CN104698453B - Passive radar signal locating method based on synthetic-aperture antenna array - Google Patents
Passive radar signal locating method based on synthetic-aperture antenna array Download PDFInfo
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
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
Technical field
The invention belongs to Radar Technology field, further relates to radar electronic warfare technology and Radar Signal Processing Technology field
In a kind of radar target Passive Location based on synthetic aperture antenna array.The present invention can be used for by small aircraft
Realize that radar target is accurately positioned.
Background technology
The method of radar target Passive Positioning has received signal strength sign (Received Signal Strength
Index, RSSI), signal arrival time difference (Time Differences of Arrival, TDOA), signal reach carrier-frequency differences
(Frequency Differences of Arrival, FDOA) and direction of arrival of signal (Direction of Arrival,
DOA) etc..It is the most frequently used radar target direction finding in active service radar countermeasure systems based on the radar target Passive Positioning technology of DOA
Location mechanism, when the mechanism itself has unavoidable drawback.
Paper " airborne array radar moving-target detection is studied with the localization method " (Xian Electronics Science and Technology University that Qu Yi is delivered
Thesis for the doctorate 2009) in propose a kind of method of estimation of DOA.The method is obtained first in the spectral space after singular value decomposition
DOA, then calculates the mutual coupling coefficient, then further estimates DOA using MUSIC methods, finally obtain more accurate DOA.The method
The deficiency of presence is, it is necessary to using aerial array and multichannel receiver, and its volume is larger and preponderance, is not suitable for
Small aircraft.
Paper " the On the Accuracy of Localization Systems Using that Yuan Shen et al. are delivered
Wideband Antenna Arrays”(IEEE Transactions on Communications,Vol.58,No.1,
Pp.270-280, January 2010.) in have studied positioning precision using broad-band antenna array.Although the paper points out day
Linear array can provide radar signal arrival bearing in real time, but when carrying out direction finding for remote radar, angle measurement error will be remote
Distance forms huge exhibition angle, causes follow-up position error excessive, so the direction finding precision based on antenna array direction-finding system will be received
Antenna aperature size is directly affected.
The patent " four rotor wing unmanned aerial vehicle autonomous positionings and control method based on laser radar " of University Of Tianjin's application is (open
Number：CN103868521A, application number：CN201410057861.3, the applying date：On 2 20th, 2014) in disclose a kind of utilization
The active positioning method of small aircraft.The method carries out the preliminary fixed of unmanned plane horizontal direction first with two-dimensional laser radar
Position, obtains the rough location value of the short transverse of unmanned plane using airborne barometer；Complementary filter algorithm, bonding machine are utilized afterwards
Accelerometer chip is carried, the unmanned plane positional information of higher frequency is obtained；It is finally based on this positional information.The patent application is present
Deficiency be the positioning mode for being simply possible to use in active transmission signal, and cannot be used for by receive ground-based radar transmitting signal
Passive Positioning mode.
The content of the invention
It is an object of the invention to overcome the shortcomings of above-mentioned prior art, it is proposed that a kind of to be based on synthetic aperture antenna array
Radar signal Passive Location.Using small aircraft, the present invention realizes that radar target is accurately positioned, overcome existing skill
The problem of baby plane cannot be applied to due to the aerial array of larger and heavier-weight using volume in art, overcome airborne
Antenna array direction-finding system is based in having overcome technology due to the problem easily found by enemy using large-scale unloaded platform
The problem will directly affected by antenna aperature size by the direction finding precision of antenna array direction-finding system.
Realize that technical thought of the invention is, proposes the new ideas of passive synthetic aperture aerial array, by different time position
Virtually it is considered as synthetic aperture antenna array element in the same receiver of different flight positions, makes full use of the space of small aircraft to transport
The cycle revolving property of dynamic characteristic and radar pulse signal, provides the radar target signal-virtual reaching time-difference accurately side of estimation
Method.
