CN104698453A - Passive radar signal locating method based on synthetic-aperture antenna array - Google Patents

Abstract

The invention discloses a passive radar signal locating method based on a synthetic-aperture antenna array. For meeting the urgent requirements of achieving precise localization of radar targets to be located through small aircrafts, virtualization of the same receiver in different flying positions at different times is viewed as a synthetic-aperture antenna array element to provide precise estimation of the signal virtualization arrival time differences of the radar targets to be located. The method is implemented through the steps of (1) performing system initialization; (2) sampling and receiving the signals of a radar to be located in a discrete mode through two aircrafts; (3) enabling the two aircrafts to determine the virtualization arrival time differences respectively; (4) determining the position of the radar to be located. The passive radar signal locating method based on the synthetic aperture antenna array can achieve radar target localization with the small aircrafts and has relatively high and stable locating performance and relatively high practical values.

Description

Based on the radar signal Passive Location of synthetic aperture antenna array

Technical field

The invention belongs to Radar Technology field, further relate to a kind of radar target Passive Location based on synthetic aperture antenna array in radar electronic warfare technology and Radar Signal Processing Technology field.The present invention can be used for realizing radar target by small aircraft and accurately locates.

Background technology

The method of radar target passive positioning has received signal strength to indicate (Received Signal StrengthIndex, RSSI), signal arrival time difference (Time Differences ofArrival, TDOA), signal arrives carrier-frequency differences (Frequency Differences ofArrival, and direction of arrival of signal (Direction ofArrival, DOA) etc. FDOA).Radar target passive positioning technology based on DOA is radar target DF and location mechanism the most frequently used in active service radar countermeasure systems, when this mechanism self exists unavoidable drawback.

The method of estimation of a kind of DOA is proposed in the paper " airborne array radar moving target detect and localization method are studied " (Xian Electronics Science and Technology University's PhD dissertation 2009) that Qu Yi delivers.Obtain DOA in the spectral space of the method first after svd, then calculate the mutual coupling coefficient, then adopt MUSIC method to estimate DOA further, the more accurate DOA of final acquisition.The deficiency that the method exists to utilize aerial array and multichannel receiver, and the comparatively large and preponderance of its volume, is not suitable for for small aircraft.

Paper " On the Accuracy of Localization Systems UsingWideband Antenna Arrays " (the IEEE Transactions on Communications that the people such as Yuan Shen deliver, Vol.58, No.1, pp.270-280, January 2010.) in have studied the positioning precision adopting broad-band antenna array.Although this paper points out that aerial array can provide radar signal arrival bearing in real time, but when carrying out direction finding for remote radar, angle measurement error will form huge exhibition angle remote, cause follow-up positioning error excessive, so will directly affecting of antenna aperture size be subject to based on the direction finding precision of antenna array direction-finding system.

Patent " four rotor wing unmanned aerial vehicles based on laser radar are independently located and the control method " (publication number: CN103868521A of University Of Tianjin's application, application number: CN201410057861.3, applying date: on February 20th, 2014) in disclose a kind of active positioning method utilizing small aircraft.First the method utilizes two-dimensional laser radar to carry out the Primary Location of unmanned plane horizontal direction, utilizes airborne barometer to obtain the rough location value of the short transverse of unmanned plane; Utilize complementary filter algorithm afterwards, in conjunction with airborne accelerometer chip, obtain the unmanned plane positional information of higher frequency; Last based on this positional information.The deficiency that this patented claim exists is, only can be used for the locator meams initiatively transmitted, and can not be used for the passive positioning mode by receiving the signal that ground-based radar is launched.

Summary of the invention

The object of the invention is to the deficiency overcoming above-mentioned prior art, propose a kind of radar signal Passive Location based on synthetic aperture antenna array.The present invention uses small aircraft to realize radar target and accurately locates, overcome in prior art owing to using volume comparatively large and the aerial array of heavier-weight and the problem of baby plane cannot be applied to, overcome airborne antenna array df system owing to utilizing large-scale unloaded platform easily by the problem that enemy finds, overcoming will by the problem directly affected of antenna aperture size based on the direction finding precision of antenna array direction-finding system in technology.

Realizing technical thought of the present invention is, the new ideas of passive synthetic aperture aerial array are proposed, different time is positioned at the same receiver of different flight position is virtual is considered as synthetic aperture antenna array element, make full use of the spatial movement characteristic of small aircraft and the cycle revolving property of radar pulse signal, provide radar target signal-virtual difference time of arrival precise Estimation Method.

