CN104181499A - Ranging passive location method under azimuth angle prior condition based on linear sparse arrays - Google Patents

Abstract

The invention provides a ranging passive location method under an azimuth angle prior condition based on linear sparse arrays. The features of a multi-station system and a single-station system of passive location are combined, on the basis that observing stations are arrayed in a small space range in a linear sparse array mode, the observing stations are used for receiving data phase information, and near-field radiation source ranging location is achieved. On the basis of meticulous analysis of a structure of observed data phase information, prior azimuth angle information is used for carrying out phase compensation on a phase fuzzy part existing in the observed data phase information, a non-phase fuzzy part existing in the observed data phase information is used for establishing an array signal model, and estimation of near-field radiation source distance is completed based on a MUSIC algorithm.

Description

Range finding passive location method based on bare cloth linear array under the priori conditions of position angle

Technical field

The present invention relates to electronic information technology technology, particularly near-field thermal radiation source passive location technology.

Background technology

Passive location refers under the electromagnetic condition of scope self non-radiating, receive passively the electromagnetic wave signal in near-field thermal radiation source, and under certain coordinate system, utilize space relative geometrical relation and variation thereof in direction and the distance sense existing between scope and radiation source, the information such as the variation of poor and/or other respective physical amount of the angle of arrival by carrying in measuring radiation source and electromagnetic wave signal, time of arrival, calculate target location, speed and the acceleration of radiation source, finally realize target is located snugly.

Passive location system is divided into Multi-Station passive location and single station passive location.

Multi-Station passive location method is mainly utilize the signal of the multiple research stations blip steady radiation source transmitting arranging and calculate corresponding observed quantity within the scope of large space, as poor in time of arrival on any two stations etc., estimate thus the information such as position in target emanation source.Under Multi-Station passive location system, between each research station time synchronized require stricter, conventionally need carry out mass data transmission and fusion, this makes multi-station positioning system generally very complicated; In addition, multi-station positioning system may there is multiple observation websites successfully to detect to receive the signal that has adopted the transmitting of radiation source low probability of intercept technology such as adaptive beam formation, thereby directly cause Multi-Station passive location system to lose efficacy.

Single station passive location method, as the method for position of singly standing firm based on observed quantities such as radiation source arrival bearings, without the data fusion between complicated time synchronized and multiple research station.But because the observed quantity in the method for single station does not often fully comprise radiation source positions information, this makes single station passive location method generally have ornamental problem.For solving single station location method ornamental problem, single station passive location method need to repeatedly be measured and longer observation interval conventionally.Under specific occasion, for solving ornamental problem, single station passive location system even also needs to do the motion of particular form.Therefore, ornamental problem often causes various single station passive location methods to be restricted in application.

Summary of the invention

Technical matters to be solved by this invention is, provides one more stably, effectively, can realize the passive location method in near-field thermal radiation source according to one batch of measurement data.

The present invention is that the range finding passive location method based on bare cloth linear array under the priori conditions of position angle, comprises the following steps for solving the problems of the technologies described above adopted technical scheme:

Step 1. is arranged on M research station on interior among a small circle straight line, and selecting a research station is No. 0 research station, the distance d of other observation station and No. 0 research station _mmeet wherein, M is research station sum in system, M>=2, and m is research station numbering m=0 ..., M-1, λ is radiation source operation wavelength, θ is the radiation source orientation angle of arrival, R ₀represent the distance of No. 0 research station of radiation source to the;

M research station received observation data by step 2., calculates the estimated values theta of the radiation source orientation angle of arrival, generates observation data matrix x (t), x (t)=a (θ, R ₀) s (t)+n (t), t=1,2 ..., N; Wherein, t is sampling instant, t=1, and 2 ..., N, N is sampling total length, the signal vector that s (t) research station receives, n (t) is white Gaussian noise vector, a (θ, R ₀) be radiant array stream shape vector, $a(\mathrm{\θ},R_0)={[1,e^{-j2\mathrm{\π}{d}_1\sin \mathrm{\θ}/\mathrm{\λ}+\mathrm{j\π}{\left(d_1\cos \mathrm{\θ}\right)}^2/\left(\mathrm{\λ}{R}_0\right)},...,e^{{-j2\mathrm{\πd}}_{M-1}\sin \mathrm{\θ}/\mathrm{\λ}+\mathrm{j\π}{\left(d_{M-1}\cos \mathrm{\θ}\right)}^2/\left(\mathrm{\λ}{R}_0\right)}]}^T,$ () ^tfor matrix transpose computing;

