CN106093901A - A kind of radar vibration measuring sensitivity computing method - Google Patents

Abstract

The invention discloses a kind of radar vibration measuring sensitivity computing method, the method is for being primarily based on micro-Vibration Targets echo-signal, and setting up micro-vibration phase derives vibration measuring model；Secondly vibration measuring model is derived according to micro-vibration phase, according to mean power P of distance pulse pressure peak signal S when target is static under noise free conditions_SMean power P with component of thermal noise N in the slow time echo of Vibration Targets place distance unit peak point composition_N, it is thus achieved that thermal noise average eguivalent Oscillation Amplitude NEA₀；Derive vibration measuring model based on micro-vibration phase, according to mean power P of phase noise_Φ, it is thus achieved that phase noise average eguivalent amplitude PEA₀；Last according to NEA₀And PEA₀, based on the output signal-to-noise ratio SNR of radar phase measurement_oMore than or equal to minimum detectable signal to noise ratio SNR_minCondition, it is thus achieved that the dynamic sensitivity S of system vibration measuring_min.The present invention can instruct vibration measuring radar system design and the effect of assessment vibration measuring radar vibration measuring performance.

Description

A kind of radar vibration measuring sensitivity computing method

Technical field

The invention belongs to radar vibration measuring technical field, be specifically related to a kind of radar vibration measuring sensitivity computing method.

Background technology

Micro-vibration generally exists at nature, as dynamic in the body of human body (heartbeat and the motion in thoracic cavity when breathing), pedestrian's hand and The vibration of the swing of leg, bridge and wing, lifting airscrew and warship and the rotation of armoring over-car antenna, ballistic missile bullet Vibration etc..According to Doppler's theorem, when electromagnetic wave irradiation to Vibration Targets, radar return Doppler can be produced by target Modulation, as long as demodulating the vibration information that echo-signal just can obtain target, thus reaches the function of vibration measurement.Radar is surveyed The application prospect shaken is quite varied: in disaster and accident rescue, passes through breathing and the heartbeat signal of ruins detection people, contributes to Find the wounded quickly；In Military Application, the vibration information utilizing the rotation information of wheel and engine can be to the army on ground It is identified with vehicle or tank；Furthermore it is also possible to by vibration measurement is carried out to bridge, machinery, state is carried out to it and carries out Monitoring and fault diagnosis.

Using radar to carry out vibration measurement and having been obtained for substantial amounts of research, the emphasis of research mostly concentrates on micro-vibration letter Number extraction on.Have a strong impact on owing to the phase place at the distance unit of target place can be caused by thermal noise and phase noise, cause Micro-vibration information is blanked, and the microvibration measuring result causing system is unreliable.But for containing thermal noise and phase noise The detection of actual radar system and the current still planless analysis method of ability of measurement micro-vibration signal and conclusion.

Content of the invention

In view of this, the present invention proposes a kind of radar vibration measuring sensitivity computing method, and vibration measuring radar system can be instructed to set Meter and the effect of assessment vibration measuring radar vibration measuring performance.

Realize that specific embodiments of the present invention are as follows:

A kind of radar vibration measuring sensitivity computing method, specifically comprises the following steps that

Step one, based on micro-Vibration Targets echo-signal, set up micro-vibration phase derive vibration measuring model；

Step 2, according to micro-vibration phase derive vibration measuring model, according to target place when target is static under noise free conditions The slow time echo-signal that distance unit peak point is constitutedMean power P_SAnd have Vibration Targets place distance under noise conditions Mean power P of component of thermal noise N in the slow time echo that unit peak point is constituted_N, it is thus achieved that thermal noise average eguivalent vibrates width Degree NEA₀；

Step 3, based on micro-vibration phase derive vibration measuring model, according to mean power P of phase noise_Φ, it is thus achieved that phase place is made an uproar Sound average eguivalent amplitude PEA₀；