The concrete steps realizing the object of the invention are as follows:

(1) system initialization:

(1a) measurement obtains radar antenna angular velocity of rotation to be positioned and anglec of rotation cycle;

(1b) according to T=Π/Ω formula, calculate the antenna circulating time period of radar to be positioned, wherein T represents the circulating time period of radar antenna to be positioned, and Π represents the anglec of rotation cycle of radar antenna to be positioned, and Ω represents the anglec of rotation speed of radar antenna to be positioned;

(1c) real time record two aircraft present positions;

(2) sampling receives radar target signal discrete to be positioned:

(2a) complex baseband signal that two aircraft receive radar pulse waveform to be positioned is obtained respectively;

(2b) to the complex baseband signal of the radar pulse waveform to be positioned that two aircraft receive, discrete sampling is carried out with sampling rate respectively;

(3) determine that virtual time of arrival is poor:

(3a) Maclaurin expansion series approaching method is utilized, matching radar antenna main lobe gain to be positioned directivity;

(3b) maximal value is utilized to search method, estimate that the 1st aircraft enters the corresponding time at i-th scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft enters the corresponding time at the gain direction center of a jth scan period of radar antenna main lobe to be positioned, estimate that the 2nd aircraft enters the corresponding time at l scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 2nd aircraft enters the corresponding time at the gain direction center of m scan period of radar antenna main lobe to be positioned,

(3c) virtual time of arrival according to the following formula, is calculated poor:

$\left\{\begin{array}{c}{\mathrm{\Ψ}}_{i,j}={\hat{t}}_{j,\max }-{\hat{t}}_{i,\max }\\ {\mathrm{\Ψ}}_{l,m}={\hat{t}}_{m,\max }-{\hat{t}}_{l,\max }\end{array}\right.$

Wherein, Ψ _i,jrepresent that the virtual time of arrival of the 1st aircraft is poor, represent the estimated value of the gain direction center of i-th scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of a jth scan period of radar antenna main lobe to be positioned corresponding time, Ψ _l,mrepresent that the virtual time of arrival of the 2nd aircraft is poor, represent the estimated value of the gain direction center of l scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of m scan period of radar antenna main lobe to be positioned corresponding time;

(4) position for the treatment of station keeping radar is estimated:

(4a) according to the following formula, longitude, the latitude of primary Calculation radar site to be positioned;

$\left\{\begin{array}{c}{x}_o^2+y_o^2+A_{i,j}{x}_o+B_{i,j}{y}_o+{\mathrm{\Θ}}_{i,j}=0\\ x_o^2+y_o^2+A_{l,m}{x}_o+B_{l,m}{y}_o+{\mathrm{\Θ}}_{l,m}=0\end{array}\right.$

Wherein, x _orepresent the longitude of radar site to be positioned, y _orepresent the latitude of radar site to be positioned, Α _i,jrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Α _l,mrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Β _i,jrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Β _l,mrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Θ _i,jrepresent in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only with the 1st position of aircraft about and the coefficient vector irrelevant with radar site to be positioned, Θ _l,mrepresent in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, only with the 2nd position of aircraft about and the coefficient vector irrelevant with radar site to be positioned;

(4b) the location estimation result of radar to be positioned is determined:

Treat station keeping radar and carry out second time location, according to the actual position converging on radar to be positioned of twice positioning result, the location estimation result of true station keeping radar.

The present invention compared with prior art has the following advantages:

First, because the present invention utilizes two small aircrafts, different reception to mistiming of signal of radar same to be positioned and the positional information of two small aircrafts achieve the accurate location of radar to be positioned, effectively overcome owing to using volume comparatively large in prior art, and the aerial array of heavier-weight and the problem of baby plane cannot be applied to.Make the present invention have better dirigibility, can carry on various aircraft.

Second, because the present invention utilizes small aircraft with the movement velocity of a direction-agile, behind adjustable predeterminable flight time interval, and the beginning in this time interval and at the end of positional information, passive synthetic aperture size in the present invention can artificially arrange and change, to effectively overcome by the problem directly affected of antenna aperture size in prior art based on the direction finding precision of antenna array direction-finding system, make the present invention have better positioning precision and reliability.

