target at the kth moment is: z k = h k (x k )+w k ,

其中，hk(.)表示第时刻的量测函数，wk表示量测噪声，取k时刻目标Pu的位置坐标xk＝[xu,k,yu,k,zu,k]T为状态量，其中xu,k,yu,k,zu,k为第k时刻待测目标的空间坐标点；Among them, h k (.) represents the measurement function at the first moment, w k represents the measurement noise, and the position coordinate x k of the target P u at time k = [x u,k ,y u,k ,zu ,k ] T is the state quantity, where x u, k , y u, k , z u, k are the spatial coordinate points of the target to be measured at the kth moment;

取第k时刻参与定位的5G基站与接收站之间的伪距误差数据集

Figure BDA0004137584030000071
为量测值，其中Nsta为第k时刻参与定位的基站数量，Δρi,k为第k时刻目标与第i组收发站之间的伪距误差；Take the pseudorange error data set between the 5G base station and the receiving station participating in the positioning at the kth moment
Figure BDA0004137584030000071
is the measured value, where N sta is the number of base stations participating in positioning at the kth moment, and Δρi ,k is the pseudorange error between the target at the kth moment and the i-th transceiver station;

从观测开始时刻到第k时刻为止，待测目标状态集合为X1:k＝{x1,x2,L,xk}，量测值集合为Zk＝{z1,z2,L,zk}；From the observation start time to the kth time, the target state set to be measured is X 1:k ={x 1 ,x 2 ,L,x k }, and the measurement value set is Z k ={z 1 ,z 2 ,L , z k };

S4、粒子初始化：构造由粒子状态与粒子权值组成的N个粒子的集合并进行粒子初始化，具体的，构造含有N个粒子的集合并对其进行初始化

Figure BDA0004137584030000081
其中/>
Figure BDA0004137584030000082
表示第i个粒子在初始时刻的状态，/>
Figure BDA0004137584030000083
为该粒子此时的权值，表示如下：/>
Figure BDA0004137584030000084
S4. Particle initialization: Construct a set of N particles composed of particle states and particle weights and perform particle initialization. Specifically, construct a set containing N particles and initialize them
Figure BDA0004137584030000081
where />
Figure BDA0004137584030000082
Indicates the state of the i-th particle at the initial moment, />
Figure BDA0004137584030000083
is the weight of the particle at this time, expressed as follows: />
Figure BDA0004137584030000084

S5、目标与收发站间伪距误差的计算：采用到达时间差定位方法，由经回波信号处理得到的直达波与目标回波时间差计算收发站与待测目标间的伪距信息，结合目标估计位置计算伪距误差，具体的，在第k时刻，外辐射源雷达定位系统由参与定位的Nsta个5G基站和一个接收站组成，具体包括以下步骤：S5. Calculation of the pseudo-range error between the target and the transceiver station: using the time difference of arrival positioning method, the pseudo-range information between the transceiver station and the target to be measured is calculated from the time difference between the direct wave and the target echo obtained by echo signal processing, and combined with target estimation Position calculation pseudo-range error, specifically, at the kth moment, the external radiation source radar positioning system is composed of N sta 5G base stations and a receiving station participating in the positioning, specifically including the following steps:

S51、以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差Δρi,k为量测值进行建模：设在第k时刻，参与定位的5G基站位置坐标分别为P1(x1,y1,z1),P2(x2,y2,z2),L,

Figure BDA0004137584030000085
其与目标间伪距分别为l1,k,l2,k,L,/>
Figure BDA0004137584030000086
接收站位置坐标为Pr(xr,yr,zr)，其与目标间伪距为lr,k，则参与定位的5G基站与接收站的伪距之和可表示为：ρi,k＝li,k+lr,k i＝1,2,L,Nsta；S51. Taking the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error Δρ i,k between the target and the transceiver station at time k as the measured value to model: set the position coordinates of the 5G base station participating in the positioning at the kth time Respectively P 1 (x 1 ,y 1 ,z 1 ), P 2 (x 2 ,y 2 ,z 2 ),L,
Figure BDA0004137584030000085
The pseudo-ranges between it and the target are l 1,k ,l 2,k ,L,/>
Figure BDA0004137584030000086
The position coordinates of the receiving station are P r (x r , y r , z r ), and the pseudo-range between it and the target is l r,k , then the sum of the pseudo-ranges between the 5G base station and the receiving station participating in the positioning can be expressed as: ρ i , k = l i, k + l r, k i = 1, 2, L, N sta ;