Step 3. utilization is calculated the estimated values theta of the radiation source orientation angle of arrival and is determined Φ, diag represents diagonal matrix, and phase compensation matrix Φ premultiplication is completed to phase compensation to observation data matrix x (t);

Step 4. is asked the auto-covariance matrix of phase compensation the data obtained matrix by auto-covariance matrix carry out Eigenvalue Decomposition, after deleting the corresponding proper vector of eigenvalue of maximum in the corresponding eigenvectors matrix of eigenwert obtaining in decomposition, obtain noise subspace matrix G, utilize noise subspace matrix G to carry out MUSIC spectrum peak search, thereby obtain the distance R of No. 0 research station of the corresponding radiation source to the of criterion function peak value ₀for near-field thermal radiation spacing is from estimated value; MUSIC spectrum peak search criterion function P used _mUSIC(R ₀) be: P _mUSIC(R ₀)=1/||G ^hΦ a (θ, R ₀) || ², wherein, || || ²for 2-norm square.

The present invention, in conjunction with passive location multistation system and single station system feature separately, provides a kind of near-field thermal radiation source passive location method between Dan Zhanyu multistation.By laying on the basis of research station with the form of Sparse array among a small circle in space, utilize research station to receive data phase information, realize a range finding location, near-field thermal radiation source.The observed quantities such as the present invention utilizes the phase information of observation data to find range, the step-out time that this point and traditional passive localization method adopt are entirely different.Due to the sparse laying in spatial domain of research station array, there is phase fuzzy problem in the array manifold vector of being portrayed by the orientation angle of arrival and distance two parameters in near-field thermal radiation source conventionally.By the structure of observation data phase information being done on the basis of careful analysis, utilize priori azimuth information to carry out phase compensation to the part that has phase ambiguity in observation data phase information, utilize the part without phase ambiguity in observation data phase information to set up array signal model, based on MUSIC algorithm complete near-field thermal radiation spacing from estimation.

Further, complete based on MUSIC algorithm near-field thermal radiation spacing from initial estimation after, recycle high-precision maximum likelihood method obtain iteratively near-field thermal radiation spacing from high precision estimate., after step 4, also comprise step 5:

Step 5: the estimated values theta of the use radiation source orientation angle of arrival and near-field thermal radiation spacing as initial value, according to maximum likelihood method criterion, adopt the plan Newton iteration acquisition radiation source orientation angle of arrival and near-field thermal radiation spacing from bidimensional parameter vector from estimated value high precision estimated value;

The criterion function of maximum likelihood method is:

$\widehat{\mathrm{\α}}={[\widehat{\mathrm{\θ}},{\hat{R}}_0]}^T=\arg \underset{\mathrm{\α}={[\mathrm{\θ},R_0]}^T}{\min }f\left(\mathrm{\α}\right),f\left(\mathrm{\α}\right)=\log |{\widehat{\mathrm{\σ}}}_s^{2}a(\mathrm{\θ},R_0)a^H(\mathrm{\θ},R_0)+{\widehat{\mathrm{\σ}}}^2{I}_M|;$

for the high precision estimated value of the radiation source orientation angle of arrival, for near-field thermal radiation spacing from high precision estimated value, represent the value of corresponding α in the time that objective function f (α) gets minimum value; || be determinant symbol, for power of radiation source estimated value, for noise power estimation value, I _mfor the unit matrix of M × M; radiant array stream shape vector a (θ, R ₀) pseudoinverse, () ^hfor the computing of Matrix Conjugate transposition, for sample auto-covariance matrix, $\hat{R}=\underset{t=1}{\overset{N}{\mathrm{\Σ}}}x\left(t\right)x^H\left(t\right)/N;$

tr{} is for getting trace of a matrix, for a (θ, R ₀) the vertical projection operator matrix of orthocomplement subspace, ${\mathrm{\Π}}_a^{\⊥}=I_M-a(\mathrm{\θ},R_0){\left[a^H(\mathrm{\θ},R_0)a(\mathrm{\θ},R_0)\right]}^{-1}{a}^H(\mathrm{\θ},R_0);$