3rd, because the present invention uses small aircraft passive positioning radar to be positioned, effectively overcome airborne antenna array df system and easily by the problem that enemy finds, make the present invention have better disguise owing to using large-scale unloaded platform.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is that the mean absolute error of positioning result of the present invention is with receiver receiving radar pulse signal signal to noise ratio (S/N ratio) change curve schematic diagram.

Embodiment:

Below in conjunction with accompanying drawing, the present invention will be further described.

With reference to accompanying drawing 1, the step that the present invention realizes is described in detail as follows.

Step 1, system initialization.

Measurement obtains radar antenna angular velocity of rotation to be positioned and anglec of rotation cycle.

According to T=Π/Ω formula, calculate the antenna circulating time period of radar to be positioned, wherein T represents the circulating time period of radar antenna to be positioned, and Π represents the anglec of rotation cycle of radar antenna to be positioned, and Ω represents the anglec of rotation speed of radar antenna to be positioned.

Real time record two aircraft present positions.

The actual position of aircraft, obtains by aircraft institute carry Beidou satellite navigation system (BDS), GPS (GPS) or inertial navigation system (INS).

Step 2, sampling receives radar target signal discrete to be positioned.

Obtain the complex baseband signal that two aircraft receive radar pulse waveform to be positioned respectively.

Wherein, x (t) represents that aircraft receives the complex baseband signal of radar pulse waveform to be positioned in the t of receiving radar signal, P represents radar antenna emissive power to be positioned, G (t) represents the to be positioned radar antenna main lobe gain directivity of aircraft corresponding to the t of receiving radar signal, the receiving gain of G ' expression aircraft receiver, a (t) represents the t at receiving radar signal, the amplitude envelope of the radio-frequency carrier of radar to be positioned, e represents with e to be the index operation at the end represent the initial phase of radar wave carrier frequency to be positioned, ξ (t) represents the t receiver Complex-valued additive random noise of aircraft at receiving radar signal, and its average is 0, and variance is

To the complex baseband signal of the radar pulse waveform to be positioned that two aircraft receive, carry out discrete sampling with sampling rate respectively.

Step 3, determines that virtual time of arrival is poor.

Utilize Maclaurin expansion series approaching method, matching radar antenna main lobe gain to be positioned directivity.

The first step, according to the following formula, by radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal, launches to carry out matching by Maclaurin series.

$G\left(t\right)\≅\mathrm{\α}+\mathrm{\βt}+{\mathrm{\γt}}^2+...{\mathrm{\λt}}^q=[1,t,t^2,...,t^q]\·{[\mathrm{\α},\mathrm{\β},\mathrm{\γ},...,\mathrm{\λ}]}^T=H\·{[\mathrm{\α},\mathrm{\β},\mathrm{\γ},...,\mathrm{\λ}]}^T$

Wherein, G (t) represents the radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal, and t represents the moment of receiving radar signal, represent approximately equal operation, α, β, γ ... λ represents the undetermined coefficient of each rank time power series of radar antenna main lobe gain directivity to be positioned matching respectively, q expression Maclaurin series launches the exponent number of G (t), when the antenna gain directivity of radar to be positioned is typical Gaussian, and q=2, H represents time power series vector, [] ^trepresenting matrix matrix transpose operation.

Second step, according to the following formula, calculates the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned.

Γ _i,k＝P·G′·A

Wherein, Γ _i,krepresent the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned, P represents radar antenna emissive power to be positioned, and the receiver receiving gain of G ' expression aircraft, A represents the amplitude of the wave carrier signal of radar to be positioned.

3rd step, according to the following formula, calculates the radar pulse strength vector of i-th scan period of radar to be positioned.

$E_i\≅{[{\mathrm{\Γ}}_{i,1}{H}_{i,1}^T,{\mathrm{\Γ}}_{i,2}{H}_{i,2}^T,...,H_{i,k},...,{\mathrm{\Γ}}_{i,N}{H}_{i,N}^T]}^T\·\mathrm{\Ψ}=H_i\·\mathrm{\Ψ}$

Wherein, E _irepresent the radar pulse strength vector of i-th scan period of radar signal to be positioned, represent approximately equal operation, [] ^trepresent vector transposition operation, Γ _i,krepresent the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned, Η _i,krepresent the time power series vector of a kth main lobe pulse of i-th scan period of radar to be positioned, wherein k=1,2 ..., N, when radar antenna main lobe gain directivity to be positioned is typical Gaussian, q=2, Η _irepresent the time power series matrix of i-th scan period of radar signal to be positioned, Ψ represents the undetermined coefficient vector of radar antenna main lobe gain directivity to be positioned matching, and N represents the number of the main lobe pulse that aircraft receives in each swing circle of radar target.

