CN105277938A

CN105277938A - Vibration amplitude high-precision microwave measurement method based on least squares estimation

Info

Publication number: CN105277938A
Application number: CN201510695565.0A
Authority: CN
Inventors: 胡程; 李阳; 王锐; 李奥林; 龙腾; 曾涛; 冯咬齐; 何琳
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2015-10-22
Filing date: 2015-10-22
Publication date: 2016-01-27

Abstract

The invention provides a method for measuring the non-contact vibration amplitude based on the least squares method. The specific process is: step 1, analyze the frequency spectrum of the complex baseband echo of the radar, and extract the amplitude of each harmonic; step 2, calculate the different harmonics Obtain the observed harmonic pair vector; step 3, assume that the target amplitude is within the intersection of the detectable ranges A _b to A _e of different harmonic pairs in the harmonic pair vector; according to the vibration amplitude step value A ₀ , Discretize A _b ~ A _e into A ₁ , A ₂ , A ₃ ... A _m ; step 4, take A ₁ , A ₂ , A ₃ ... A _m as the estimated value of the target vibration amplitude in turn, and calculate each In the case of the harmonic pair vector, the harmonic pair matrix Jm is obtained; Step 5, calculating the sum of each row of Jm The sum of the mean square errors; then according to the least square estimation, based on the smallest J _i (A), the final estimated value of the target vibration amplitude is obtained. This method is directly based on the ratio of a pair of harmonics to obtain the vibration amplitude with higher accuracy, which is of great significance for radar to measure the vibration amplitude of the target with high precision.

Description

A High-precision Microwave Measurement Method of Vibration Amplitude Based on Least Square Estimation

技术领域technical field

本发明属于雷达高精度振动测量技术领域，具体涉及一种基于最小二乘估计的振动幅度高精度微波测量方法。The invention belongs to the technical field of radar high-precision vibration measurement, and in particular relates to a high-precision microwave measurement method for vibration amplitude based on least square estimation.

背景技术Background technique

传统的振动测量器件包括位移和速度传感器。其中一个最广泛使用的是加速度计，压电式加速度计可以输出一个正比于其接触目标的加速度的电信号。另一种接触式测量仪器是线性可变差动变压器，可作为位移传感器直接测量振动目标的位移。然而受限于接触式测量，这些仪器的应用领域具有局限性。Traditional vibration measurement devices include displacement and velocity sensors. One of the most widely used is the accelerometer, a piezoelectric accelerometer that outputs an electrical signal proportional to the acceleration of the object it is in contact with. Another contact measuring instrument is the linear variable differential transformer, which can be used as a displacement sensor to directly measure the displacement of a vibrating target. However, due to contact measurement, the application fields of these instruments are limited.

一些非接触振动测量仪器是基于激光的，如激光测振仪，激光干涉仪和激光位移传感器等。这些设备成本高，而且也具有局限性，如不可避免的校准和狭窄的检测范围。另一方面，由于具有高精度、可从杂波中分离出目标、成本较低等优势，基于雷达的振动测量近些年吸引了很多研究者的兴趣。雷达测振的主要应用包括生命体征信号测量、机械结构故障检测，工程结构监测等。相关研究者利用雷达测量人体的心率和呼吸率，通过对比机械结构正常工作时的振动参数来检测其健康状态，而通过测量如楼层、塔楼和桥梁的工程结构的振动参数来监测它们的状态。Some non-contact vibration measurement instruments are laser-based, such as laser vibrometers, laser interferometers and laser displacement sensors, etc. These devices are costly and also have limitations such as unavoidable calibration and narrow detection ranges. On the other hand, due to the advantages of high precision, ability to separate targets from clutter, and low cost, radar-based vibration measurement has attracted the interest of many researchers in recent years. The main applications of radar vibration measurement include vital sign signal measurement, mechanical structure fault detection, engineering structure monitoring, etc. Relevant researchers use radar to measure the heart rate and breathing rate of the human body, detect their health status by comparing the vibration parameters of mechanical structures during normal operation, and monitor their status by measuring the vibration parameters of engineering structures such as floors, towers and bridges.