Intending Newton iteration process is:

α ^k+1＝α ^k-μ _kH ^-1(α ^k)f′(α ^k)；

Wherein, α ^kthe radiant array stream shape vector α estimated value that k step iteration obtains, μ _kbe the iteration step length of k step, H is the black plug Hessian matrix of objective function f (α) or the approximate matrix of its positive definite, f ' (α ^k) be the gradient of objective function; Iteration stop criterion is || H ^-1(α ^k) f ' (α ^k) || be less than and specify numerical value ε and matrix H positive definite, or iterations reaches default maximum times;

Step 6: utilize the estimated values theta of the radiation source orientation angle of arrival and near-field thermal radiation spacing from high precision estimated value R complete radiation source location.

The invention has the beneficial effects as follows to there is same multistation system and equally utilize space dimension, there is again single station passive location system and lay fast feature, can realize the features such as range finding location, near-field thermal radiation source according to a batch of measurement data.

Brief description of the drawings

Fig. 1 is the geometirc illustration of passive location problem of the present invention under right hand rectangular coordinate system.Consider in space plane on a certain straight line among a small circle in M research station of sparse laying (between research station, maximum distance is no more than a certain threshold value), receive a near-field thermal radiation source T from azimuth angle theta radiation signal.

Fig. 2 is the range finding root-mean-square error statistics that adopts instantiation mode of the present invention to measure under different orientations prior imformation condition, and ordinate is range error root-mean-square value, and unit is rice, horizontal ordinate is azimuth angle theta=-70 ° ,-50 °, and-30 °,-10 °, 0 °, 20 °, 30 °, 40 °, 60 °, 70 °, unit is degree.

Fig. 3 is the relative range finding root-mean-square error statistics that adopts instantiation mode of the present invention to measure under different orientations prior imformation condition, and ordinate is relative range error root-mean-square value (ratio value, therefore without unit), horizontal ordinate is azimuth angle theta=-70 ° ,-50 °, and-30 °,-10 °, 0 °, 20 °, 30 °, 40 °, 60 °, 70 °, unit is degree.

Embodiment

As shown in Figure 1, select a research station as true origin, be designated as research station No. 0, and array place, research station straight line is decided to be to X-axis, in the space plane that near-field thermal radiation source and X-axis form, set up XY right hand rectangular coordinate system.Near field radiation source is rotated in a counter-clockwise direction to the angle inswept to coordinate axis Y to the ray OT between true origin, be defined as forward orientation and arrive angle.

The inventive method crucial equation used is:

(R _m) ²＝(R ₀) ²+(d _m) ²-2R ₀d _msinθ

This equation is in the triangle forming in " radiation source-true origin-the m research station ", draws according to the cosine law.Wherein, R _mrepresent the distance of radiation source to m research station, subscript m value is m=0,1 ..., M-1, M represents research station number.R ₀represent the distance of No. 0 research station of radiation source to the.D _mrepresent the distance of No. 0 research station, m research station to the, subscript m value is m=0,1 ..., M-1.θ (90 ° of < θ≤90 °) is the radiation source orientation angle of arrival, is called for short position angle.

The inventive method radiation source used to the distance of m research station is:

$R_m=R_0{(1+{\left(\frac{d_m}{R_0}\right)}^2-2\frac{d_m}{R_0}\sin \mathrm{\&theta;})}^{1/2}\&ap;R_0[1-\frac{d_m}{R_0}\sin \mathrm{\&theta;}+\frac{1}{2}{\left(\frac{d_m\cos \mathrm{\&theta;}}{R_0}\right)}^2]$

This equation is to utilize x=(d _m/ R ₀) ²-2 (d _m/ R ₀) principle of sin θ much smaller than 1, to the R being obtained by the cosine law _mcarry out Taylor series expansion approximate.Wherein, R _mrepresent the distance of radiation source to m research station.R ₀represent the distance of No. 0 research station of radiation source to the.D _mrepresent the distance of No. 0 research station, m research station to the.θ represents radiation source position angle.