4th step, according to the following formula, calculates the estimated value of the undetermined coefficient vector of the matching of radar antenna main lobe gain directivity to be positioned.

$\widehat{\mathrm{\Ψ}}={[\widehat{\mathrm{\α}},\widehat{\mathrm{\β}},\widehat{\mathrm{\γ}},...,\widehat{\mathrm{\λ}}]}^T={\left({H_i}^T{H}_i\right)}^{-1}{H_i}^T{E}_i$

Wherein, represent the estimated value of the undetermined coefficient vector of the matching of radar antenna main lobe gain directivity to be positioned, t represents the moment of receiving radar signal, [] ^trepresenting matrix matrix transpose operation, represent the estimated value of the undetermined coefficient of radar antenna main lobe gain directivity to be positioned matching respectively, Η _irepresent the time power series matrix of i-th scan period of radar to be positioned, [] ^-1the inverse matrix operation of representing matrix, E _irepresent the radar pulse strength vector of i-th scan period of radar to be positioned.

5th step, according to the following formula, calculates the estimated value of the radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal.

$\hat{G}\left(t\right)=\widehat{\mathrm{\α}}+\widehat{\mathrm{\β}}t+\widehat{\mathrm{\γ}}{t}^2+...+\widehat{\mathrm{\λ}}{t}^q$

Wherein, represent the gain estimated value of radar antenna main lobe gain directivity to be positioned in the t of receiving radar signal, t represents the moment of receiving radar signal, represent the estimated value of the undetermined coefficient of the matching of radar antenna main lobe gain directivity to be positioned respectively, q expression Maclaurin series launches the exponent number of G (t), when the antenna gain directivity of radar to be positioned is typical Gaussian, and q=2.

Maximal value is utilized to search method, estimate that the 1st aircraft enters the corresponding time at i-th scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft enters the corresponding time at the gain direction center of a jth scan period of radar antenna main lobe to be positioned, estimate that the 2nd aircraft enters the corresponding time at l scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 2nd aircraft enters the corresponding time at the gain direction center of m scan period of radar antenna main lobe to be positioned.

According to the following formula, virtual time of arrival is calculated poor.

$\left\{\begin{array}{c}{\mathrm{\Ψ}}_{i,j}={\hat{t}}_{j,\max }-{\hat{t}}_{i,\max }\\ {\mathrm{\Ψ}}_{l,m}={\hat{t}}_{m,\max }-{\hat{t}}_{l,\max }\end{array}\right.$

Wherein, Ψ _i,jrepresent that the virtual time of arrival of the 1st aircraft is poor, represent the estimated value of the gain direction center of i-th scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of a jth scan period of radar antenna main lobe to be positioned corresponding time, Ψ _l,mrepresent that the virtual time of arrival of the 2nd aircraft is poor, represent the estimated value of the gain direction center of l scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of m scan period of radar antenna main lobe to be positioned corresponding time.

Step 4, the position for the treatment of station keeping radar is estimated.

According to the following formula, longitude, the latitude of primary Calculation radar site to be positioned.

$\left\{\begin{array}{c}{x}_o^2+y_o^2+A_{i,j}{x}_o+B_{i,j}{y}_o+{\mathrm{\Θ}}_{i,j}=0\\ x_o^2+y_o^2+A_{l,m}{x}_o+B_{l,m}{y}_o+{\mathrm{\Θ}}_{l,m}=0\end{array}\right.$

Wherein,

$A_{i,j}=-2x_i+\frac{y_j-y_i}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{i,j}-(j-i)\·\mathrm{\Π}}$

$B_{i,j}=-2y_i-\frac{x_j-x_i}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{i,j}-(j-i)\·\mathrm{\Π}}$

${\mathrm{\Θ}}_{i,j}=x_i^2+y_i^2-\frac{x_i\·y_j-y_i\·x_j}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{i,j}-(j-i)\·\mathrm{\Π}}$

$A_{l,m}=-2x_l+\frac{y_m-y_l}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{l,m}-(m-l)\·\mathrm{\Π}}$

$B_{l,m}=-2y_l-\frac{x_m-x_l}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{l,m}-(m-l)\·\mathrm{\Π}}$