Step 4, the thermal noise average eguivalent Oscillation Amplitude NEA obtaining according to step 2₀The phase place obtaining with step 3 is made an uproar Sound average eguivalent amplitude PEA₀, it is thus achieved that the output signal-to-noise ratio SNR of radar phase measurement_o, based on the output noise of radar phase measurement Compare SNR_oMore than or equal to minimum detectable signal to noise ratio SNR_minCondition, it is thus achieved that the amplitude that minimum detectable range measures, according to radar survey The sensitivity S of vibration_minFor minimum detectable mean amplitude of tide, it is thus achieved that the dynamic sensitivity S of radar vibration measuring_min。

Further, the detailed process of step one is as follows:

Radar launches linear FM signal to Vibration Targets, and enters row distance pulse pressure to echo-signal, it is assumed that target is being shaken There is not more walking about apart from unit, it is thus achieved that slow time signal E of Vibration Targets place distance unit peak point is during Dong:

$\left\{\begin{array}{c}E=S+N\\ S=S_0{e}^{({\mathrm{j\Φ}}_{s0}+j\frac{4{\mathrm{\πR}}_0}{\mathrm{\λ}}+j\frac{4\mathrm{\π}M\left(t\right)}{\mathrm{\λ}}+{\mathrm{j\Φ}}_{sn}(t\left)\right)}\\ N=N\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, S is component of signal in the slow time echo that micro-Vibration Targets place distance unit peak point is constituted, S₀Represent The echo strength of micro-Vibration Targets, Φ_s0It is the phase place entrained by target backscattering coefficient σ, R₀Being the distance of target, λ is for sending out Penetrating signal wavelength, M (t) is the vibration signal of target, Φ_snT () is the phase noise that target echo carries；

OrderIf | 4 π M (t)/λ |, | Φ_sn(t)|,Formula (1) is done Taylor series expansion, the phase measurement of the E after Taylor series expansion deducts target phase place under static state, it is thus achieved that Only related to intended vibratory and noise phase term, i.e.

$\begin{array}{c}{\mathrm{\Φ}}_M=\∠E/\stackrel{\‾}{S}\\ =\∠(1+j\frac{4\mathrm{\π}M\left(t\right)}{\mathrm{\λ}}+\frac{N}{\stackrel{\‾}{S}}+{\mathrm{j\Φ}}_{sn}(t)+o)\\ ={\tan }^{-1}\left(\frac{\frac{4\mathrm{\π}M\left(t\right)}{\mathrm{\λ}}+\mathrm{Im}\left(\frac{N}{\stackrel{\‾}{S}}\right)+{\mathrm{\Φ}}_{sn}\left(t\right)+\mathrm{Im}\left(o\right)}{1+\mathrm{Re}\left(\frac{N}{\stackrel{\‾}{S}}\right)+\mathrm{Re}\left(o\right)}\right)\end{array}---\left(2\right)$

Wherein, Re () and Im () represents real and imaginary part respectively, and o is the unified representation of every high-order a small amount of；

Based on | 4 π M (t)/λ |, | Φ_sn(t)|,Obtain micro-vibration phase derive vibration measuring model:

${\mathrm{\Φ}}_M\≈\frac{4\mathrm{\π}M\left(t\right)}{\mathrm{\λ}}+\mathrm{Im}\left(\frac{N}{\stackrel{\‾}{S}}\right)+{\mathrm{\Φ}}_{sn}\left(t\right)---\left(3\right).$

Further, the detailed process of step 2 is as follows:

The slow time echo-signal that when target is static under noise free conditions, target place distance unit peak point is constituted's Mean power P_SFor

$P_S=E\left(\right|\stackrel{\‾}{S}{|}^2)=\frac{P_t{G}_t{G}_r{\mathrm{\λ}}^2\mathrm{\σ}}{{\left(4\mathrm{\π}\right)}^3{R_0}^{4}L}\·\frac{T_p}{PRT}---\left(6\right)$