S52、构造待测目标的状态转移模型：基站与接收站间的距离分别为d1,d2,L,

Figure BDA0004137584030000087
待测目标位置坐标为Pu(xu,k,yu,k,zu,k)，由回波信号处理得到直达波与目标回波时间差分别为Δτ1,k,Δτ2,k,L,/>
Figure BDA0004137584030000091
光速用c表示，根据关系式Δτi,k×c＝ρi,k-di i＝1,2,L,Nsta，k时刻待测参与定位的5G基站与接收站之间的伪距之和可表示为：ρi,k＝Δτi,k×c+di i＝1,2,L,Nsta；S52. Construct the state transition model of the target to be measured: the distances between the base station and the receiving station are d 1 , d 2 , L,
Figure BDA0004137584030000087
The position coordinates of the target to be measured are P u (x u,k ,y u,k ,zu ,k ), and the time differences between the direct wave and the target echo obtained by echo signal processing are Δτ 1,k , Δτ 2,k , L, />
Figure BDA0004137584030000091
The speed of light is represented by c, according to the relationship Δτ i,k ×c=ρ i,k -d i i=1,2,L,N sta , the pseudo-range between the 5G base station and the receiving station to be measured at time k The sum can be expressed as: ρ i,k =Δτ i,k ×c+d i i=1,2,L,N sta ;

S53、构造待测目标的量测模型：由于量测噪声的存在，根据空间位置几何关系会得到多个可能的目标位置，对得到的所有可能目标位置坐标值取平均作为初始目标估计位置，则在目标估计位置

Figure BDA0004137584030000092
处参与定位的5G基站与接收站之间的伪距之和可以表示为：/>
Figure BDA0004137584030000093
S53. Construct the measurement model of the target to be measured: Due to the existence of measurement noise, multiple possible target positions will be obtained according to the spatial position geometric relationship, and the average of all possible target position coordinates obtained is used as the initial target estimated position, then at the estimated position of the target
Figure BDA0004137584030000092
The sum of the pseudo-ranges between the 5G base station and the receiving station participating in the positioning can be expressed as: />
Figure BDA0004137584030000093

则伪距误差可以表示为：

Figure BDA0004137584030000094
Then the pseudorange error can be expressed as:
Figure BDA0004137584030000094

S54、输出第k时刻的伪距误差量测集：最终得到第k时刻由多站测得的伪距误差量测集为：

Figure BDA0004137584030000095
S54. Output the pseudorange error measurement set at the kth moment: finally obtain the pseudorange error measurement set measured by multiple stations at the kth moment:
Figure BDA0004137584030000095

S6、粒子权值更新：由获得的量测数据集对生成粒子的权值进行更新并计算经过归一化后的粒子权值，具体包括由获得的量测数据集

Figure BDA0004137584030000096
对生成粒子的权值进行更新，表示如下：/>
Figure BDA0004137584030000097
S6. Particle weight update: update the weight of generated particles from the obtained measurement data set and calculate the normalized particle weight, specifically including the obtained measurement data set
Figure BDA0004137584030000096
Update the weight of the generated particles, expressed as follows: />
Figure BDA0004137584030000097

其中，

Figure BDA0004137584030000098
为似然函数，/>
Figure BDA0004137584030000099
为重要密度函数，/>
Figure BDA00041375840300000910
为先验密度函数，若重要密度函数/>
Figure BDA00041375840300000911
与先验密度函数/>
Figure BDA0004137584030000101
相等，则粒子权值可以表示为：/>
Figure BDA0004137584030000102
in,
Figure BDA0004137584030000098
is the likelihood function, />
Figure BDA0004137584030000099
is the important density function, />
Figure BDA00041375840300000910
is the prior density function, if the important density function/>
Figure BDA00041375840300000911
with the prior density function />
Figure BDA0004137584030000101
equal, the particle weight can be expressed as: />
Figure BDA0004137584030000102

在低空环境下，假设各站与目标之间伪距误差彼此独立，则似然函数可以表示为：

Figure BDA0004137584030000103
In the low-altitude environment, assuming that the pseudo-range errors between each station and the target are independent of each other, the likelihood function can be expressed as:
Figure BDA0004137584030000103