${\mathrm{\Θ}}_{l,m}=x_l^2+y_m^2-\frac{x_l\·y_m-y_l\·x_m}{\mathrm{\Ω}\·{\mathrm{\Ψ}}_{l,m}-(m-l)\·\mathrm{\Π}}$

X _orepresent the longitude of radar site to be positioned, y _orepresent the latitude of radar site to be positioned, Α _i,jrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Α _l,mrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Β _i,jrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Β _l,mrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Θ _i,jrepresent in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only with the 1st position of aircraft about and the coefficient vector irrelevant with radar site to be positioned, Θ _l,mrepresent in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, only with the 2nd position of aircraft about and the coefficient vector irrelevant with radar site to be positioned, x _irepresent the longitude of the 1st aircraft in the position of i-th scan period of radar to be positioned, y _irepresent the latitude of the 1st aircraft in the position of i-th scan period of radar to be positioned, x _jrepresent the longitude of the 1st aircraft in the position of a jth scan period of radar to be positioned, y _jrepresent the latitude of the 1st aircraft in the position of a jth scan period of radar to be positioned, x _lrepresent the longitude of the 2nd aircraft in the position of l scan period of radar to be positioned, y _lrepresent the latitude of the 2nd aircraft in the position of l scan period of radar to be positioned, x _mrepresent the longitude of the 2nd aircraft in the position of m scan period of radar to be positioned, y _mrepresent the latitude of the 2nd aircraft in the position of m scan period of radar to be positioned.

Solving equations obtains the estimated result of the position of radar to be positioned.

$\begin{array}{cc}{\hat{x}}_o=\frac{-K_2\±\sqrt{K_2^2-4K_1\·K_3}}{2K_1}& {\hat{y}}_o=\frac{-K_4\±\sqrt{K_4^2-4K_1\·K_5}}{2K_1}\end{array}$

Wherein

Κ ₁＝(Α _i,j-Α _l,m) ²+(Β _i,j-Β _l,m) ²

Κ ₂＝(Α _l,mΒ _i,j-Α _i,jΒ _l,m)(Β _i,j-Β _l,m)+2(Θ _i,j-Θ _l,m)(Α _i,j-Α _l,m)

Κ ₃＝(Θ _i,j-Θ _l,m) ²+(Θ _l,mΒ _i,j-Θ _i,jΒ _l,m)(Β _i,j-Β _l,m)

Κ ₄＝(Β _l,mΑ _i,j-Β _i,jΑ _l,m)(Α _i,j-Α _l,m)+2(Θ _i,j-Θ _l,m)(Β _i,j-Β _l,m)

Κ ₅＝(Θ _i,j-Θ _l,m) ²+(Θ _l,mΑ _i,j-Θ _i,jΑ _l,m)(Α _i,j-Α _l,m)

represent the estimated value of the longitude of radar site to be positioned, represent the estimated value of the latitude of radar site to be positioned.

Determine the location estimation result of radar to be positioned.

Treat station keeping radar and carry out second time location, according to the actual position converging on radar to be positioned of twice positioning result, the location estimation result of true station keeping radar.

Effect of the present invention can be proved further by emulation experiment below:

1. simulated conditions:

Passive positioning target selection U.S. Raytheon Co. AN/SPS49 air search radar system in emulation experiment of the present invention, its frequency range f=850 ~ 942MHz, antenna angular velocity of rotation Ω=36 °, anglec of rotation cycle Π=360 °, level orientation beam angle θ ₃=3.3 °, pulse repetition rate PRF=1000Hz, then pulse launch time interval PRI=1/PRF=1ms, each anglec of rotation resolution ax θ=Ω/PRF=0.036 ° of radar antenna, number of pulses N in level orientation beam angle _p=(θ ₃pRF)/Ω ≈ 91.7, time pulse signal width τ=125 μ s, then pulse duty factor γ=τ/PRI=12.5%, antenna main lobe wave beam horizontal directivity pattern is Gaussian type, adopts following classical mathematics model:

$G\left(t\right)=\exp (-4\ln \sqrt{2}{(\mathrm{\Ω}/{\mathrm{\θ}}_3)}^2{t}^2)$

Wherein, Maclaurin (Maclaurin) exponent number is chosen as q=2 rank.