Wherein, P_tLaunch power, G for emitter_tFor transmitter antenna gain (dBi), G_rFor receiving antenna gain, σ is that target is backward Scattering coefficient, λ is for launching signal wavelength, R₀For the distance of target, L is system loss, T_pFor launching signal pulse width, PRT is Pulse repetition period；

The mean power of the thermal noise N of target place distance unit is designated as P_N, then:

P_N=E (| N |²)=kT₀F_nB_v (7)

Wherein k is Boltzmann constant, T₀For room temperature, F_nFor receiver noise factor, B_vFor vibration signal bandwidth；

Derive vibration measuring model based on micro-vibration phase, according to (6) and (7), it is thus achieved that thermal noise average eguivalent Oscillation Amplitude NEA₀:

$\begin{array}{c}{\mathrm{NRA}}_0=\frac{\mathrm{\λ}}{4\mathrm{\π}}\sqrt{E\left(\right|\mathrm{Im}\left(\frac{N}{\stackrel{\‾}{S}}\right){|}^2)}=\frac{\mathrm{\λ}}{4\mathrm{\π}}\sqrt{\frac{P_N}{2P_S}}\\ =\frac{\mathrm{\λ}}{4\mathrm{\π}}\sqrt{\frac{{\mathrm{kT}}_0{F}_n{B}_v}{\frac{2P_t{G}_t{G}_r{\mathrm{\λ}}^2}{{\left(4\mathrm{\π}\right)}^3{R_0}^{4}L}\·\mathrm{\σ}\·\frac{T_p}{PRT}}}\end{array}---\left(8\right).$

Further, the detailed process of step 3 is:

The phase noise Φ that target echo carries_snMean power P of (t)_Φ:

$P_{\mathrm{\Φ}}=4{\∫}_{-B_v/2}^{B_v/2}{S}_{\mathrm{\φ}}\left(f_m\right){\sin }^2\left({\mathrm{\πf}}_m\frac{2R_0}{c}\right){\mathrm{df}}_m---\left(9\right)$

Wherein, S_φ(f_m) it is phase noise double-side band power spectral density, f_mIt is frequency, R₀For the distance of target, c is the light velocity, B_vFor vibration signal bandwidth；

Derive vibration measuring model based on micro-vibration phase, the phase noise Φ carrying according to target echo_snThe mean power of (t) P_Φ, it is thus achieved that Mean Oscillation amplitude PEA₀

${\mathrm{PEA}}_0=\frac{\mathrm{\λ}}{4\mathrm{\π}}\sqrt{E\left(\right|{\mathrm{\Φ}}_{sn}\left(t\right){|}^2)}=\frac{\mathrm{\λ}}{4\mathrm{\π}}\sqrt{P_{\mathrm{\Φ}}}---\left(10\right)$

Further, the detailed process of step 4 is:

Based on PEA₀For Mean Oscillation amplitude and NEA₀For thermal noise average eguivalent Oscillation Amplitude；Radar phase measurement defeated Go out signal to noise ratio snr_oFor:

${\mathrm{SNR}}_o=\frac{{\stackrel{\‾}{M}}^2}{{{\mathrm{PEA}}_0}^2+{{\mathrm{NEA}}_0}^2}---\left(11\right)$

Wherein,It is target mean amplitude of tide,T is vibration duration, and M (t) is that target is shaken Dynamic amplitude, t is the time；

Based on output signal-to-noise ratio SNR_oMore than or equal to minimum detectable signal to noise ratio, i.e. SNR_o≥SNR_min, system vibration measuring is moved Sensitivity S_minFor minimum detectable mean amplitude of tide, the then sensitivity S that system vibration measuring is moved_minFor

$S_{\min }=\sqrt{{\mathrm{SNR}}_{\min }({\mathrm{NEA}}_0^2+{\mathrm{PEA}}_0^2)}---\left(12\right).$

Beneficial effect:

(1) micro-vibration phase that the present invention is set up derives vibration measuring model, calculates simple, and easily realizes, by heat Noise and the impact on vibration measuring for the phase noise are converted into average eguivalent Oscillation Amplitude, can reflect that thermal noise and phase place are made an uproar intuitively The influence degree to vibration measurement precision for the sound.