Realize comprising the following steps that for the object of the invention：
(1) system initialization：
(1a) measurement obtains radar antenna anglec of rotation speed to be positioned and anglec of rotation cycle；
(1b) circulating time period of radar antenna to be positioned according to T=Π/Ω formula, is calculated, wherein T represents to be positioned
The circulating time period of radar antenna, Π represent the anglec of rotation cycle of radar antenna to be positioned, and Ω represents radar day to be positioned
The anglec of rotation speed of line；
(1c) two aircraft present positions of real time record；
(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) complex baseband signal of the radar pulse waveform to be positioned received to two aircraft, is entered with sampling rate respectively
Row discrete sampling；
(3) determine virtual reaching time-difference：
(3a) using Maclaurin expansion series approaching method, it is fitted radar antenna main lobe gain directivity to be positioned；
(3b) method is searched using maximum, estimate that the 1st aircraft enters i-th scanning of radar antenna main lobe to be positioned
The corresponding time at cycle gain directivity center, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft is entered
The corresponding time at the gain direction center of j-th scan period of radar antenna main lobe to be positioned, estimate that the 2nd aircraft enters
Enter the corresponding time at l-th scan period gain direction center of radar antenna main lobe to be positioned, through adjustable predeterminable winged
After row time interval, estimate that the 2nd aircraft enters the gain direction of m-th scan period of radar antenna main lobe to be positioned
The corresponding time at center；
(3c) according to the following formula, calculate virtual reaching time-difference：
Wherein, Ψi,jThe virtual reaching time-difference of the 1st aircraft is represented,Represent radar antenna main lobe to be positioned
The estimated value of the gain direction center correspondence time of i-th scan period,Represent the jth of radar antenna main lobe to be positioned
The estimated value of the gain direction center correspondence time of individual scan period, Ψl,mRepresent the virtual time of advent of the 2nd aircraft
Difference,The estimated value of the gain direction center correspondence time of l-th scan period of radar antenna main lobe to be positioned is represented,Represent the estimated value of the gain direction center correspondence time of m-th scan period of radar antenna main lobe to be positioned；
(4) estimated the position for treating station keeping radar：
(4a) according to the following formula, the longitude of primary Calculation radar site to be positioned, latitude；
Wherein, xoRepresent the longitude of radar site to be positioned, yoRepresent the latitude of radar site to be positioned, Ai,jRepresent the 1st
The coefficient vector of radar site longitude to be positioned, A in the nonlinear equation of radar site to be positioned constructed by individual aircraftl,mTable
Show 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,
Βi,jRepresent the coefficient of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 1st aircraft
Vector, Βl,mRepresent radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft
Coefficient vector, Θi,jIn representing the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only fly with the 1st
Row device position about and the coefficient vector unrelated with radar site to be positioned, Θl,mRepresent to be positioned constructed by the 2nd aircraft
In the nonlinear equation of radar site, only with the 2nd position of aircraft about and unrelated with radar site to be positioned coefficient arrow
Amount；
(4b) determine the location estimation result of radar to be positioned：
Treating station keeping radar carries out second positioning, according to the true position for converging on radar to be positioned of positioning result twice
Put, determine the location estimation result of radar to be positioned.
The present invention has advantages below compared with prior art：
First, as the present invention utilizes two small aircrafts, the radar same to be positioned arrived in different receptions
The positional information of the time difference of signal and two small aircrafts realizes being accurately positioned for radar to be positioned, effectively overcomes
Due to larger using volume in prior art, and the aerial array of heavier-weight and the problem of baby plane cannot be applied to.Make
Obtain of the invention with more preferable motility, can carry on various aircraft.
Second, due to the present invention using small aircraft with the movement velocity of a direction-agile, through adjustable predeterminable
Behind flight time interval, and the positional information at the beginning and end of this time interval, the passive synthesis hole in the present invention
Footpath be sized to it is artificial arrange and change, effectively overcome the direction finding precision based on antenna array direction-finding system in prior art
The problem that will be directly affected by antenna aperature size so that the present invention has more preferable positioning precision and reliability.
3rd, as the present invention uses small aircraft Passive Positioning radar to be positioned, effectively overcome airborne antenna
Array df system is due to the problem easily found by enemy using large-scale unloaded platform so that the present invention has preferably hidden
Covering property.
Description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is that the mean absolute error of the positioning result of the present invention receives the change of radar pulse signal signal to noise ratio with receiver
Curve synoptic diagram.
Specific embodiment：
The present invention will be further described below in conjunction with the accompanying drawings.
Referring to the drawings 1, it is described in detail as follows the step of realize to the present invention.
Step 1, system initialization.
Measurement obtains radar antenna anglec of rotation speed to be positioned and anglec of rotation cycle.