In emulation experiment of the present invention, the antagonism monitoring system default configuration parameters of aircraft institute carry is: receiver sample frequency F _s=20MHz, the flying speed υ=50m/s of aircraft, aircraft linearly flies to any direction at short notice, the variance of position of aircraft measuring error single positioning aircraft flight time Δ T _i,j=Δ T _l,m=60s, receiver receiving radar pulse signal signal to noise ratio snr=20dB, D _irepresent at t _imoment aircraft s _i=[x _i, y _i] ^twith radar target s to be positioned _o=[x _o, y _o] ^tbetween actual distance, $D_i=\sqrt{{(x_i-x_o)}^2+{(y_i-y_o)}^2},$ Emulate under the following conditions respectively.

Simulated conditions 1: in cartesian coordinate system, the position of radar 1 to be positioned is s _{o, 1}=[80,80] ^t, the position of the 1st aircraft is s _{i, 1}=[0,0] ^t, the position of the 2nd aircraft is s _{l, 1}=[0,160] ^t, now radar target s _{o, 1}corresponding D _ifor aircraft and radar target line with between angle Λ _i,lbe 90 °.

Simulated conditions 2: in cartesian coordinate system, the position of radar 2 to be positioned is s _{o, 2}=[100,100] ^t, the position of the 1st aircraft is s _{i, 1}=[0,0] ^t, the position of the 2nd aircraft is s _{l, 2}=[0,200] ^t, now radar target s _{o, 1}corresponding D _ifor aircraft and radar target line with between angle Λ _i,lbe 90 °.

2. emulate content:

Apply the present invention respectively in simulated conditions 1 and simulated conditions 2 times, to aircraft at a distance of different distance D _iradar target s to be positioned _o,icarry out passive positioning.As shown in Figure 2, in Fig. 2, the coordinate axis of horizontal direction represents receiver receiving radar pulse signal signal to noise ratio (S/N ratio), in Fig. 2, the coordinate axis of vertical direction represents the mean absolute error of positioning result, the point that in Fig. 2, solid circles indicates represents as pulse repetition rate PRF=1000Hz, and after application the present invention, position is s _{o, 2}=[100,100] ^tthe mean absolute error curve of positioning result of radar to be positioned, the curve indicated with empty circles in Fig. 2 represents as pulse repetition rate PRF=1000Hz, and after application the present invention, position is s _{o, 1}=[80,80] ^tthe mean absolute error curve of positioning result of radar to be positioned, in Fig. 2, fork indicates point and represents as pulse repetition rate PRF=500Hz, and applying position after the present invention is s _{o, 2}=[100,100] ^tthe mean absolute error curve of positioning result of radar to be positioned, the curve that Fig. 2 hollow core triangle indicates represents as pulse repetition rate PRF=500Hz, and after application the present invention, position is s _{o, 1}=[80,80] ^tthe mean absolute error curve of positioning result of radar to be positioned, the point that in Fig. 2, solid pentagram indicates represents as pulse repetition rate PRF=2000Hz, and after application the present invention, position is s _{o, 2}=[100,100] ^tthe mean absolute error curve of positioning result of radar to be positioned, the curve that Fig. 2 hollow core square indicates represents as pulse repetition rate PRF=2000Hz, and after application the present invention, position is s _{o, 1}=[80,80] ^tthe mean absolute error curve of positioning result of radar to be positioned.

As seen from Figure 2, when pulse repetition rate PRF is identical and receiver receiving radar pulse signal signal to noise ratio (S/N ratio) is identical, the present invention is directed to s _{o, 1}with s _{o, 2}the performance of mean absolute error of positioning result almost identical; When pulse repetition rate PRF is identical, institute's algorithm of carrying is for s _{o, 1}with s _{o, 2}the performance of mean absolute error of positioning result become excellent along with the increase of receiver receiving radar pulse signal signal to noise ratio (S/N ratio), when the increase along with receiver receiving radar pulse signal signal to noise ratio (S/N ratio), the performance boost of the mean absolute error of positioning result will weaken gradually, this is because the performance that now receiver receiving radar pulse signal signal to noise ratio (S/N ratio) has been large enough to differ from accurate virtual time of arrival is limit; When receiver receiving radar pulse signal signal to noise ratio (S/N ratio) is identical, the present invention is directed to s _{o, 1}with s _{o, 2}the mean absolute error performance of positioning result become excellent along with the increase of pulse repetition rate PRF, this is because along with the increase of PRF, the number of pulses that aircraft receives within the single radar scanning cycle increases, virtual difference performance boost time of arrival.