In the inventive method, radiation source spherical wave wavefront from m research station to the time delay true origin is:

${\mathrm{\&tau;}}_m=\frac{\sqrt{{\left(R_0\right)}^2+{\left(d_m\right)}^2-2R_0{d}_m\sin \mathrm{\&theta;}}-R_0}{c}\&ap;\frac{-d_m\sin \mathrm{\&theta;}}{c}+\frac{{\left(d_m\cos \mathrm{\&theta;}\right)}^2}{2c{R}_0}$

Wherein, τ _mrepresent emitter Signals wavefront from m (m=1 ..., M-1) number research station is to the time delay between true origin. represent extraction of square root computing.R ₀represent the distance of No. 0 research station of radiation source to the.C represents the light velocity.D _mrepresent the distance of No. 0 research station, m research station to the.θ represents radiation source position angle.

The inventive method research station used data are:

$\begin{array}{c}{x}_m\left(t\right)=s\left(t\right)e^{{j2\mathrm{\&pi;f}}_c{\mathrm{\&tau;}}_m}+n_m\left(t\right)\\ =s\left(t\right)e^{{-j2\mathrm{\&pi;d}}_m\sin \mathrm{\&theta;}/\mathrm{\&lambda;}+\mathrm{j\&pi;}{\left(d_m\cos \mathrm{\&theta;}\right)}^2/\left(\mathrm{\&lambda;}{R}_0\right)}+n_m\left(t\right),t=\mathrm{1,2},...,N\end{array}$

Wherein, x _m(t) represent the data that m research station is exported.S (t) represents the signal data that research station receives.N _m(t) stable Gaussian white noise while representing empty on m research station, it distributes and obeys N (0, σ ²).λ represents radiation source operation wavelength.T represents sampling instant, and the value of t is t=1,2 ..., N, N is data total length.Phase information in this equation forms by two, and these two the condition differences without phase ambiguity.For only relevant with radiation source position angle Section 1, work as d _mwhen value is no more than half-wavelength without phase ambiguity; For Section 2, work as d _mvalue meets time without phase ambiguity.In actual location problem, due to the sparse laying in research station, research station is to distance d between true origin _mand distance between adjacent research station is conventionally all much larger than half-wavelength, therefore Section 1 exists phase ambiguity conventionally.Under Near Field, only have as research station array pitch d _mmeet time Section 2 there is phase ambiguity.Under Near Field, research station spacing is rationally set in conjunction with the operation wavelength of passive location system, can in wider near field range, make Section 2 phase place meet in whole array manifold vector meaning above-mentioned without fuzzy inequality condition, for whole research station array manifold vector all the time without fuzzy.

To those skilled in the art, according to receiving the common technology that calculated signals position angle is this area, existing multiple disclosed method, such as phase-interferometer method and space spectrometry etc., for the present invention, disclosedly can all be applicable to the position angle in the present invention in the hope of azimuthal method so existing, of the present invention focus on calculating near-field thermal radiation spacing from, position angle as calculate near-field thermal radiation spacing from priori.The present invention utilizes position angle priori, and the Section 1 that has phase ambiguity is compensated, and then utilizes without the part of phase ambiguity and sets up range finding model, adopt Estimation of Spatial Spectrum MUSIC method obtain near-field thermal radiation spacing from initial estimation.On this basis, application high precision maximum likelihood method, the uncompensated data model based on complete near initial estimation result, carry out iteration optimizing with obtain near-field thermal radiation spacing from high precision estimate, thereby realize its goal of the invention.Thereby the inventive method comprises:

Step 1. matrixing is processed observation data: the plural form observation data x that M research station received _m(t) (m=0,1 ..., M-1) write as matrix form x (t);