那么，粒子权值可以表示为：

Figure BDA0004137584030000104
Then, the particle weight can be expressed as:
Figure BDA0004137584030000104

归一化后的粒子权值可以表示为：

Figure BDA0004137584030000105
The normalized particle weights can be expressed as:
Figure BDA0004137584030000105

S7、粒子重采样：用有效粒子数描述粒子的匮乏程度并与门限粒子数比较，若小于门限粒子数则对粒子进行重采样，否则结束循环，具体的，使用有效粒子数作为一个指标对粒子的匮乏程度进行描述，其估计值可以表示为：

Figure BDA0004137584030000106
S7. Particle resampling: Use the effective number of particles to describe the degree of scarcity of particles and compare it with the threshold number of particles. If it is less than the threshold number of particles, resample the particles, otherwise end the cycle. Specifically, use the number of effective particles as an indicator to resample the particles To describe the degree of scarcity, its estimated value can be expressed as:
Figure BDA0004137584030000106

门限粒子数估计值可以表示为：

Figure BDA0004137584030000107
The threshold particle number estimate can be expressed as:
Figure BDA0004137584030000107

若Neff＜Nth，则对粒子进行重采样，否则记录有效粒子集，令

Figure BDA0004137584030000108
If N eff <N th , resample the particles, otherwise record the effective particle set, let
Figure BDA0004137584030000108

S8、目标状态提取：从粒子集中提取目标状态，得到经定位优化后的低空目标位置，具体的，由式

Figure BDA0004137584030000109
提取目标状态xk＝[xu,k,yu,k,zu,k]T，得到经定位优化后的低空目标位置Pu(xu,k,yu,k,zu,k)坐标，重复该过程直到目标轨迹结束。S8. Target state extraction: extract the target state from the particle concentration, and obtain the low-altitude target position after positioning optimization. Specifically, the formula
Figure BDA0004137584030000109
Extract the target state x k ＝[x u,k ,y u,k ,zu ,k ] T , and obtain the optimized low-altitude target position P u (x u,k ,y u,k ,zu ,k ) coordinates, repeat this process until the end of the target trajectory.

基于上述方法，采用基于时间差的定位方法得到伪距信息，以目标到参与定位的5G基站与接收站之间的伪距误差作为量测值，通过对接收到的回波信号进行处理得到初步定位以及伪距信息作为先验信息，构造目标状态转移模型与量测模型，通过粒子滤波算法对待测目标位置进行估计，最终实现目标定位，降低了低空复杂环境下杂波与干扰对目标定位的影响。Based on the above method, the pseudo-range information is obtained by using the positioning method based on time difference, and the pseudo-range error between the target and the 5G base station participating in the positioning and the receiving station is used as the measurement value, and the preliminary positioning is obtained by processing the received echo signal And the pseudo-range information is used as prior information to construct the target state transition model and measurement model, estimate the position of the target to be measured through the particle filter algorithm, and finally achieve target positioning, reducing the impact of clutter and interference on target positioning in low-altitude complex environments .

上述说明，使本领域专业技术人员能够实现或使用本发明。对这些实施例的多种修改对本领域的专业技术人员来说将是显而易见的，本文中所定义的一般原理可以在不脱离本发明的精神或范围的情况下，在其它实施例中实现。因此，本发明将不会被限制于本文所示的这些实施例，而是要符合与本文所公开的原理和新颖特点相一致的最宽的范围。The above description enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (7)