According to T=Π/Ω formula, the circulating time period of radar antenna to be positioned is calculated, wherein T represents radar to be positioned
The circulating time period of antenna, Π represent the anglec of rotation cycle of radar antenna to be positioned, and Ω represents radar antenna to be positioned
Anglec of rotation speed.
Two aircraft present positions of real time record.
The actual position of aircraft, can pass through aircraft institute carry Beidou satellite navigation system (BDS), global positioning system
(GPS) or inertial navigation system (INS) obtain.
Step 2, sampling receive radar target signal discrete to be positioned.
The complex baseband signal that two aircraft receive radar pulse waveform to be positioned is obtained respectively.
Wherein, x (t) represents that aircraft receives the complex radical of radar pulse waveform to be positioned in the t for receiving radar signal
Band signal, P represent radar antenna transmission power to be positioned, and G (t) is represented corresponding to t of the aircraft in reception radar signal
Radar antenna main lobe gain directivity to be positioned, G ' represent aircraft receiver reception gain, a (t) represent receive thunder
Up to the t of signal, the amplitude envelope of the radio-frequency carrier of radar to be positioned, e represent the index operation with e as bottom,Represent undetermined
The initial phase of position radar carrier wave, ξ (t) represent aircraft in the t receiver Complex-valued additive random noise for receiving radar signal, its
Average is 0, and variance is
The complex baseband signal of the radar pulse waveform to be positioned received by two aircraft, respectively with sampling rate carry out from
Dispersion is sampled.
Step 3, it is determined that virtual reaching time-difference.
Using Maclaurin expansion series approaching method, radar antenna main lobe gain directivity to be positioned is fitted.
The first step, according to the following formula, by radar antenna main lobe gain direction to be positioned corresponding to the t of reception radar signal
Property, launch to be fitted with Maclaurin series.
Wherein, G (t) represents the radar antenna main lobe gain directivity to be positioned corresponding to the t for receiving radar signal,
T represents the moment for receiving radar signal,Approximately equal operation is represented, α, beta, gamma ... λ represent radar antenna master to be positioned respectively
The undetermined coefficient of each rank time power series of lobe gain direction fitting, q expressions launch the exponent number of G (t) with Maclaurin series,
When the antenna main lobe gain direction of radar to be positioned is typical Gaussian, q=2, H express time power series vector,
[·]TRepresenting matrix transposition is operated.
Second step, according to the following formula, calculates the reception letter of k-th main lobe pulse of i-th scan period of radar to be positioned
Number system gain factor.
Γi,k=PG ' A
Wherein, Γi,kThe system for representing the reception signal of k-th main lobe pulse of i-th scan period of radar to be positioned
Gain coefficient, P represent radar antenna transmission power to be positioned, and G ' represents the receiver reception gain of aircraft, and A represents to be positioned
The amplitude of radar carrier wave.
3rd step, according to the following formula, calculates the radar pulse strength vector of i-th scan period of radar to be positioned.
Wherein, EiThe radar pulse strength vector of i-th scan period of radar to be positioned is represented,Represent approximately equal
Operation, []TRepresent vector transposition operation, Γi,kRepresent k-th main lobe pulse of i-th scan period of radar to be positioned
Receive the system gain factor of signal, Ηi,kRepresent the time of k-th main lobe pulse of i-th scan period of radar to be positioned
Power series vector, wherein k=1,2 ..., N, when radar antenna main lobe gain directivity to be positioned is typical Gaussian, Ηi
The time power level matrix number of i-th scan period of radar to be positioned is represented, Ψ represents radar antenna main lobe gain side to be positioned
The undetermined coefficient vector of tropism fitting, N represent the main lobe pulse that aircraft is received in each swing circle of radar target
Number.
4th step, according to the following formula, calculates the undetermined coefficient vector of radar antenna main lobe gain directivity fitting to be positioned
Estimated value.
Wherein,The estimated value of the undetermined coefficient vector of the fitting of radar antenna main lobe gain directivity to be positioned is represented,
[·]TRepresenting matrix transposition is operated,Treating for radar antenna main lobe gain directivity fitting to be positioned is represented respectively
Determine the estimated value of coefficient, ΗiRepresent the time power level matrix number of i-th scan period of radar to be positioned, []-1Representing matrix
Inverse matrix operation, EiRepresent the radar pulse strength vector of i-th scan period of radar to be positioned.