Step 2. phase compensation: utilize position angle prior imformation, determine phase compensation matrix Φ, by Φ premultiplication to vector x (t), to existing the Section 1 of phase ambiguity to carry out phase compensation in the each element of x (t);

Step 3.MUSIC method range finding: utilize the array data through phase compensation in step 2, by the auto-covariance matrix of gained array data after compensation r carries out Eigenvalue Decomposition, delete the corresponding proper vector of eigenvalue of maximum from eigenvectors matrix after, obtain noise subspace matrix G, utilize this noise subspace matrix and according to MUSIC method criterion, in distance dimension, make spectrum peak search, obtain near-field thermal radiation source distance estimations, go to step 4;

Step 4. maximum likelihood method range finding: utilize original observed data in step 1, based on its auto-covariance matrix R, and utilize near-field thermal radiation spacing in priori azimuth information and step 3 from estimated value as initial value, according to maximum likelihood method criterion, adopt and intend the Newton iteration method, obtain near-field thermal radiation source side parallactic angle and estimate apart from the high precision of bidimensional parameter vector.Known to consideration because of position angle priori, get maximum likelihood distance estimations value and be the near-field thermal radiation source result of finally finding range, complete invention task.

In step 1, the observation data x of plural form (t) is expressed as:

x(t)＝a(θ,R ₀)s(t)+n(t),t＝1,2,...,N

Wherein, x (t) is research station observation data matrix, and t is sampling instant, and value is t=1,2 ..., N, a (θ, R ₀) be radiant array stream shape vector, be expressed as:

$a(\mathrm{\&theta;},R_0)={[1,e^{-j2\mathrm{\&pi;}{d}_1\sin \mathrm{\&theta;}/\mathrm{\&lambda;}+\mathrm{j\&pi;}{\left(d_1\cos \mathrm{\&theta;}\right)}^2/\left(\mathrm{\&lambda;}{R}_0\right)},...,e^{{-j2\mathrm{\&pi;d}}_{M-1}\sin \mathrm{\&theta;}/\mathrm{\&lambda;}+\mathrm{j\&pi;}{\left(d_{M-1}\cos \mathrm{\&theta;}\right)}^2/\left(\mathrm{\&lambda;}{R}_0\right)}]}^T$

Wherein () ^tfor matrix transpose computing, for near-field thermal radiation source signal vector, n (t)～N (0, σ ²i _m) be white Gaussian noise vector, I _mfor the unit matrix of M × M.

In step 2, phase compensation matrix Φ is a diagonal matrix, and its expression formula is:

$\mathrm{\&Phi;}=\mathrm{diag}\{1,e^{j2\mathrm{\&pi;}{d}_1\sin \mathrm{\&theta;}/\mathrm{\&lambda;}},...,e^{j2\mathrm{\&pi;}{d}_{M-1}\sin \mathrm{\&theta;}/\mathrm{\&lambda;}}\}$

In step 3, the auto-covariance matrix of gained array data after compensation meet as drag:

$\tilde{R}=E\{\mathrm{\&Phi;x}\left(t\right)x^H\left(t\right){\mathrm{\&Phi;}}^H\}={\mathrm{\&sigma;}}_s^2\mathrm{\&Phi;a}(\mathrm{\&theta;},R_0)a^H(\mathrm{\&theta;},R_0){\mathrm{\&Phi;}}^H+{\mathrm{\&sigma;}}^2{I}_M$

Wherein () ^hfor the computing of Matrix Conjugate transposition.Will feature decomposition, its eigenwert sequence is λ ₁> λ ₂=...=λ _m, these eigenwert characteristic of correspondence vectors are u ₁... u _k, u _k+1... u _m, noise subspace matrix is G=[u ₂u ₃... u _m].The MUSIC spectrum peak search criterion function used of finding range is:

P _MUSIC(R ₀)＝1/||G ^HΦa(θ,R ₀)|| ²

Wherein || || ²for vectorial 2-norm square.When calculating, by sample auto-covariance matrix replace.