已公开的一种雷达振动幅度提取方法是基于非线性多普勒相位调制，经过振动目标散射后，雷达基带回波信号可分解为一系列幅度由目标振动幅度决定的谐波，通过获取一对谐波的幅值比来反演目标振幅。然而，噪声会造成谐波幅值的偏移，由于反演的振幅对谐波幅值很敏感，因而会引入不小的误差。A disclosed radar vibration amplitude extraction method is based on nonlinear Doppler phase modulation. After the vibration target is scattered, the radar baseband echo signal can be decomposed into a series of harmonics whose amplitude is determined by the target vibration amplitude. By obtaining a pair of The amplitude ratio of the harmonics is used to invert the target amplitude. However, the noise will cause the shift of the harmonic amplitude, and since the amplitude of the inversion is very sensitive to the harmonic amplitude, a considerable error will be introduced.

发明内容Contents of the invention

有鉴于此，本发明的目的是提供一种基于最小二乘法的非接触振动幅度的测量方法，振动目标的后向散射信号可展开为一系列谐波，基于最小二乘法同时利用这些谐波反演目标振动幅度，对提高目标振动幅度的测量精度具有重要意义。In view of this, the purpose of the present invention is to provide a method for measuring the non-contact vibration amplitude based on the least squares method. The backscattering signal of the vibrating target can be expanded into a series of harmonics, and these harmonics can be reflected based on the least squares method. It is of great significance to improve the measurement accuracy of the target vibration amplitude.

实现本发明的技术方案如下：Realize the technical scheme of the present invention as follows:

一种基于最小二乘法的非接触振动幅度的测量方法，具体过程为：A method for measuring non-contact vibration amplitude based on the least square method, the specific process is:

步骤一、分析雷达的复基带回波的频谱，提取出各个谐波的幅值H₁、H₂、H₃…H_N，其中N为预设的观测谐波的数量；Step 1. Analyze the frequency spectrum of the complex baseband echo of the radar, and extract the amplitudes H ₁ , H ₂ , H ₃ ... H _N of each harmonic, where N is the number of preset observed harmonics;

步骤二、计算不同谐波对的比值，获得观测谐波对向量其中l＞k，该谐波对向量中存在N(N-1)/2个元素；Step 2. Calculate the ratio of different harmonic pairs to obtain the observed harmonic pair vector Where l>k, there are N(N-1)/2 elements in the harmonic pair vector;

步骤三、假设目标振幅在谐波对向量中不同谐波对的可检测范围的交集A_b～A_e内；根据预期的测振幅度精度，定义一个振动幅度步进值A₀，根据所述A₀将A_b～A_e离散化为A₁、A₂、A₃……A_m，m＝(A_e-A_b)/A₀代表谐波对矩阵中存在的谐波对向量的个数；Step 3. Assume that the target amplitude is in the harmonic pair vector In the intersection of the detectable ranges of different harmonic pairs in A _b ～A _e ; according to the expected vibration amplitude accuracy, define a vibration amplitude step value A ₀ , and discretize A _b ～A _e according to A ₀ as A ₁ , A ₂ , A ₃ ... A _m , m=(A _e -A _b )/A ₀ represents the number of harmonic pair vectors existing in the harmonic pair matrix;

步骤四、依次将A₁、A₂、A₃……A_m作为目标振动幅度估计值，计算出每一情况下谐波对向量，得到谐波对矩阵Jm；Step 4. _Taking A ₁ , A ₂ , A ₃ .

$J J m m = = [\begin{matrix} {\overset{&RightArrow; &Right Arrow;}{x x}}_{11} \\ {\overset{&RightArrow; &Right Arrow;}{x x}}_{22} \\ ... ... \\ {\overset{&RightArrow; &Right Arrow;}{x x}}_{m m} \end{matrix}] = = [\begin{matrix} {H h}_{1212} / / {H h}_{1111} & ... ... & {H h}_{11 l l} / / {H h}_{11 k k} & ... ... & {H h}_{11 N N} / / {H h}_{11 ((N N - - 11))} \\ {H h}_{22 twenty two} / / {H h}_{21 twenty one} & .. .. & {H h}_{22 l l} / / {H h}_{22 k k} & ... ... & {H h}_{22 N N} / / {H h}_{22 ((N N - - 11))} \\ ... ... \\ {H h}_{m m 22} / / {H h}_{m m 11} & ... ... & {H h}_{m m l l} / / {H h}_{m m k k} & ... ... & {H h}_{m m N N} / / {H h}_{m m ((N N - - 11))} \end{matrix}]$