5th step, according to the following formula, calculates radar antenna main lobe gain directivity to be positioned in the t for receiving radar signal
Gain estimated value.
Wherein,Represent gain of the radar antenna main lobe gain directivity to be positioned in the t for receiving radar signal
Estimated value, t represent the moment for receiving radar signal,Radar antenna main lobe gain directivity to be positioned is represented respectively
The estimated value of the undetermined coefficient of fitting, q expressions launch the exponent number of G (t) with Maclaurin series, as the antenna master of radar to be positioned
When lobe gain direction is typical Gaussian, q=2.
Method is searched using maximum, estimates that the 1st aircraft enters i-th scan period of radar antenna main lobe to be positioned
The corresponding time at gain direction center, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft is entered undetermined
The corresponding time at the gain direction center of j-th scan period of position radar antenna main lobe, estimate that the 2nd aircraft is entered and treat
The corresponding time at l-th scan period gain direction center of station keeping radar antenna main lobe, when adjustable predeterminable flight
Between be spaced after, estimate that the 2nd aircraft enters the gain direction center of m-th scan period of radar antenna main lobe to be positioned
The corresponding time.
According to the following formula, calculate virtual reaching time-difference.
Wherein, Ψi,jThe virtual reaching time-difference of the 1st aircraft is represented,Represent radar antenna main lobe to be positioned
The estimated value of the gain direction center correspondence time of i-th scan period,Represent the jth of radar antenna main lobe to be positioned
The estimated value of the gain direction center correspondence time of individual scan period, Ψl,mRepresent the virtual time of advent of the 2nd aircraft
Difference,The estimated value of the gain direction center correspondence time of l-th scan period of radar antenna main lobe to be positioned is represented,Represent the estimated value of the gain direction center correspondence time of m-th scan period of radar antenna main lobe to be positioned.
Step 4, the position for treating station keeping radar are estimated.
According to the following formula, the longitude of primary Calculation radar site to be positioned, latitude.
Wherein,
xoRepresent the longitude of radar site to be positioned, yoRepresent the latitude of radar site to be positioned, Ai,jRepresent the 1st flight
The coefficient vector of radar site longitude to be positioned, A in the nonlinear equation of radar site to be positioned constructed by devicel,mRepresent the 2nd
The coefficient vector of radar site longitude to be positioned, Β in the nonlinear equation of radar site to be positioned constructed by aircrafti,jRepresent
The coefficient vector of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by 1st aircraft,
Βl,mRepresent the coefficient of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft
Vector, Θi,jIn representing the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only with the 1st aircraft position
It is equipped with and closes and the coefficient vector unrelated with radar site to be positioned, Θl,mRepresent radar position to be positioned constructed by the 2nd aircraft
In the nonlinear equation put, only with the 2nd position of aircraft about and the coefficient vector unrelated with radar site to be positioned, xiTable
Show longitude of the 1st aircraft in the position of i-th scan period of radar to be positioned, yiRepresent the 1st aircraft undetermined
The latitude of the position of i-th scan period of position radar, xjRepresent j-th scanning week of the 1st aircraft in radar to be positioned
The longitude of the position of phase, yjRepresent latitude of the 1st aircraft in the position of j-th scan period of radar to be positioned, xlRepresent
Longitude of 2nd aircraft in the position of l-th scan period of radar to be positioned, ylRepresent the 2nd aircraft to be positioned
The latitude of the position of l-th scan period of radar, xmRepresent m-th scan period of the 2nd aircraft in radar to be positioned
Position longitude, ymRepresent latitude of the 2nd aircraft in the position of m-th scan period of radar to be positioned.
Solving equations obtain the estimated result of the position of radar to be positioned.
Wherein
K1=(Ai,j-Al,m)2+(Βi,j-Βl,m)2
K2=(Al,mΒi,j-Ai,jΒl,m)(Βi,j-Βl,m)+2(Θi,j-Θl,m)(Ai,j-Al,m)
K3=(Θi,j-Θl,m)2+(Θl,mΒi,j-Θi,jΒl,m)(Βi,j-Βl,m)
K4=(Βl,mAi,j-Βi,jAl,m)(Ai,j-Al,m)+2(Θi,j-Θl,m)(Βi,j-Βl,m)
K5=(Θi,j-Θl,m)2+(Θl,mAi,j-Θi,jAl,m)(Ai,j-Al,m)
The estimated value of the longitude of radar site to be positioned is represented,Represent the estimation of the latitude of radar site to be positioned
Value.