In step 4, the auto-covariance matrix R of original multiple observation data meets as drag:

$R=E\left\{x\left(t\right)x^H\left(t\right)\right\}={\mathrm{\&sigma;}}_s^{2}a(\mathrm{\&theta;},R_0)a^H(\mathrm{\&theta;},R_0)+{\mathrm{\&sigma;}}^2{I}_M$

Wherein E{} is for getting expectation computing.The criterion function of maximum likelihood method is:

$\widehat{\mathrm{\&alpha;}}={[\widehat{\mathrm{\&theta;}},{\hat{R}}_0]}^T=\underset{\mathrm{\&alpha;}={[\mathrm{\&theta;},R_0]}^T}{\min }f\left(\mathrm{\&alpha;}\right)=\underset{\mathrm{\&alpha;}={[\mathrm{\&theta;},R_0]}^T}{\min }\log |{\widehat{\mathrm{\&sigma;}}}_s^{2}a(\mathrm{\&theta;},R_0)a^H(\mathrm{\&theta;},R_0)+{\widehat{\mathrm{\&sigma;}}}^2{I}_M|$

Wherein || be determinant symbol, power of radiation source is estimated noise power estimation ${\widehat{\mathrm{\&sigma;}}}^2=\mathrm{Tr}\left\{{\mathrm{\&Pi;}}_a^{\&perp;}\hat{R}\right\}/(M-1),$ Tr{} is for getting trace of a matrix. ${\mathrm{\&Pi;}}_a^{\&perp;}=I_M-a(\mathrm{\&theta;},R_0){\left[a^H(\mathrm{\&theta;},R_0)a(\mathrm{\&theta;},R_0)\right]}^{-1}{a}^H(\mathrm{\&theta;},R_0)$ To a (θ, R ₀) the vertical projection operator matrix of orthocomplement subspace. a (θ, R ₀) pseudoinverse, sample auto-covariance matrix vector in element be near-field thermal radiation spacing from estimated value.

The iterative process of intending the Newton iteration method is:

α ^k+1＝α ^k-μ _kH ^-1(α ^k)f′(α ^k)

Wherein α ^kit is the α estimated value that k step iteration obtains.μ _kit is the iteration step length of k step.H is the Hessian matrix of cost function f (α) or the approximate matrix of its positive definite, f ' (α ^k) be the gradient of cost function.Iteration stop criterion is || H ^-1(α ^k) f ' (α ^k) || be less than some appointment numerical value ε and H positive definite, or iterations reaches default maximum times.

Embodiment

Present embodiment taking the research station of 7 sparse layings on straight line, 3 centimetres of near-field thermal radiation source operation wavelengths and apart from research station 30.5 kms as example, i.e. M=7, λ=3cm, R ₀=30.5km.Taking high order end research station on straight line as true origin, place, research station straight line is abscissa axis, sets up right hand rectangular coordinate system.The spacing of all the other six research station range coordinate initial points is respectively d ₁=10m, d ₂=20m, d ₃=35m, d ₄=60m, d ₅=83m, d ₆=100m.The observation data total length that this example receives is N=1000, and signal to noise ratio (S/N ratio) is 15dB.Investigate near-field thermal radiation source with 10 azimuth angle theta=-70 ° ,-50 ° ,-30 ° ,-10 °, 0 °, 20 °, 30 °, 40 °, 60 °, range performance of the present invention when 70 ° of priorities are incident to research station array.For each position angle, do 200 Monte-Carlo experiments, calculate range finding root-mean-square error and relative range finding root-mean-square error.