Claims (3)

1., based on a radar signal Passive Location for synthetic aperture antenna array, comprise the steps:

(1) system initialization:

(1a) measurement obtains radar antenna angular velocity of rotation to be positioned and anglec of rotation cycle;

(1b) according to T=Π/Ω formula, calculate the antenna circulating time period of radar to be positioned, wherein T represents the circulating time period of radar antenna to be positioned, and Π represents the anglec of rotation cycle of radar antenna to be positioned, and Ω represents the anglec of rotation speed of radar antenna to be positioned;

(1c) real time record two aircraft present positions;

(2) sampling receives radar target signal discrete to be positioned:

(2a) complex baseband signal that two aircraft receive radar pulse waveform to be positioned is obtained respectively;

(2b) to the complex baseband signal of the radar pulse waveform to be positioned that two aircraft receive, discrete sampling is carried out with sampling rate respectively;

(3) determine that virtual time of arrival is poor:

(3a) Maclaurin expansion series approaching method is utilized, matching radar antenna main lobe gain to be positioned directivity;

(3b) maximal value is utilized to search method, estimate that the 1st aircraft enters the corresponding time at i-th scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft enters the corresponding time at the gain direction center of a jth scan period of radar antenna main lobe to be positioned, estimate that the 2nd aircraft enters the corresponding time at l scan period gain direction center of radar antenna main lobe to be positioned, behind adjustable predeterminable flight time interval, estimate that the 2nd aircraft enters the corresponding time at the gain direction center of m scan period of radar antenna main lobe to be positioned,

(3c) virtual time of arrival according to the following formula, is calculated poor:

$\left\{\begin{array}{c}{\mathrm{\Ψ}}_{i,j}={\hat{t}}_{j,\max }-{\hat{t}}_{i,\max }\\ {\mathrm{\Ψ}}_{l.m}={\hat{t}}_{m,\max }-{\hat{t}}_{l,\max }\end{array}\right.$

Wherein, Ψ _i,jrepresent that the virtual time of arrival of the 1st aircraft is poor, represent the estimated value of the gain direction center of i-th scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of a jth scan period of radar antenna main lobe to be positioned corresponding time, Ψ _l,mrepresent that the virtual time of arrival of the 2nd aircraft is poor, represent the estimated value of the gain direction center of l scan period of radar antenna main lobe to be positioned corresponding time, represent the estimated value of the gain direction center of m scan period of radar antenna main lobe to be positioned corresponding time;

(4) position for the treatment of station keeping radar is estimated:

(4a) according to the following formula, longitude, the latitude of primary Calculation radar site to be positioned;

$\left\{\begin{array}{c}{x}_o^2+y_o^2+A_{i,j}{x}_o+B_{i,j}{y}_o+{\mathrm{\Θ}}_{i,j}=0\\ x_o^2+y_o^2\text{+}{A}_{l,m}{x}_o+B_{l,m}{y}_o+{\mathrm{\Θ}}_{l,m}=0\end{array}\right.$

Wherein, x _orepresent the longitude of radar site to be positioned, y _orepresent the latitude of radar site to be positioned, Α _i,jrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Α _l,mrepresent the coefficient vector of radar site longitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Β _i,jrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, Β _l,mrepresent the coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, Θ _i,jrepresent in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only with the 1st position of aircraft about and the coefficient vector irrelevant with radar site to be positioned, Θ _l,mrepresent in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft, only with the 2nd position of aircraft about and the coefficient vector irrelevant with radar site to be positioned;

(4b) the location estimation result of radar to be positioned is determined:

Treat station keeping radar and carry out second time location, according to the actual position converging on radar to be positioned of twice positioning result, the location estimation result of true station keeping radar.

2. the radar signal Passive Location based on synthetic aperture antenna array according to claim 1, is characterized in that, the complex baseband signal described in step (2a) is as follows:

Wherein, x (t) represents that aircraft receives the complex baseband signal of radar pulse waveform to be positioned in the t of receiving radar signal, P represents radar antenna emissive power to be positioned, G (t) represents the to be positioned radar antenna main lobe gain directivity of aircraft corresponding to the t of receiving radar signal, the receiving gain of G ' expression aircraft receiver, a (t) represents the t at receiving radar signal, the amplitude envelope of the radio-frequency carrier of radar to be positioned, e represents with e to be the index operation at the end represent the initial phase of radar wave carrier frequency to be positioned, ξ (t) represents the t receiver Complex-valued additive random noise of aircraft at receiving radar signal, and its average is 0, and variance is