Determine the location estimation result of radar to be positioned.
Treating station keeping radar carries out second positioning, according to the true position for converging on radar to be positioned of positioning result twice
Put, determine the location estimation result of radar to be positioned.
The effect of the present invention can be further proved by simulations below experiment：
1. simulated conditions：
Raytheon Co. AN/SPS49 air search radars system of the Passive Positioning target selection U.S. in the emulation experiment of the present invention
System, its frequency range f=850～942MHz, antenna rotation angle speed Ω=36 °, anglec of rotation cycle Π=360 °, level
Azimuth beamwidth θ3=3.3 °, pulse recurrence frequency PRF=1000Hz, then pulse launch time interval PRI=1/PRF=
1ms, each anglec of rotation resolution ax θ of radar antenna=Ω/PRF=0.036 °, number of pulses in level orientation beam angle
Np=(θ3PRF)/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, using following classical mathematics model：
Wherein, Maclaurin (Maclaurin) exponent number is selected as q=2 ranks.
In the emulation experiment of the present invention, the antagonism monitoring system default configuration parameters of aircraft institute carry are：Receiver is sampled
Frequency Fs=20MHz, the flight speed υ=50m/s of aircraft, aircraft at short notice to any direction along rectilinear flight,
The variance of position of aircraft measurement errorSingle positioning aircraft flight time Δ Ti,j=Δ Tl,m=60s, receives
Machine receives radar pulse signal signal to noise ratio snr=20dB, DiRepresent in tiMoment aircraft si=[xi,yi]TWith radar to be positioned
Target so=[xo,yo]TBetween actual distance,Emulated under the following conditions respectively.
Simulated conditions 1：In cartesian coordinate system, the position of radar to be positioned 1 is so,1=[80,80]T, the 1st aircraft
Position be si,1=[0,0]T, the position of the 2nd aircraft is sl,1=[0,160]T, now radar target so,1Correspondence DiForAircraft and radar target lineWithBetween angle Λi,lIt is 90 °.
Simulated conditions 2：In cartesian coordinate system, the position of radar to be positioned 2 is so,2=[100,100]T, the 1st flight
The position of device is si,1=[0,0]T, the position of the 2nd aircraft is sl,2=[0,200]T, now radar target so,1Correspondence DiForAircraft and radar target lineWithBetween angle Λi,lIt is 90 °.
2. emulation content：
Respectively using the present invention under simulated conditions 1 and simulated conditions 2, to aircraft D at different distancesiIt is undetermined
Position radar target so,iCarry out Passive Positioning.As shown in Fig. 2 the coordinate axess of horizontal direction represent that receiver receives radar in Fig. 2
Pulse signal signal to noise ratio, in Fig. 2, the coordinate axess of vertical direction represent the mean absolute error of positioning result, solid circles in Fig. 2
The point of sign is represented when pulse recurrence frequency PRF=1000Hz, is s using position after the present inventiono,2=[100,100]TTreat
The mean absolute error curve of the positioning result of station keeping radar, the curve indicated with empty circles in Fig. 2 are represented and are repeated when pulse
During frequency PRF=1000Hz, it is s using position after the present inventiono,1=[80,80]TRadar to be positioned positioning result it is average
Absolute error curve, in Fig. 2, fork sign point is represented when pulse recurrence frequency PRF=500Hz, using position after the present invention is
so,2=[100,100]TRadar to be positioned positioning result mean absolute error curve, in Fig. 2 hollow triangle sign
Curve is represented when pulse recurrence frequency PRF=500Hz, is s using position after the present inventiono,1=[80,80]TThunder to be positioned
The mean absolute error curve of the positioning result for reaching, in Fig. 2, the point of solid five-pointed star sign is represented when pulse recurrence frequency PRF=
During 2000Hz, it is s using position after the present inventiono,2=[100,100]TRadar to be positioned positioning result average absolute miss
Difference curve, in Fig. 2, the curve of open squares sign is represented when pulse recurrence frequency PRF=2000Hz, after the present invention
Position is so,1=[80,80]TRadar to be positioned positioning result mean absolute error curve.