Embodiment flow process is as follows:

Step 1. in 10 investigated position angles, from azimuth angle theta=-70 °, using selected when forward angle is as priori, structure phase compensation matrix Φ;

Step 2. is set up the sample autocorrelation matrix of the array received data of plural form:

$\hat{R}=\underset{t=1}{\overset{1000}{\mathrm{\&Sigma;}}}x\left(t\right)x^H\left(t\right)/1000$

Step 3. is calculated the sample auto-covariance matrix of gained after phase compensation:

$\hat{\tilde{R}}=\mathrm{\&Phi;}\hat{R}{\mathrm{\&Phi;}}^H$

Make matrix feature decomposition, the matrix being formed by all further features vector except its eigenvalue of maximum characteristic of correspondence vector, as the estimation of noise subspace matrix, symbol is designated as

Step 4. is by current azimuth value and matrix the range finding criterion function of substitution MUSIC method, makes spectrum peak search in distance dimension, and step-size in search is taken as 1 km.Get the range finding estimated value of distance value corresponding under spectrum peak as near-field thermal radiation source;

Step 5. is using the range finding estimated value obtaining in current azimuth value and step 4 as iteration initial value, and the criterion function of substitution maximum likelihood method is intended Newton iteration.Intend μ in Newton iteration process _k=(1/2) ^k, ε=10 ^-6, default maximum iteration time is 50 times.After iterative process stops, obtain position angle and the estimated value apart from bidimensional parameter vector.Only need to be concerned about distance parameter estimated value get its as near-field thermal radiation spacing from final estimated value;

Step 6. repeating step 2-5, make 200 times Monte-Carlo emulation experiment, (numerical value more approaches 0 with relative range finding root-mean-square error to calculate range finding root-mean-square error (numerical value is less, and distance accuracy is higher), distance accuracy is higher), computing formula is:

Wherein be the l time near-field thermal radiation spacing in Monte-Carlo emulation experiment from final estimated value;

Step 7. selects next position angle as working as forward angle, goes to step 1, until 10 position angles are all investigated complete.

Fig. 2 is the range finding root-mean-square error statistics that adopts instantiation mode of the present invention to measure under different orientations prior imformation condition, and ordinate is range error root-mean-square value, and unit is rice, horizontal ordinate is azimuth angle theta=-70 ° ,-50 °, and-30 °,-10 °, 0 °, 20 °, 30 °, 40 °, 60 °, 70 °, unit is degree.

Fig. 3 is the relative range finding root-mean-square error statistics that adopts instantiation mode of the present invention to measure under different orientations prior imformation condition, and ordinate is relative range error root-mean-square value (ratio value, therefore without unit), horizontal ordinate is azimuth angle theta=-70 ° ,-50 °, and-30 °,-10 °, 0 °, 20 °, 30 °, 40 °, 60 °, 70 °, unit is degree.

Visible in figure, for the near-field thermal radiation source of distance 30.5 kms, range error root mean square under each position angle priori conditions of investigating is all hundred meters of magnitudes, relatively range error is all in several magnitude at percent zero point, and these two evaluation indexes have all illustrated validity of the present invention.

Claims (2)

1. the range finding passive location method based on bare cloth linear array under the priori conditions of position angle, is characterized in that, comprises the following steps:

Step 1. is arranged on M research station on interior among a small circle straight line, and selecting a research station is No. 0 research station, the distance d of other observation station and No. 0 research station _mmeet wherein, M is research station sum in system, M>=2, and m is research station numbering m=0 ..., M-1, λ is radiation source operation wavelength, θ is the radiation source orientation angle of arrival, R ₀represent the distance of No. 0 research station of radiation source to the;

M research station received observation data by step 2., calculates the estimated values theta of the radiation source orientation angle of arrival, generates observation data matrix x (t), x (t)=a (θ, R ₀) s (t)+n (t), t=1,2 ..., N; Wherein, t is sampling instant, t=1, and 2 ..., N, N is sampling total length, the signal vector that s (t) research station receives, n (t) is white Gaussian noise vector, a (θ, R ₀) be radiant array stream shape vector, $a(\mathrm{\&theta;},R_0)={[1,e^{-j2\mathrm{\&pi;}{d}_1\sin \mathrm{\&theta;}/\mathrm{\&lambda;}+\mathrm{j\&pi;}{\left(d_1\cos \mathrm{\&theta;}\right)}^2/\left(\mathrm{\&lambda;}{R}_0\right)},...,e^{{-j2\mathrm{\&pi;d}}_{M-1}\sin \mathrm{\&theta;}/\mathrm{\&lambda;}+\mathrm{j\&pi;}{\left(d_{M-1}\cos \mathrm{\&theta;}\right)}^2/\left(\mathrm{\&lambda;}{R}_0\right)}]}^T,$ () ^tfor matrix transpose computing;