步骤五、计算Jm的每一行和的均方误差和，得到Step 5. Calculate the sum of each line of Jm The sum of the mean square errors of

${J J}_{i i} ((A A)) = = {Σ Σ}_{k k = = 11}^{N N - - 11} {Σ Σ}_{l l = = k k + + 11}^{N N} {(({H h}_{i i l l} / / {H h}_{i i k k} - - {H h}_{l l} / / {H h}_{k k}))}^{22} - - - - - - ((1212))$

其中，i＝1,2……m；Among them, i=1,2...m;

然后根据最小二乘估计，基于最小的J_i(A)，获得目标振动幅度的估计值 Then according to the least squares estimation, based on the smallest J _i (A), the estimated value of the target vibration amplitude is obtained

本发明具有如下有益效果：The present invention has following beneficial effects:

本发明的一种基于最小二乘法的非接触振动幅度的测量方法，基于最小二乘法同时利用雷达基带回波的多个谐波，该算法较直接基于一对谐波比而获取振动幅度的精度更高。因此，本发明的方法对雷达高精度测量目标振动幅度有重要意义。A non-contact vibration amplitude measurement method based on the least square method of the present invention uses multiple harmonics of the radar baseband echo at the same time based on the least square method, and the algorithm is more directly based on a pair of harmonic ratios to obtain the accuracy of the vibration amplitude higher. Therefore, the method of the present invention is of great significance for the radar to measure the vibration amplitude of the target with high precision.

附图说明Description of drawings

图1为本发明基于最小二乘法的非接触振动幅度的测量方法的流程图。FIG. 1 is a flow chart of the non-contact vibration amplitude measurement method based on the least square method of the present invention.

图2雷达基带回波的谐波系数比与目标振幅和雷达波长比A/λ的函数关系。Fig. 2 The relationship between the harmonic coefficient ratio of radar baseband echo and the target amplitude and radar wavelength ratio A/λ.

图3仿真时的基带回波的频谱。The frequency spectrum of the baseband echo during simulation in Fig. 3 .

图4为利用蒙特卡洛仿真得到的各方法反演出的目标振幅的均值。Fig. 4 is the average value of the target amplitudes inverted by various methods obtained by Monte Carlo simulation.

图5为实验观测目标和实验场景；其中图5(a)为观测目标振动标定仪，图5(b)为实验场景。Figure 5 shows the experimental observation target and the experimental scene; where Figure 5(a) is the vibration calibration instrument for the observed target, and Figure 5(b) is the experimental scene.

具体实施方式detailed description

下面结合附图并举实施例，对本发明进行详细描述。The present invention will be described in detail below with reference to the accompanying drawings and examples.

不考虑幅度，连续波雷达发射的单频信号可表示为：Regardless of the amplitude, the single-frequency signal transmitted by the continuous wave radar can be expressed as:

s_T(t)＝cos(2πf_ct+φ(t))(1)s _T (t)＝cos(2πf _c t+φ(t))(1)

其中，f_c为信号载频，φ(t)为相噪。如果该信号被在距离d₀附近作位移为x(t)的振动目标反射，则信号从发射到接收经过的距离为2d(t)＝2d₀+2x(t)。接收信号可表示为：Among them, f _c is the signal carrier frequency, φ (t) is the phase noise. If the signal is reflected by a vibrating target with displacement x(t) around the distance d ₀ , the distance traveled by the signal from transmission to reception is 2d(t)=2d ₀ +2x(t). The received signal can be expressed as:

${s the s}_{R R} ((t t)) = = c c o o s the s [[22 {πf πf}_{c c} ((t t - - \frac{22 d d ((t t - - d d ((t t)) / / c c))}{c c})) + + φ φ ((t t - - \frac{22 d d ((t t - - d d ((t t)) / / c c))}{c c}))]] - - - - - - ((22))$

其中，c为光速。where c is the speed of light.

替代d(t-d(t)/c)＝d₀+x(t-d(t)/c)得：Substitute d(td(t)/c)=d ₀ +x(td(t)/c) to get:

${s the s}_{R R} ((t t)) = = c c o o s the s [[22 {πf πf}_{c c} t t - - \frac{44 {πd πd}_{00}}{λ λ} - - \frac{44 π π x x ((t t - - d d ((t t)) / / c c))}{λ λ} + + φ φ ((t t - - \frac{22 {d d}_{00}}{c c} - - \frac{22 x x ((t t - - d d ((t t)) / / c c))}{c c}))]] - - - - - - ((44))$

其中，雷达波长λ＝c/f_c。Wherein, the radar wavelength λ=c/f _c .