3. the radar signal Passive Location based on synthetic aperture antenna array according to claim 1, is characterized in that, the concrete steps of the Maclaurin expansion series approaching method described in step (3a) are as follows:

The first step, according to the following formula, by radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal, launch to carry out matching by Maclaurin series:

G(t)≌α+βt+γt ²+…λt ^q＝[1,t,t ²,…,t ^q]·[α,β,γ,…,λ] ^T＝H·[α,β,γ,…,λ] ^T

Wherein, G (t) represents the radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal, t represents the moment of receiving radar signal, ≌ represents that approximately equal operates, α, β, γ ... λ represents the undetermined coefficient of each rank time power series of radar antenna main lobe gain directivity to be positioned matching respectively, q expression Maclaurin series launches the exponent number of G (t), when the antenna gain directivity of radar to be positioned is typical Gaussian, q=2, H represent time power series vector, [] ^trepresenting matrix matrix transpose operation;

Second step, according to the following formula, calculates the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned:

Γ _i,k＝P·G′·A

Wherein, Γ _i,krepresent the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned, P represents radar antenna emissive power to be positioned, the receiver receiving gain of G ' expression aircraft, and A represents the amplitude of the wave carrier signal of radar to be positioned;

3rd step, according to the following formula, calculates the radar pulse strength vector of i-th scan period of radar to be positioned:

$E_i\≅{[{\mathrm{\Γ}}_{i,1}{H}_{i,1}^T,{\mathrm{\Γ}}_{i,2}{H}_{i,2}^T,...,H_{i,k},...,{\mathrm{\Γ}}_{i,N}{H}_{i,N}^T]}^T\·\mathrm{\Ψ}=H_i\·\mathrm{\Ψ}$

Wherein, E _irepresent the radar pulse strength vector of i-th scan period of radar signal to be positioned, ≌ represents that approximately equal operates, [] ^trepresent vector transposition operation, Γ _i,krepresent the system gain factor of the Received signal strength of a kth main lobe pulse of i-th scan period of radar to be positioned, Η _i,krepresent the time power series vector of a kth main lobe pulse of i-th scan period of radar to be positioned, wherein k=1,2 ..., N, when radar antenna main lobe gain directivity to be positioned is typical Gaussian, q=2, Η _irepresent the time power series matrix of i-th scan period of radar signal to be positioned, Ψ represents the undetermined coefficient vector of radar antenna main lobe gain directivity to be positioned matching, and N represents the number of the main lobe pulse that aircraft receives in each swing circle of radar target;

4th step, according to the following formula, calculates the estimated value of the undetermined coefficient vector of the matching of radar antenna main lobe gain directivity to be positioned:

$\widehat{\mathrm{\Ψ}}={[\widehat{\mathrm{\α}},\widehat{\mathrm{\β}},\widehat{\mathrm{\γ}},...,\widehat{\mathrm{\λ}}]}^T={\left({H_i}^T{H}_i\right)}^{-1}{H_i}^T{E}_i$

Wherein, represent the estimated value of the undetermined coefficient vector of the matching of radar antenna main lobe gain directivity to be positioned, t represents the moment of receiving radar signal, [] ^trepresenting matrix matrix transpose operation, represent the estimated value of the undetermined coefficient of radar antenna main lobe gain directivity to be positioned matching respectively, Η _irepresent the time power series matrix of i-th scan period of radar to be positioned, [] ^-1the inverse matrix operation of representing matrix, E _irepresent the radar pulse strength vector of i-th scan period of radar to be positioned;

5th step, according to the following formula, calculates the estimated value of the radar antenna main lobe gain directivity to be positioned corresponding to the t of receiving radar signal:

$\hat{G}\left(t\right)=\widehat{\mathrm{\α}}+\widehat{\mathrm{\β}}t+\widehat{\mathrm{\γ}}{t}^2+...+\widehat{\mathrm{\λ}}{t}^q$

Wherein, represent the gain estimated value of radar antenna main lobe gain directivity to be positioned in the t of receiving radar signal, t represents the moment of receiving radar signal, represent the estimated value of the undetermined coefficient of the matching of radar antenna main lobe gain directivity to be positioned respectively, q expression Maclaurin series launches the exponent number of G (t), when the antenna gain directivity of radar to be positioned is typical Gaussian, and q=2.