(2) the radar vibration measuring sensitivity computing method that the present invention proposes, not only has and instructs vibration measuring radar system design, also The effect of vibration measuring radar vibration measuring performance can be assessed.

(3) present invention has carried out the analysis of system for the micro-vibration signal measurement capability of radar system, gives minimum Can detect the relation of Oscillation Amplitude and thermal noise and phase noise power, this conclusion has for the design of vibration measuring radar system parameters Important directive significance.

Brief description

Fig. 1 is the curve map with distance change for the NEA0；

Fig. 2 is X-band radar phase noise specifications figure；

Fig. 3 is the curve map with distance change for the PEA0；

Fig. 4 is the curve map with distance change for the vibration measuring sensitivity；

Fig. 5 is radar vibration measuring Calculation of Sensitivity flow chart.

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with the accompanying drawings, describes the present invention.

A kind of radar vibration measuring sensitivity computing method, its concrete steps include:

Step one, based on micro-Vibration Targets echo-signal, set up micro-vibration phase derive vibration measuring model；

Radar launches linear FM signal to Vibration Targets, and enters row distance pulse pressure to echo-signal, it is assumed that target is being shaken There is not more walking about apart from unit, it is thus achieved that slow time signal E of Vibration Targets place distance unit peak point is during Dong:

$\left\{\begin{array}{c}E=S+N\\ S=S_0{e}^{({\mathrm{j\Φ}}_{s0}+j\frac{4{\mathrm{\πR}}_0}{\mathrm{\λ}}+j\frac{4\mathrm{\π}M\left(t\right)}{\mathrm{\λ}}+{\mathrm{j\Φ}}_{sn}(t\left)\right)}\\ N=N\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, S and N is respectively component of signal in the slow time echo that micro-Vibration Targets place distance unit peak point is constituted And component of thermal noise, S₀Represent the echo strength of micro-Vibration Targets, Φ_s0It is the phase place entrained by target backscattering coefficient σ, R₀ Being the distance of target, λ is for launching signal wavelength, and M (t) is the vibration signal of target, Φ_snT () is phase noise；

OrderDistance unit in target place when representing that under noise free conditions, target is static The slow time echo-signal that peak point is constituted.Assume

$|4\mathrm{\&pi;}M\left(t\right)/\mathrm{\&lambda;}|,\left|{\mathrm{\&Phi;}}_{sn}\left(t\right)\right|,\left|N\right|/\left|\stackrel{\&OverBar;}{S}\right|<<1---\left(2\right)$

I.e. intended vibratory signal, phase noise, thermal noise and the ratio of object element static reflected wave amplitude is far smaller than 1, This condition is all to set up for microvibration measuring.Do Taylor series expansion to formula (1) formula and obtain following expression:

$\begin{array}{c}E=S+N\\ =\stackrel{\&OverBar;}{S}\&CenterDot;(1+j(\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+{\mathrm{\&Phi;}}_{sn}\left(t\right))+o(\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}})+o({\mathrm{\&Phi;}}_{sn}\left(t\right)\left)\right)\\ +N\left(t\right)\end{array}---\left(3\right)$

Wherein, o () represents higher order indefinite small.

The phase measurement of the E after Taylor series expansion deducts target phase place under static state, can obtain Only related to intended vibratory and noise phase term, i.e.

$\begin{array}{c}{\mathrm{\&Phi;}}_M=\&angle;E/\stackrel{\&OverBar;}{S}\\ =\&angle;(1+j\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\frac{N}{\stackrel{\&OverBar;}{S}}+{\mathrm{j\&Phi;}}_{sn}(t)+o)\\ ={\tan }^{-1}\left(\frac{\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+{\mathrm{\&Phi;}}_{sn}\left(t\right)+\mathrm{Im}\left(o\right)}{1+\mathrm{Re}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+\mathrm{Re}\left(o\right)}\right)\end{array}---\left(4\right)$

Wherein, Re () and Im () represents real and imaginary part respectively, and o is the unified representation of every high-order a small amount of.