考虑到目标的振动周期T＞＞d₀/c，则x(t-d(t)/c)中的d(t)/c可忽略，则Considering the vibration period of the target T>>d ₀ /c, then d(t)/c in x(td(t)/c) can be ignored, then

${s the s}_{R R} ((t t)) \approx \approx c c o o s the s [[22 {πf πf}_{c c} t t - - \frac{44 {πd πd}_{00}}{λ λ} - - \frac{44 π π x x ((t t))}{λ λ} + + φ φ ((t t - - \frac{22 {d d}_{00}}{c c} - - \frac{22 x x ((t t))}{c c}))]] - - - - - - ((55))$

又由于x(t)＜＜d₀，且相噪函数是慢变化，则接收信号可表示为：And because x(t)<<d ₀ , and the phase noise function changes slowly, the received signal can be expressed as:

${s the s}_{R R} ((t t)) \approx \approx c c o o s the s [[22 {πf πf}_{c c} t t - - \frac{44 {πd πd}_{00}}{λ λ} - - \frac{44 π π x x ((t t))}{λ λ} + + φ φ ((t t - - \frac{22 {d d}_{00}}{c c}))]] - - - - - - ((66))$

利用复信号解调技术，得到基带I/Q输出可表示为：Using complex signal demodulation technology, the baseband I/Q output can be expressed as:

${s the s}_{I I} ((t t)) = = c c o o s the s [[θ θ + + \frac{44 π π x x ((t t))}{λ λ} + + Δ Δ φ φ ((t t))]] - - - - - - ((77))$

${s the s}_{Q Q} ((t t)) = = s the s i i n no [[θ θ + + \frac{44 π π x x ((t t))}{λ λ} + + Δ Δ φ φ ((t t))]] - - - - - - ((88))$

其中，θ为d₀和目标表面反射引起的相位，而Δφ(t)为总的残留相位噪声。where θ is the phase due to d ₀ and reflections from the target surface, and Δφ(t) is the total residual phase noise.

对于单频振动的目标，其位移可表示为x(t)＝Asin(2πf_vt)，结合基带I/Q路输出，得雷达复基带回波信号可表示为傅里叶级数：For a target vibrating at a single frequency, its displacement can be expressed as x(t)=Asin(2πf _v t), combined with the output of the baseband I/Q channel, the complex baseband echo signal of the radar can be expressed as a Fourier series:

$\begin{matrix} {s the s}_{B B} ((t t)) = = {s the s}_{I I} ((t t)) + + j j \cdot &Center Dot; {s the s}_{Q Q} ((t t)) \\ = = exp exp {{j j [[\frac{44 π π A A sin sin ((22 {πf πf}_{v v} t t))}{λ λ} + + φ φ + + Δ Δ φ φ ((t t))]]}} \\ = = {Σ Σ}_{n no = = - - ∞ ∞}^{∞ ∞} {J J}_{n no} ((\frac{44 π π A A}{λ λ})) exp exp {{j j ((22 {πnf πnf}_{v v} t t + + φ φ))}} \end{matrix} - - - - - - ((99))$

其中，φ＝θ+Δφ(t)为总的残留相位，J_n(x)为n阶第一类贝塞尔函数。由于e^jφ的模值恒为1，所以不会影响信号幅度。因此，当载波频率固定时，s_B(t)的各谐波的幅值仅由变量为目标振动幅度的贝塞尔系数决定。Wherein, φ=θ+Δφ(t) is the total residual phase, and J _n (x) is the n-order Bessel function of the first kind. Since the modulus of e ^jφ is always 1, it will not affect the signal amplitude. Therefore, when the carrier frequency is fixed, the magnitude of each harmonic of s _B (t) is determined only by the Bessel coefficient whose variable is the target vibration magnitude.