1.一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：包括以下步骤：1. A 5G external radiation source radar low-altitude target location method based on particle filter, is characterized in that: comprise the following steps: S1、收发站间信号同步：通过光纤信道实现所有参与定位的收发站间信号的高精度时间同步；S1. Signal synchronization between transceiver stations: realize high-precision time synchronization of signals between all transceiver stations participating in positioning through fiber optic channels; S2、回波信号处理：外辐射源雷达系统信号接收端采用参考信道和监测信道分别接收直达波和目标回波信号，对接收信号进行处理得到直达波与目标回波时间差；S2. Echo signal processing: The signal receiving end of the external radiation source radar system uses the reference channel and the monitoring channel to receive the direct wave and target echo signals respectively, and processes the received signals to obtain the time difference between the direct wave and the target echo; S3、目标状态转移模型与量测模型的建立：以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差Δρi,k为量测值，构造待测目标的状态转移模型与量测模型；S3. Establishment of target state transition model and measurement model: take the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error Δρ i,k between the target and the transceiver station at time k as the measured value, construct the target to be measured State transition model and measurement model; S4、粒子初始化：构造由粒子状态与粒子权值组成的N个粒子的集合并进行粒子初始化；S4. Particle initialization: Construct a set of N particles composed of particle states and particle weights and perform particle initialization; S5、目标与收发站间伪距误差的计算：采用到达时间差定位方法，由经回波信号处理得到的直达波与目标回波时间差计算收发站与待测目标间的伪距信息，结合目标估计位置计算伪距误差；S5. Calculation of the pseudo-range error between the target and the transceiver station: using the time difference of arrival positioning method, the pseudo-range information between the transceiver station and the target to be measured is calculated from the time difference between the direct wave and the target echo obtained by echo signal processing, and combined with target estimation Position calculation pseudo-range error; S6、粒子权值更新：由获得的量测数据集对生成粒子的权值进行更新并计算经过归一化后的粒子权值；S6. Particle weight update: update the weight of generated particles from the obtained measurement data set and calculate the normalized particle weight; S7、粒子重采样：用有效粒子数描述粒子的匮乏程度并与门限粒子数比较，若小于门限粒子数则对粒子进行重采样，否则结束循环；S7. Particle resampling: use the effective number of particles to describe the degree of scarcity of particles and compare it with the threshold number of particles. If it is less than the threshold number of particles, resample the particles, otherwise end the cycle; S8、目标状态提取：从粒子集中提取目标状态，得到经定位优化后的低空目标位置。S8. Target state extraction: extract the target state from the particle concentration, and obtain the low-altitude target position after positioning optimization. 2.根据权利要求1所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S3包括设目标在第k时刻的状态为xk，则其状态转移模型可以表示为：2. A kind of 5G external radiation source radar low-altitude target location method based on particle filter according to claim 1, it is characterized in that: said S3 includes setting the state of the target at the kth moment as x k , then its state transition model It can be expressed as: xk＝fk(xk-1)+vk，x k =f k (x k-1 )+v k , 其中，fk(.)表示第k时刻的状态转移函数，vk表示运动过程噪声；目标在第k时刻对应的量测模型表达式为：Among them, f k (.) represents the state transition function at the kth moment, and v k represents the noise of the motion process; the measurement model expression corresponding to the target at the kth moment is: zk＝hk(xk)+wk，z k =h k (x k )+w k , 其中，hk(.)表示第k时刻的量测函数，wk表示量测噪声，取k时刻目标Pu的位置坐标xk＝[xu,k,yu,k,zu,k]T为状态量，其中xu,k,yu,k,zu,k为第k时刻待测目标的空间坐标点；Among them, h k (.) represents the measurement function at the kth moment, w k represents the measurement noise, and the position coordinate x k of the target P u at the time k = [x u,k ,y u,k ,zu ,k ] T is the state quantity, where x u, k , y u, k , z u, k are the spatial coordinate points of the target to be measured at the kth moment; 取第k时刻参与定位的5G基站与接收站之间的伪距误差数据集
Figure FDA0004137584010000025
为量测值，其中Nsta为第k时刻参与定位的基站数量，Δρi,k为第k时刻与第i组收发站之间的伪距误差；Take the pseudorange error data set between the 5G base station and the receiving station participating in the positioning at the kth moment
Figure FDA0004137584010000025