Under the small-signal condition hypothesis of formula (2), formula (4) can be write as under conditions of first approximation:

${\mathrm{\&Phi;}}_M\&ap;\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+{\mathrm{\&Phi;}}_{sn}\left(t\right)---\left(5\right)$

Formula (5) is micro-vibration phase and derives vibration measuring model, it discloses intended vibratory, target echo, thermal noise, mesh The contribution to target place distance unit phase measurement for the phase noise that mark echo carries.Copy synthetic aperture radar noise Equivalence backscattering coefficient NE σ⁰Concept, thermal noise and phase noise are converted into average eguivalent Oscillation Amplitude and divide by the present invention Analyse their impacts on vibration measurement.

Step 2, according to micro-vibration phase derive vibration measuring model, according to target place when target is static under noise free conditions Mean power P of slow time echo-signal S that distance unit peak point is constituted_SWith Vibration Targets place distance unit peak point structure Mean power P of component of thermal noise N in the slow time echo becoming_N, it is thus achieved that thermal noise average eguivalent Oscillation Amplitude NEA₀；

The slow time echo-signal that when target is static under noise free conditions, target place distance unit peak point is constituted's Mean power P_SFor

$P_S=E\left(\right|\stackrel{\&OverBar;}{S}{|}^2)=\frac{P_t{G}_t{G}_r{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R_0}^{4}L}\&CenterDot;\frac{T_p}{PRT}---\left(6\right)$

Wherein, P_tLaunch power, G for emitter_tFor transmitter antenna gain (dBi), G_rFor receiving antenna gain, σ is that target is backward Scattering coefficient, λ is for launching signal wavelength, T_pFor pulse width, R₀For the distance of target, L is system loss, T_pFor launching signal Pulse width, PRT is the pulse repetition period.

The mean power of the thermal noise N of target place distance unit is designated as P_N, then:

P_N=E (| N |²)=kT₀F_nB_v (7)

Wherein k is Boltzmann constant, T₀For room temperature, F_nFor receiver noise factor, B_vFor vibration signal bandwidth.

Derive vibration measuring model based on micro-vibration phase, according to (6) and (7), it is thus achieved that the impact of vibration measuring precision is weighed by thermal noise Index is thermal noise average eguivalent Oscillation Amplitude NEA₀:

$\begin{array}{c}{\mathrm{NRA}}_0=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{E\left(\right|\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right){|}^2)}=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{\frac{P_N}{2P_S}}\\ =\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{\frac{{\mathrm{kT}}_0{F}_n{B}_v}{\frac{2P_t{G}_t{G}_r{\mathrm{\&lambda;}}^2}{{\left(4\mathrm{\&pi;}\right)}^3{R_0}^{4}L}\&CenterDot;\mathrm{\&sigma;}\&CenterDot;\frac{T_p}{PRT}}}\end{array}---\left(8\right)$

Step 3, based on micro-vibration phase derive vibration measuring model, according to mean power P of phase noise_Φ, it is thus achieved that phase place is made an uproar Sound average eguivalent amplitude PEA₀；

The phase noise Φ that target echo carries_snT the mean power of () is designated as P_Φ, then:

$P_{\mathrm{\&Phi;}}=4{\&Integral;}_{-B_v/2}^{B_v/2}{S}_{\mathrm{\&phi;}}\left(f_m\right){\sin }^2\left({\mathrm{\&pi;f}}_m\frac{2R_0}{c}\right){\mathrm{df}}_m---\left(9\right)$

Wherein, S_φ(f_m) it is phase noise double-side band power spectral density, f_mIt is frequency, R₀For the distance of target, c is the light velocity. The form of the double-side band power spectrum of the phase noise that target echo carries is as shown in (9).