由式(8)知，目标的振动频率可以直接通过获取雷达复基带回波信号的基频而得到。另一方面，l和k阶谐波的幅值比：According to formula (8), the vibration frequency of the target can be directly obtained by obtaining the fundamental frequency of the radar complex baseband echo signal. On the other hand, the magnitude ratio of the l and k order harmonics:

$\frac{{H h}_{l l}}{{H h}_{k k}} = = \frac{| | {J J}_{l l} ((\frac{44 π π A A}{λ λ})) {e e}^{j j φ φ} | |}{| | {J J}_{k k} ((\frac{44 π π A A}{λ λ})) {e e}^{j j φ φ} | |} = = | | \frac{{J J}_{l l} ((44 π π A A / / λ λ))}{{J J}_{k k} ((44 π π A A / / λ λ))} | | - - - - - - ((1010))$

令l＝2，k＝1，得到谐波幅值比如图2所示。由于非线性，同一谐波比对应着不同的振动幅度。为了能解出A，需要为每个谐波对都定义1个可检测范围，使得谐波幅值比在0.2-5之间。相对于λ进行归一化，列出前几个谐波比的可检测范围如下表所示：Let l=2, k=1, get the harmonic amplitude ratio as shown in Figure 2. Due to nonlinearity, the same harmonic ratio corresponds to different vibration amplitudes. In order to solve A, it is necessary to define a detectable range for each harmonic pair, so that the harmonic amplitude ratio is between 0.2-5. Normalized relative to λ, the detectable range of the first few harmonic ratios is listed in the table below:

表1不同谐波对的可检测范围Table 1 Detectable range of different harmonic pairs

谐波对harmonic pair H₂/H₁ H ₂ /H ₁ H₃/H₁ H ₃ /H ₁ H₃/H₂ H ₃ /H ₂ 可检测范围下限Lower limit of detectable range 0.0620.062 0.1530.153 0.0930.093 可检测范围上限Detectable range upper limit 0.2880.288 0.2890.289 0.3910.391

当目标振动幅度在某一谐波对的可检测范围内时，虽然可以反演出目标振动幅度，但是噪声会引起谐波幅值的偏移，而反演结果对谐波幅值的误差很敏感，因而会导致测量结果中存在不可忽略的误差。改进方法是基于最小二乘法，同时利用多个谐波对，最小化噪声的影响，如图1所示，具体操作阐述如下：When the target vibration amplitude is within the detectable range of a certain harmonic pair, although the target vibration amplitude can be inverted, the noise will cause the offset of the harmonic amplitude, and the inversion result is very sensitive to the error of the harmonic amplitude , resulting in non-negligible errors in the measurement results. The improved method is based on the least squares method and uses multiple harmonic pairs at the same time to minimize the impact of noise, as shown in Figure 1. The specific operations are described as follows:

步骤一、分析雷达的复基带回波的频谱，提取出各个谐波的幅值H₁，H₂，H₃…H_N，其中N为预设的观测谐波的数量。Step 1: Analyze the frequency spectrum of the complex baseband echo of the radar, and extract the amplitudes H ₁ , H ₂ , H ₃ . . . H _N of each harmonic, where N is the number of preset observed harmonics.

步骤二、计算不同谐波对的比值，获得观测谐波对向量该谐波对向量中，存在N(N-1)/2个元素。Step 2. Calculate the ratio of different harmonic pairs to obtain the observed harmonic pair vector In the harmonic pair vector, there are N(N-1)/2 elements.

步骤三、假设目标振幅在谐波对向量中不同谐波对的可检测范围的交集A_b～A_e内。根据预期的测振幅度精度，定义一个振动幅度步进值A₀，可依据该值将A_b～A_e离散化为A₁、A₂、A₃……A_m，m＝(A_e-A_b)/A₀代表谐波对矩阵中存在的谐波对向量的个数。Step 3. Assume that the target amplitude is in the harmonic pair vector Within the intersection of the detectable ranges of different harmonic pairs in A _b to A _e . According to the expected vibration amplitude accuracy, define a vibration amplitude step value A ₀ , and A _b ~ A _e can be discretized into A ₁ , A ₂ , A ₃ ... A _m according to this value, m=(A _e - A _b )/A ₀ represents the number of harmonic pair vectors existing in the harmonic pair matrix.