From Figure 2 it can be seen that when pulse recurrence frequency PRF is identical and receiver reception radar pulse signal signal to noise ratio is identical
When, the present invention is directed to so,1With so,2Positioning result mean absolute error performance it is almost identical；When pulse recurrence frequency PRF
When identical, carried algorithm is directed to so,1With so,2Positioning result mean absolute error performance with receiver receive radar arteries and veins
Rush the increase of Signal-to-Noise and become excellent, when the increase that radar pulse signal signal to noise ratio is received with receiver, positioning result
The performance boost of mean absolute error gradually will weaken, this is because now receiver receives radar pulse signal signal to noise ratio foot
It is enough big to can accurate virtual reaching time-difference performance limit；When receiver reception radar pulse signal signal to noise ratio is identical, this
It is bright for so,1With so,2The mean absolute error performance of positioning result become excellent with the increase of pulse recurrence frequency PRF, this
The increase with PRF is because, the number of pulses increase that aircraft was received within the single radar scanning cycle, when virtually reaching
Between difference performance boost.
Claims (3)
1. a kind of radar signal Passive Location based on synthetic aperture antenna array, comprises the steps：
(1) system initialization：
(1a) measurement obtains radar antenna anglec of rotation speed to be positioned and anglec of rotation cycle；
(1b) circulating time period of radar antenna to be positioned according to T=Π/Ω formula, is calculated, wherein T represents radar to be positioned
The circulating time period of antenna, Π represent the anglec of rotation cycle of radar antenna to be positioned, and Ω represents radar antenna to be positioned
Anglec of rotation speed；
(1c) two aircraft present positions of real time record；
(2) complex baseband signal for treating station keeping radar impulse waveform carries out discretization：
(2a) complex baseband signal that two aircraft receive radar pulse waveform to be positioned is obtained respectively；
(2b) complex baseband signal of the radar pulse waveform to be positioned received by two aircraft, respectively with sampling rate carry out from
Dispersion is sampled；
(3) determine virtual reaching time-difference：
(3a) using Maclaurin expansion series approaching method, it is fitted radar antenna main lobe gain directivity to be positioned；
(3b) method is searched using maximum, estimate that the 1st aircraft enters i-th scan period of radar antenna main lobe to be positioned
The corresponding time at gain direction center, behind adjustable predeterminable flight time interval, estimate that the 1st aircraft is entered undetermined
The corresponding time at the gain direction center of j-th scan period of position radar antenna main lobe, estimate that the 2nd aircraft is entered and treat
The corresponding time at l-th scan period gain direction center of station keeping radar antenna main lobe, when adjustable predeterminable flight
Between be spaced after, estimate that the 2nd aircraft enters the gain direction center of m-th scan period of radar antenna main lobe to be positioned
The corresponding time；
(3c) according to the following formula, calculate virtual reaching time-difference：
Wherein, Ψi,jThe virtual reaching time-difference of the 1st aircraft is represented,Represent i-th of radar antenna main lobe to be positioned
The estimated value of the gain direction center correspondence time of scan period,Represent radar antenna main lobe to be positioned j-th is swept
Retouch the estimated value of the gain direction center correspondence time in cycle, Ψl,mThe virtual reaching time-difference of the 2nd aircraft is represented,The estimated value of the gain direction center correspondence time of l-th scan period of radar antenna main lobe to be positioned is represented,Represent the estimated value of the gain direction center correspondence time of m-th scan period of radar antenna main lobe to be positioned；
(4) estimated the position for treating station keeping radar：
(4a) according to the following formula, the longitude of primary Calculation radar site to be positioned, latitude；
Wherein, xoRepresent the longitude of radar site to be positioned, yoRepresent the latitude of radar site to be positioned, Ai,jRepresent that the 1st flies
The coefficient vector of radar site longitude to be positioned, A in the nonlinear equation of radar site to be positioned constructed by row devicel,mRepresent the 2nd
The coefficient vector of radar site longitude to be positioned, Β in the nonlinear equation of radar site to be positioned constructed by individual aircrafti,jTable
Show 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,
Βl,mRepresent the coefficient of radar site latitude to be positioned in the nonlinear equation of radar site to be positioned constructed by the 2nd aircraft
Vector, Θi,jIn representing the nonlinear equation of radar site to be positioned constructed by the 1st aircraft, only with the 1st aircraft position
It is equipped with and closes and the coefficient vector unrelated with radar site to be positioned, Θl,mRepresent radar position to be positioned constructed by the 2nd aircraft
In the nonlinear equation put, only with the 2nd position of aircraft about and the coefficient vector unrelated with radar site to be positioned；
(4b) determine the location estimation result of radar to be positioned：
Treating station keeping radar carries out second positioning, according to the actual position for converging on radar to be positioned of positioning result twice,
Determine the location estimation result of radar to be positioned.