It is phase noise average eguivalent Oscillation Amplitude PEA that definition phase noise affects measurement index to vibration measuring precision₀, based on Micro-vibration phase derives vibration measuring model, the phase noise Φ carrying according to target echo_snT the mean power of () is designated as P_Φ, it is thus achieved that

${\mathrm{PEA}}_0=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{E\left(\right|{\mathrm{\&Phi;}}_{sn}\left(t\right){|}^2)}=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{P_{\mathrm{\&Phi;}}}=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{4{\&Integral;}_{-B_v/2}^{B_v/2}{S}_{\mathrm{\&phi;}}\left(f_m\right){\sin }^2\left({\mathrm{\&pi;f}}_m\frac{2R_0}{c}\right){\mathrm{df}}_m}---\left(10\right)$

Step 4, the thermal noise average eguivalent Oscillation Amplitude NEA obtaining according to step 2₀The phase place obtaining with step 3 is made an uproar Sound average eguivalent amplitude PEA₀, it is thus achieved that the output signal-to-noise ratio SNR of radar phase measurement_o, based on the output noise of radar phase measurement Compare SNR_oMore than or equal to minimum detectable signal to noise ratio SNR_minCondition, it is thus achieved that the amplitude that minimum detectable range measures, according to system survey The sensitivity S of vibration_minFor minimum detectable mean amplitude of tide, obtain the dynamic sensitivity S of system vibration measuring_min。

Derive vibration measuring model, the output signal-to-noise ratio SNR of radar phase measurement according to micro-vibration phase_oFor:

${\mathrm{SNR}}_o=\frac{{\stackrel{\&OverBar;}{M}}^2}{{{\mathrm{PEA}}_0}^2+{{\mathrm{NEA}}_0}^2}---\left(11\right)$

Wherein,It is target mean amplitude of tide, be defined asT is vibration duration, and M (t) is Intended vibratory amplitude, t is the time.

Meet minimum detectable signal to noise ratio based on output signal-to-noise ratio, i.e. SNR_o≥SNR_min, the dynamic sensitivity of system vibration measuring S_minFor minimum detectable mean amplitude of tide, the then sensitivity S that system vibration measuring is moved_minFor

$S_{\min }=\sqrt{{\mathrm{SNR}}_{\min }({\mathrm{NEA}}_0^2+{\mathrm{PEA}}_0^2)}---\left(12\right)$

Embodiment

Give a cases of design to calculate vibration measuring sensitivity.Table 1 is vibration measuring radar system design parameter.

Table 1 radar system design parameter

Launch power	5w
		Transmitter antenna gain (dBi)	35dBi
Receiving antenna gain	35dBi
		Wavelength	X-band
Loss	22dB
		Receiver noise factor	6.5dB

Thermal noise average eguivalent Oscillation Amplitude NEA₀

It based on above-mentioned parameter design, is calculated NEA by formula (8)₀With the curve of distance change, as shown in Figure 1.

Phase noise average eguivalent Oscillation Amplitude PEA₀

The phase noise of X-band radar is as shown in Figure 2.

It according to formula (10), is calculated PEA₀With the curve apart from change as shown in Figure 3.

Vibration measuring sensitivity

If SNR_min=2dB, calculates the curve with distance change for the vibration measurement sensitivity of system according to formula (12), as Shown in Fig. 4.

Finally give the flow chart of radar vibration measuring Calculation of Sensitivity as shown in Figure 5.Since then, just complete/achieve one Method for radar vibration measuring Calculation of Sensitivity.

In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention. All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's Within protection domain.