$J J m m = = [\begin{matrix} {\overset{&RightArrow; &Right Arrow;}{x x}}_{11} \\ {\overset{&RightArrow; &Right Arrow;}{x x}}_{22} \\ ... ... \\ {\overset{&RightArrow; &Right Arrow;}{x x}}_{m m} \end{matrix}] = = [\begin{matrix} {H h}_{1212} / / {H h}_{1111} & ... ... & {H h}_{11 l l} / / {H h}_{11 k k} & ... ... & {H h}_{11 N N} / / {H h}_{11 ((N N - - 11))} \\ {H h}_{22 twenty two} / / {H h}_{21 twenty one} & .. .. & {H h}_{22 l l} / / {H h}_{22 k k} & ... ... & {H h}_{22 N N} / / {H h}_{22 ((N N - - 11))} \\ ... ... \\ {H h}_{m m 22} / / {H h}_{m m 11} & ... ... & {H h}_{m m l l} / / {H h}_{m m k k} & ... ... & {H h}_{m m N N} / / {H h}_{m m ((N N - - 11))} \end{matrix}] - - - - - - ((1111))$

其中，i＝1,2……m；Among them, i=1,2...m;

理论上观测的谐波对数量越多，测振幅度精度越高。然而，随着N的增大，可检测范围会变窄。所以，N值应该适当选取。Theoretically, the more harmonic pairs observed, the higher the accuracy of vibration amplitude measurement. However, as N increases, the detectable range becomes narrower. Therefore, the value of N should be selected appropriately.

具体应用：concrete application:

1.通过监测人体生命信号(呼吸和心跳)，来检测人体健康状态。1. By monitoring human life signals (breathing and heartbeat), to detect human health status.

2.非接触监测机械结构和复杂工程结构(楼层，桥梁等)，从而实现故障检测。2. Non-contact monitoring of mechanical structures and complex engineering structures (floors, bridges, etc.) to achieve fault detection.

3.为微波窃听技术提供基础。3. Provide the foundation for microwave eavesdropping technology.

实施例：Example:

在本实例中，选取的N值为3。由表1知，此时谐波对向量的可检测范围为0.153λ～0.288λ。由于残留相位不会影响信号的幅度，所以可令φ＝0。加上复高斯噪声，雷达基带回波可以表示为：In this example, the selected value of N is 3. Known from Table 1, the detectable range of the harmonic pair vector is 0.153λ～0.288λ at this time. Since the residual phase will not affect the amplitude of the signal, we can make φ=0. Adding complex Gaussian noise, the radar baseband echo can be expressed as:

${sn sn}_{B B} ((t t)) = = exp exp {{j j [[\frac{44 π π A A s the s i i n no ((22 {πf πf}_{v v} t t))}{λ λ}]]}} + + w w ((t t)) - - - - - - ((1212))$

其中，w(t)为复高斯噪声。由于高斯噪声是随机的，所以有必要进行多次仿真，分析最终的统计结果。相关的仿真参数如下：where w(t) is complex Gaussian noise. Since Gaussian noise is random, it is necessary to perform multiple simulations to analyze the final statistical results. The relevant simulation parameters are as follows:

表2仿真参数Table 2 Simulation parameters

参数parameter A/λA/λ f_v(Hz)f _v (Hz) SNR(dB)SNR(dB) 值value 0.230.23 1010 -9-9

其中一次的仿真结果为：sn_B(t)的频谱如图3所示，分别利用谐波对H₂/H₁，H₃/H₁和H₃/H₂，反演出的目标振幅为和误差分别为1.56％，1.35％和6.87％。令幅度步进为A₀＝0.0001λ，然后利用本发明中的方法，反演出的目标振幅为十分接近真值。One of the simulation results is: the frequency spectrum of sn _B (t) is shown in Figure 3, using the harmonic pairs H ₂ /H ₁ , H ₃ /H ₁ and H ₃ /H ₂ respectively, the inversion target amplitude is and The errors are 1.56%, 1.35%, and 6.87%, respectively. Let the amplitude step be A ₀ =0.0001λ, and then use the method in the present invention to invert the target amplitude as very close to the true value.