2. the radar signal Passive Location based on synthetic aperture antenna array according to claim 1, its feature exist
In the complex baseband signal described in step (2a) is as follows：
Wherein, x (t) represents that aircraft is taken a message in the complex radical that the t for receiving radar signal receives radar pulse waveform to be positioned
Number, P represents radar antenna transmission power to be positioned, and G (t) represents treating corresponding to t of the aircraft in reception radar signal
Station keeping radar antenna main lobe gain direction, G ' represent the reception gain of aircraft receiver, and a (t) is represented and received radar letter
Number t, the amplitude envelope of the radio-frequency carrier of radar to be positioned, e represent the index operation with e as bottom,Represent thunder to be positioned
Up to the initial phase of carrier wave, ξ (t) represents aircraft in the t receiver Complex-valued additive random noise for receiving radar signal, its average
For 0, variance is
3. the radar signal Passive Location based on synthetic aperture antenna array according to claim 1, its feature exist
In comprising the following steps that for, the Maclaurin expansion series approaching method described in step (3a)：
The first step, according to the following formula, by radar antenna main lobe gain directivity to be positioned corresponding to the t of reception radar signal,
Launch to be fitted with Maclaurin series：
Wherein, G (t) represents the radar antenna main lobe gain directivity to be positioned corresponding to the t for receiving radar signal, t tables
Show the moment for receiving radar signal,Approximately equal operation is represented, α, beta, gamma ... λ represent radar antenna main lobe to be positioned respectively
The undetermined coefficient of each rank time power series of gain direction fitting, q expressions launch the exponent number of G (t) with Maclaurin series, when
When the antenna main lobe gain direction of radar to be positioned is typical Gaussian, q=2, H express time power series vector, []T
Representing matrix transposition is operated；
Second step, according to the following formula, calculates the reception signal of k-th main lobe pulse of i-th scan period of radar to be positioned
System gain factor：
Γi,k=PG ' A
Wherein, Γi,kRepresent the system gain of the reception signal of k-th main lobe pulse of i-th scan period of radar to be positioned
Coefficient, P represent radar antenna transmission power to be positioned, and G ' represents the receiver reception gain of aircraft, and A represents radar to be positioned
The amplitude of carrier wave；
3rd step, according to the following formula, calculates the radar pulse strength vector of i-th scan period of radar to be positioned：
Wherein, EiRepresent the radar pulse strength vector of i-th scan period of radar to be positioned, Ηi,kRepresent radar to be positioned
I-th scan period k-th main lobe pulse time power series vector, wherein k=1,2 ..., N, ΗiRepresent to be positioned
The time power level matrix number of i-th scan period of radar, Ψ represent radar antenna main lobe gain directivity fitting to be positioned
Undetermined coefficient vector, N represent the number of the main lobe pulse that aircraft is received in each swing circle of radar target；
4th step, according to the following formula, calculates the estimation of the undetermined coefficient vector of radar antenna main lobe gain directivity fitting to be positioned
Value：
Wherein,The estimated value of the undetermined coefficient vector of radar antenna main lobe gain directivity fitting to be positioned is represented,The estimated value of the undetermined coefficient of radar antenna main lobe gain directivity fitting to be positioned, [] are represented respectively-1Table
Show inverse of a matrix matrix manipulation；
5th step, according to the following formula, calculates increasing of the radar antenna main lobe gain directivity to be positioned in the t for receiving radar signal
Beneficial estimated value：
Wherein,Represent that radar antenna main lobe gain directivity to be positioned is estimated in the gain of the t for receiving radar signal
Value.
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| CN110850401B (en) * | 2019-08-27 | 2022-06-28 | 天津大学 | RFID label positioning method based on motion model and synthetic aperture |
| CN111736187B (en) * | 2020-06-22 | 2022-05-24 | 北京理工大学 | High-precision high-sensitivity single-satellite GNSS positioning method based on passive synthetic aperture |
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