is the measured value, where N sta is the number of base stations involved in positioning at the kth moment, and Δρi ,k is the pseudorange error between the kth moment and the i-th group of transceiver stations; 从观测开始时刻到第k时刻为止，待测目标状态集合为X1:k＝{x1,x2,L,xk}，量测值集合为Zk＝{z1,z2,L,zk}。From the observation start time to the kth time, the target state set to be measured is X 1:k ={x 1 ,x 2 ,L,x k }, and the measurement value set is Z k ={z 1 ,z 2 ,L , z k }. 3.根据权利要求2所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S4具体包括，构造含有N个粒子的集合并对其进行初始化
Figure FDA0004137584010000021
其中
Figure FDA0004137584010000022
表示第i个粒子在初始时刻的状态，/>
Figure FDA0004137584010000023
为该粒子此时的权值，表示如下：3. A particle filter-based 5G external radiation source radar low-altitude target location method according to claim 2, characterized in that: said S4 specifically includes constructing a set containing N particles and initializing it
Figure FDA0004137584010000021
in
Figure FDA0004137584010000022
Indicates the state of the i-th particle at the initial moment, />
Figure FDA0004137584010000023
is the weight of the particle at this time, expressed as follows:
Figure FDA0004137584010000024
Figure FDA0004137584010000024
 4.根据权利要求3所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S5包括在第k时刻，外辐射源雷达定位系统由参与定位的Nsta个5G基站和一个接收站组成，具体包括以下步骤：4. A kind of 5G external radiation source radar low-altitude target location method based on particle filter according to claim 3, it is characterized in that: said S5 comprises that at the kth moment, the external radiation source radar positioning system is composed of N sta who participate in positioning It consists of two 5G base stations and one receiving station, which specifically includes the following steps: S51、以k时刻待测目标位置坐标为状态量，k时刻目标与收发站之间伪距误差Δρi,k为量测值进行建模：设在第k时刻，参与定位的5G基站位置坐标分别为P1(x1,y1,z1),P2(x2,y2,z2),L,
Figure FDA0004137584010000031
其与目标间伪距分别为l1,k,l2,k,L,/>
Figure FDA0004137584010000032
接收站位置坐标为Pr(xr,yr,zr)，其与目标间伪距为lr,k，则参与定位的5G基站与接收站的伪距之和可表示为：S51. Taking the position coordinates of the target to be measured at time k as the state quantity, and the pseudo-range error Δρ i,k between the target and the transceiver station at time k as the measured value to model: set the position coordinates of the 5G base station participating in the positioning at the kth time Respectively P 1 (x 1 ,y 1 ,z 1 ), P 2 (x 2 ,y 2 ,z 2 ),L,
Figure FDA0004137584010000031
The pseudo-ranges between it and the target are l 1,k ,l 2,k ,L,/>
Figure FDA0004137584010000032
The position coordinates of the receiving station are P r (x r , y r , z r ), and the pseudo-range between it and the target is l r,k , then the sum of the pseudo-ranges between the 5G base stations participating in the positioning and the receiving station can be expressed as: ρi,k＝li,k+lr,k i＝1,2,L,Nsta；ρ i,k = l i,k +l r,k i=1,2,L,N sta ; S52、构造待测目标的状态转移模型：基站与接收站间的距离分别为d1,d2,L,
Figure FDA0004137584010000033
待测目标位置坐标为Pu(xu,k,yu,k,zu,k)，由回波信号处理得到直达波与目标回波时间差分别为Δτ1,k,Δτ2,k,L,/>
Figure FDA0004137584010000034
光速用c表示，根据关系式Δτi,k×c＝ρi,k-dii＝1,2,L,Nsta，k时刻待测参与定位的5G基站与接收站之间的伪距之和可表示为：S52. Construct the state transition model of the target to be measured: the distances between the base station and the receiving station are d 1 , d 2 , L,
Figure FDA0004137584010000033
The position coordinates of the target to be measured are P u (x u,k ,y u,k ,zu ,k ), and the time differences between the direct wave and the target echo obtained by echo signal processing are Δτ 1,k , Δτ 2,k , L, />
Figure FDA0004137584010000034
The speed of light is represented by c, according to the relationship Δτ i,k ×c=ρ i,k -d i i=1,2,L,N sta , the pseudo-range between the 5G base station and the receiving station to be measured at time k The sum can be expressed as: ρi,k＝Δτi,k×c+di i＝1,2,L,Nsta；ρ i,k =Δτ i,k ×c+d i i=1,2,L,N sta ; S53、构造待测目标的量测模型：由于量测噪声的存在，根据空间位置几何关系会得到多个可能的目标位置，对得到的所有可能目标位置坐标值取平均作为初始目标估计位置，则在目标估计位置
Figure FDA0004137584010000035
处参与定位的5G基站与接收站之间的伪距之和可以表示为：S53. Construct the measurement model of the target to be measured: Due to the existence of measurement noise, multiple possible target positions will be obtained according to the spatial position geometric relationship, and the average of all possible target position coordinates obtained is used as the initial target estimated position, then at the estimated position of the target