Claims (5)

1. a radar vibration measuring sensitivity computing method, it is characterised in that specifically comprise the following steps that

Step one, based on micro-Vibration Targets echo-signal, set up micro-vibration phase derive vibration measuring model；

Step 2, according to micro-vibration phase derive vibration measuring model, according to target place distance when target is static under noise free conditions The slow time echo-signal that unit peak point is constitutedMean power P_SAnd have under noise conditions Vibration Targets place distance unit Mean power P of component of thermal noise N in the slow time echo that peak point is constituted_N, it is thus achieved that thermal noise average eguivalent Oscillation Amplitude NEA₀；

Step 3, based on micro-vibration phase derive vibration measuring model, according to mean power P of phase noise_Φ, it is thus achieved that phase noise etc. Effect mean amplitude of tide PEA₀；

Step 4, the thermal noise average eguivalent Oscillation Amplitude NEA obtaining according to step 2₀The phase noise etc. obtaining with step 3 Effect mean amplitude of tide PEA₀, it is thus achieved that the output signal-to-noise ratio SNR of radar phase measurement_o, based on the output signal-to-noise ratio of radar phase measurement SNR_oMore than or equal to minimum detectable signal to noise ratio SNR_minCondition, it is thus achieved that the amplitude that minimum detectable range measures, according to radar vibration measuring Dynamic sensitivity S_minFor minimum detectable mean amplitude of tide, it is thus achieved that the dynamic sensitivity S of radar vibration measuring_min。

2. a kind of radar vibration measuring sensitivity computing method as claimed in claim 1, it is characterised in that the detailed process of step one is such as Under:

Radar launches linear FM signal to Vibration Targets, and enters row distance pulse pressure to echo-signal, it is assumed that target is vibrated Journey does not occur more walking about apart from unit, it is thus achieved that slow time signal E of Vibration Targets place distance unit peak point is:

$\left\{\begin{array}{c}E=S+N\\ S=S_0{e}^{({\mathrm{j\&Phi;}}_{s0}+j\frac{4{\mathrm{\&pi;R}}_0}{\mathrm{\&lambda;}}+j\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+{\mathrm{j\&Phi;}}_{sn}(t\left)\right)}\\ N=N\left(t\right)\end{array}\right.---\left(1\right)$

Wherein, S is component of signal in the slow time echo that micro-Vibration Targets place distance unit peak point is constituted, S₀Represent micro-shaking The echo strength of moving-target, Φ_s0It is the phase place entrained by target backscattering coefficient σ, R₀Being the distance of target, λ is for launching letter Number wavelength, M (t) is the vibration signal of target, Φ_snT () is the phase noise that target echo carries；

OrderIfTaylor series are done to formula (1) Launching, the phase measurement of the E after Taylor series expansion deducts target phase place under static state, it is thus achieved that only and target Vibrate the phase term related with noise, i.e.

$\begin{array}{c}{\mathrm{\&Phi;}}_M=\&angle;E/\stackrel{\&OverBar;}{S}\\ =\&angle;\left(1+j\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\frac{N}{\stackrel{\&OverBar;}{S}}+{\mathrm{j\&Phi;}}_{sn}\left(t\right)+o\right)\\ ={\tan }^{-1}\left(\frac{\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+{\mathrm{\&Phi;}}_{sn}\left(t\right)+\mathrm{Im}\left(o\right)}{1+\mathrm{Re}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+Re\left(o\right)}\right)\end{array}---\left(2\right)$

Wherein, Re () and Im () represents real and imaginary part respectively, and o is the unified representation of every high-order a small amount of；

Based onObtain micro-vibration phase derive vibration measuring model:

${\mathrm{\&Phi;}}_M\&ap;\frac{4\mathrm{\&pi;}M\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right)+{\mathrm{\&Phi;}}_{sn}\left(t\right)---\left(3\right).$

3. a kind of radar vibration measuring sensitivity computing method as claimed in claim 2, it is characterised in that the detailed process of step 2 is such as Under:

The slow time echo-signal that when target is static under noise free conditions, target place distance unit peak point is constitutedAverage work( Rate P_SFor