The prior imformation θ that step 3. utilization is calculated the radiation source orientation angle of arrival determines Φ, diag represents diagonal matrix, and phase compensation matrix Φ premultiplication is completed to phase compensation to observation data matrix x (t);

Step 4. is asked the auto-covariance matrix of phase compensation the data obtained matrix by auto-covariance matrix carry out Eigenvalue Decomposition, after deleting the corresponding proper vector of eigenvalue of maximum in the corresponding eigenvectors matrix of eigenwert obtaining in decomposition, obtain noise subspace matrix G, utilize noise subspace matrix G to carry out MUSIC spectrum peak search, thereby obtain the distance R of No. 0 research station of the corresponding radiation source to the of criterion function peak value ₀for near-field thermal radiation spacing is from estimated value; MUSIC spectrum peak search criterion function P used _mUSIC(R ₀) be: P _mUSIC(R ₀)=1/||G ^hΦ a (θ, R ₀) || ², wherein, || || ²for 2-norm square.

2. the range finding passive location method based on bare cloth linear array under the priori conditions of position angle as claimed in claim 1, is characterized in that, also comprises step 5 after step 4:

Step 5: the priori value θ of the use radiation source orientation angle of arrival and near-field thermal radiation spacing as initial value, according to maximum likelihood method criterion, adopt the plan Newton iteration acquisition radiation source orientation angle of arrival and near-field thermal radiation spacing from bidimensional parameter vector from estimated value high precision estimated value;

The criterion function of maximum likelihood method is:

$\widehat{\mathrm{\&alpha;}}={[\widehat{\mathrm{\&theta;}},{\hat{R}}_0]}^T=\arg \underset{\mathrm{\&alpha;}={[\mathrm{\&theta;},R_0]}^T}{\min }f\left(\mathrm{\&alpha;}\right),f\left(\mathrm{\&alpha;}\right)=\log |{\widehat{\mathrm{\&sigma;}}}_s^{2}a(\mathrm{\&theta;},R_0)a^H(\mathrm{\&theta;},R_0)+{\widehat{\mathrm{\&sigma;}}}^2{I}_M|;$

for the high precision estimated value of the radiation source orientation angle of arrival, for near-field thermal radiation spacing from high precision estimated value, represent the value of corresponding α in the time that objective function f (α) gets minimum value; || be determinant symbol, for power of radiation source estimated value, for noise power estimation value, I _mfor the unit matrix of M × M; radiant array stream shape vector a (θ, R ₀) pseudoinverse, () ^hfor the computing of Matrix Conjugate transposition, for sample auto-covariance matrix, $\hat{R}=\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}x\left(t\right)x^H\left(t\right)/N;$

tr{} is for getting trace of a matrix, for a (θ, R ₀) the vertical projection operator matrix of orthocomplement subspace, ${\mathrm{\&Pi;}}_a^{\&perp;}=I_M-a(\mathrm{\&theta;},R_0){\left[a^H(\mathrm{\&theta;},R_0)a(\mathrm{\&theta;},R_0)\right]}^{-1}{a}^H(\mathrm{\&theta;},R_0);$

Intending Newton iteration process is:

α ^k+1＝α ^k-μ _kH ^-1(α ^k)f′(α ^k)；

Wherein, α ^kthe radiant array stream shape vector α estimated value that k step iteration obtains, μ _kbe the iteration step length of k step, H is the black plug Hessian matrix of objective function f (α) or the approximate matrix of its positive definite, f ' (α ^k) be the gradient of objective function; Iteration stop criterion is || H ^-1(α ^k) f ' (α ^k) || be less than and specify numerical value ε and matrix H positive definite, or iterations reaches default maximum times;

Step 6: utilize radiation source orientation angle of arrival θ and near-field thermal radiation spacing from high precision estimated value complete radiation source location.