Figure FDA0004137584010000035
The sum of the pseudoranges between the 5G base station and the receiving station participating in the positioning can be expressed as:
Figure FDA0004137584010000036
Figure FDA0004137584010000036
 则伪距误差可以表示为：Then the pseudorange error can be expressed as:
Figure FDA0004137584010000041
Figure FDA0004137584010000041
 S54、输出第k时刻的伪距误差量测集：最终得到第k时刻由多站测得的伪距误差量测集为：S54. Output the pseudorange error measurement set at the kth moment: finally obtain the pseudorange error measurement set measured by multiple stations at the kth moment:
Figure FDA0004137584010000042
Figure FDA0004137584010000042
 5.根据权利要求4所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S6具体包括由获得的量测数据集
Figure FDA0004137584010000043
对生成粒子的权值进行更新，表示如下：5. A particle filter-based 5G external radiation source radar low-altitude target location method according to claim 4, characterized in that: said S6 specifically includes the measurement data set obtained by
Figure FDA0004137584010000043
Update the weights of generated particles as follows:
Figure FDA0004137584010000044
Figure FDA0004137584010000044
 其中，
Figure FDA0004137584010000045
为似然函数，/>
Figure FDA0004137584010000046
为重要密度函数，/>
Figure FDA0004137584010000047
为先验密度函数，若重要密度函数/>
Figure FDA0004137584010000048
与先验密度函数/>
Figure FDA0004137584010000049
相等，则粒子权值可以表示为：in,
Figure FDA0004137584010000045
is the likelihood function, />
Figure FDA0004137584010000046
is the important density function, />
Figure FDA0004137584010000047
is the prior density function, if the important density function/>
Figure FDA0004137584010000048
with the prior density function />
Figure FDA0004137584010000049
equal, the particle weight can be expressed as:
Figure FDA00041375840100000410
Figure FDA00041375840100000410
 在低空环境下，假设各站与目标之间伪距误差彼此独立，则似然函数可以表示为：In the low-altitude environment, assuming that the pseudo-range errors between each station and the target are independent of each other, the likelihood function can be expressed as:
Figure FDA00041375840100000411
Figure FDA00041375840100000411
 那么，粒子权值可以表示为：Then, the particle weight can be expressed as:
Figure FDA00041375840100000412
Figure FDA00041375840100000412
 归一化后的粒子权值可以表示为：The normalized particle weights can be expressed as:
Figure FDA0004137584010000051
Figure FDA0004137584010000051
 6.根据权利要求5所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S7包括使用有效粒子数作为一个指标对粒子的匮乏程度进行描述，其估计值可以表示为：6. A particle filter-based 5G external radiation source radar low-altitude target location method according to claim 5, characterized in that: said S7 includes using the number of effective particles as an index to describe the degree of scarcity of particles, and its estimation Values can be expressed as:
Figure FDA0004137584010000052
Figure FDA0004137584010000052
 门限粒子数估计值可以表示为：The threshold particle number estimate can be expressed as:
Figure FDA0004137584010000053
Figure FDA0004137584010000053
 若Neff＜Nth，则对粒子进行重采样，否则记录有效粒子集，令
Figure FDA0004137584010000054
If N eff <N th , resample the particles, otherwise record the effective particle set, let
Figure FDA0004137584010000054
 7.根据权利要求6所述的一种基于粒子滤波的5G外辐射源雷达低空目标定位方法，其特征在于：所述S8包括由式
Figure FDA0004137584010000055
提取目标状态xk＝[xu,k,yu,k,zu,k]T，得到经定位优化后的低空目标位置Pu(xu,k,yu,k,zu,k)坐标，重复该过程直到目标轨迹结束。7. A kind of 5G external radiation source radar low-altitude target location method based on particle filter according to claim 6, it is characterized in that: said S8 comprises by formula
Figure FDA0004137584010000055
Extract the target state x k ＝[x u,k ,y u,k ,zu ,k ] T , and obtain the optimized low-altitude target position P u (x u,k ,y u,k ,zu ,k ) coordinates, repeat this process until the end of the target trajectory.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117491988A (en) * 2023-12-29 2024-02-02 中国电子科技集团公司第十四研究所 Particle filtering broadband multi-frequency low-altitude angle measurement method
CN117491988B (en) * 2023-12-29 2024-03-22 中国电子科技集团公司第十四研究所 A particle filter broadband multi-frequency low-altitude angle measurement method

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