进行蒙特卡洛仿真，所得各方法反演出的归一化振幅如图4所示，其中A21，A31和A32分别代表利用谐波对H₂/H₁，H₃/H₁和H₃/H₂反演出的振幅，而A321代表新方法反演的振幅。图中，A321最接近真值。可见，相对于直接利用一个谐波对反演出目标振幅的方法，本发明的方法具有更高的精度。Monte Carlo simulation is carried out, and the normalized amplitudes obtained by each method are shown in Figure 4, where A21, A31 and A32 represent the harmonic pairs H ₂ /H ₁ , H ₃ /H ₁ and H ₃ /H respectively ₂ inverts the amplitude, while A321 represents the amplitude inverted by the new method. In the figure, A321 is closest to the true value. It can be seen that, compared with the method of inverting the target amplitude directly by using a harmonic pair, the method of the present invention has higher accuracy.

为了验证结果，进行了相关的振动测量实验。观测目标为振动标定仪上的角反(图5(a))，实验场景如图5(b)所示。振动标定仪带动角反作振幅为663.5μm，振动频率为10Hz的单频振动。将雷达放置在距离目标约30m处，测量结果如下：To verify the results, related vibration measurement experiments were carried out. The observation target is the angular reflection on the vibration calibration instrument (Fig. 5(a)), and the experimental scene is shown in Fig. 5(b). The vibration calibration instrument drives a single-frequency vibration with an amplitude of 663.5 μm and a vibration frequency of 10 Hz. Place the radar at a distance of about 30m from the target, and the measurement results are as follows:

分别利用谐波对H₂/H₁，H₃/H₁和H₃/H₂，反演出的目标振幅为和误差分别为8.29％，4.63％和25.74％。利用新方法，设置幅度步进为0.1μm，反演出的目标振幅为误差为0.12％。可见，新方法可大幅度提高目标振动幅度的测量精度。Using the harmonic pairs H ₂ /H ₁ , H ₃ /H ₁ and H ₃ /H ₂ respectively, the inversion target amplitude is and The errors are 8.29%, 4.63%, and 25.74%, respectively. Using the new method, set the amplitude step to 0.1 μm, and the target amplitude of the inversion is The error is 0.12%. It can be seen that the new method can greatly improve the measurement accuracy of the target vibration amplitude.

综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. based on a measuring method for the non-contacting vibration amplitude of least square method, it is characterized in that, detailed process is:

The frequency spectrum of the complex base band echo of step one, Analysis of Radar, extracts the amplitude H of each harmonic wave ₁, H ₂, H ₃h _n, wherein N is the quantity of default observation harmonic wave;

Step 2, calculate the right ratio of different harmonic wave, obtain observation harmonic wave to vector wherein l > k, this harmonic wave is to there is N (N-1)/2 element in vector;

Step 3, hypothetical target amplitude at harmonic wave to vector what middle different harmonic wave was right can the common factor A of sensing range _b~ A _ein; According to the vibration measuring amplitude precision of expection, define an Oscillation Amplitude step value A ₀, according to described A ₀by A _b~ A _ediscretely turn to A ₁, A ₂, A ₃a _m, m=(A _e-A _b)/A ₀represent harmonic wave to the number of the harmonic wave existed in matrix to vector;

Step 4, successively by A ₁, A ₂, A ₃a _mas intended vibratory amplitude estimation value, under calculating each situation, harmonic wave is to vector, obtains harmonic wave to matrix J m;

J m = [\begin{matrix} {\overset{&RightArrow;}{x}}_{1} \\ {\overset{&RightArrow;}{x}}_{2} \\ ... \\ {\overset{&RightArrow;}{x}}_{m} \end{matrix}] = [\begin{matrix} \begin{matrix} H_{12} / H_{11} & ... & H_{1 l} / H_{1 k} & ... & H_{1 N} / H_{1 (N - 1)} \end{matrix} \\ \begin{matrix} H_{22} / H_{21} & ... & H_{2 l} / H_{2 k} & ... & H_{2 N} / H_{2 (N - 1)} \end{matrix} \\ ... \\ \begin{matrix} H_{m 2} / H_{m 1} & ... & H_{m l} / H_{m k} & ... & H_{m N} / H_{m (N - 1)} \end{matrix} \end{matrix}]

Step 5, calculate Jm every a line and square error and, obtain

J_{i} (A) = Σ_{k = 1}^{N - 1} Σ_{l = k + 1}^{N} {(H_{i l} / H_{i k} - H_{l} / H_{k})}^{2} - - - (12)

Wherein, i=1,2 ... m;

Then according to least-squares estimation, based on minimum J _i(A) the final estimated value of intended vibratory amplitude, is obtained