$P_S=E\left(\right|\stackrel{\&OverBar;}{S}{|}^2)=\frac{P_t{G}_t{G}_r{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R_0}^{4}L}\&CenterDot;\frac{T_p}{PRT}---\left(6\right)$

Wherein, P_tLaunch power, G for emitter_tFor transmitter antenna gain (dBi), G_rFor receiving antenna gain, σ is target back scattering Coefficient, λ is for launching signal wavelength, R₀For the distance of target, L is system loss, T_pFor launching signal pulse width, PRT is pulse Repetition period；

The mean power of the thermal noise N of target place distance unit is designated as P_N, then:

P_N=E (| N²|)=kT₀F_nB_v (7)

Wherein k is Boltzmann constant, T₀For room temperature, F_nFor receiver noise factor, B_vFor vibration signal bandwidth；

Derive vibration measuring model based on micro-vibration phase, according to (6) and (7), it is thus achieved that thermal noise average eguivalent Oscillation Amplitude NEA₀:

$\begin{array}{c}{\mathrm{NEA}}_0=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{E\left(|\mathrm{Im}\left(\frac{N}{\stackrel{\&OverBar;}{S}}\right){|}^2\right)}=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{\frac{P_N}{2P_S}}\\ =\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{\frac{{\mathrm{kT}}_0{F}_n{B}_v}{\frac{2P_t{G}_t{G}_r{\mathrm{\&lambda;}}^2}{{\left(4\mathrm{\&pi;}\right)}^3{R_0}^{4}L}\&CenterDot;\mathrm{\&sigma;}\&CenterDot;\frac{T_p}{PRT}}}\end{array}---\left(8\right).$

4. a kind of radar vibration measuring sensitivity computing method as claimed in claim 2, it is characterised in that the detailed process of step 3 For:

The phase noise Φ that target echo carries_snMean power P of (t)_Φ:

$P_{\mathrm{\&Phi;}}=4{\&Integral;}_{-B_v/2}^{B_v/2}{S}_{\mathrm{\&phi;}}\left(f_m\right){\sin }^2\left({\mathrm{\&pi;f}}_m\frac{2R_0}{c}\right){\mathrm{df}}_m---\left(9\right)$

Wherein, S_φ(f_m) it is phase noise double-side band power spectral density, f_mIt is frequency, R₀For the distance of target, c is the light velocity, B_vFor Vibration signal bandwidth；

Derive vibration measuring model based on micro-vibration phase, the phase noise Φ carrying according to target echo_snMean power P of (t)_Φ, Obtain Mean Oscillation amplitude PEA₀

${\mathrm{PEA}}_0=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{E\left(\right|{\mathrm{\&Phi;}}_{sn}\left(t\right){|}^2)}=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\sqrt{P_{\mathrm{\&Phi;}}}---\left(10\right).$

5. a kind of radar vibration measuring sensitivity computing method as claimed in claim 2, it is characterised in that the detailed process of step 4 For:

Based on PEA₀For Mean Oscillation amplitude and NEA₀For thermal noise average eguivalent Oscillation Amplitude；The output letter of radar phase measurement Make an uproar and compare SNR_oFor:

${\mathrm{SNR}}_o=\frac{{\stackrel{\&OverBar;}{M}}^2}{{{\mathrm{PEA}}_0}^2+{{\mathrm{NEA}}_0}^2}---\left(11\right)$

Wherein,It is target mean amplitude of tide,T is vibration duration, and M (t) is that intended vibratory shakes Width, t is the time；

Based on output signal-to-noise ratio SNR_oMore than or equal to minimum detectable signal to noise ratio, i.e. SNR_o≥SNR_min, the dynamic spirit of system vibration measuring Sensitivity S_minFor minimum detectable mean amplitude of tide, the then sensitivity S that system vibration measuring is moved_minFor

$S_{\min }=\sqrt{{\mathrm{SNR}}_{\min }({\mathrm{NEA}}_0^2+{\mathrm{PEA}}_0^2)}---\left(12\right).$