CN105676174A - Single-station passive rapid positioning method based on phase difference and least square method - Google Patents

Abstract

The invention discloses a single-station passive rapid positioning method based on phase difference and a least square method, and mainly solves the problems that the correlation of radiation sources are not sufficiently used, the positioning precision is relatively low and the positioning time is long in the prior art. The method comprises the steps that baseband signals are obtained and accumulated to obtain a baseband signal string; matched filtering is carried out on the baseband signal string, multiple interpolation is carried out on a result of matched filtering, and a peak sampling complex signal is extracted; phase difference is carried out on the peak sampling complex signal, and the least square method is used to estimate an optimal modulation frequency; phase compensation is carried out on the peak sampling complex signal by utilizing the optimal modulation frequency; Fourier transformer is carried out on a compensated signal to obtain a high-precision direction finding result; and according to the high-precision direction finding result, the distance to a radiation source is calculated, and further the position of the radiation source is obtained. According to the invention, the concept of synthetic aperture radar is applied to the aspect of investigation and positioning, the method has the advantages of high positioning precision and short positioning time, and the method can be used to investigate targets and position interference sources.

Description

Stand passive method for rapidly positioning based on the list of phase difference method of least squares

Technical field

The invention belongs to signal processing technology field, in particular to the passive localization method of one, can be used for scouting of singly standing.

Background technology

Refer to without source electricity and detecting scattering source or source of radiation and obtain on the basis about positional parameter by single reconnaissance equipment or multiple reconnaissance equipment, utilize suitable data processing means, it is determined that go out scattering source or source of radiation position in three dimensions.

Multistation location and mono-station location can be simply divided into without source electricity. Multistation location passage is deployed in the fusion that the target emanation signal that the website in different geographical position receives carries out signal rank or data-level, thus reaches the object of location. Apply wider in signal equipment is located; And radar emission antenna often wave beam is narrower, it is very difficult to ensureing that multiple receiving station can receive target signal, simultaneously the time lock mechanism of multistation requires equipment complicated, and mono-station location is not owing to almost having the problems referred to above, thus obtains and pays close attention to widely.

Single passive location completes object location by single observation platform passive received radiation source signal, is the important means obtaining target location information, has been applied to the fields such as the supervision of important goal position, urgent rescue, intelligent transportation and anti-terrorism stability maintenance. Mono-station location maximum feature compared with multistation location is an only observation platform, and equipment is simple, dispose flexibly, maneuvering characteristics is strong, has therefore played vital role in spaceborne, machine load, the multi-motion platform object location such as carrier-borne.

The research of current mono-station location method, comprises DF and location, difference time of arrival location, Doppler frequency and velocity of variation location, phase differential and velocity of variation location thereof and above-mentioned combination localization method etc. Wherein, Doppler frequency velocity of variation location and phase change rate location are comparatively conventional, these two kinds of methods, in order to improve target locating ability, have employed the particle filter method etc. as comprised Newton iteration method, Kalman filtering and extended method thereof, Bayesian Estimation theory. 2004 start, and Italy adopts double antenna to realize doppler changing rate positioning experiment on vertiplane.The method places 2 interferometer antennas in aircraft both sides, utilizes its frequency level difference measurements to locate. Experimental result shows the best position of the method at squint angle ± 45 degree, both sides place, and other positions are all by decline; Being about 5km at orientation distance, under locating 35 seconds time conditions, target location error will more than 10%.

Above-mentioned mono-station location method is all the nonlinearities change characteristic that make use of target and reconnaissance equipment change in location, have employed the estimation of noncoherent accumulation method realize target position. But the development along with modern radar technology, the radio frequency source stability of radar is significantly improved; Radar, under imaging, space time processing isotype, all can have longer signal stationary phase, scouts the coherency obtaining signal and obviously strengthens. Conventional mono-station location method can not effectively utilize the dependency of signal, it is necessary to the very long accumulation time.

Summary of the invention

It is an object of the invention to the deficiency for above-mentioned prior art, it is proposed to a kind of list based on phase difference method of least squares is stood passive method for rapidly positioning, to reduce computing amount, improves positioning precision, it is achieved quick position.

The technology of the present invention thinking is, the correlation technique of synthetic aperture imaging radar is applied to scouting field, utilizes the coherency of source of radiation, by antenna array long for the synthesis of long time integration signal-virtual, making it not meet far field condition, namely the quadratic phase of antenna array cannot be ignored; The quadratic phase utilizing phase difference method of least squares this to be can not ignore is estimated, and then the inverse relation utilizing quadratic phase and source of radiation distance realizes the estimation to radiant source target position. Implementation step comprises as follows:

(1) reconnaissance equipment does linear uniform motion, carries out instantaneous frequency measurement and direction finding to received signal, obtains frequency measurement resultWith direction finding resultAnd utilize frequency measurement resultCarry out mixing and eliminate carrier frequency, obtain baseband signal u_r(t);

(2) to baseband signal u_rT () accumulates, obtain the baseband signal of one group of accumulation:

u_r1(t),u_r2(t),…u_ri(t)…u_rn(t), i=1,2,3 ... n,

Wherein, n represents the accumulation total number of pulse;

(3) baseband signal of accumulation is carried out matched filtering:

(3a) select one of them as with reference to signal u in the baseband signal of accumulation_r0(t);

(3b) Reference Signal u_r0T () and all accumulation pulse signals carry out convolution, obtain one group of convolution results u₁(t),u₂(t),…u_i(t)…u_n(t);

(4) to each convolution results u_iT () carries out many times of interpolation, obtain sampled signal v_iT (), extracts interpolation result v_iThe sampled complex uu at (t) peak value place_iT (), obtains peak value sampling complex signal matrix:

M=[uu₁(t),uu₂(t),…uu_i(t)…uu_n(t)];

(5) peak value sampling complex signal matrix M is carried out phase difference least square, estimate optimum frequency modulation rate

(5a) extract front n-m the element of peak value sampling complex signal matrix M and rear n-m element respectively, form the first peak value matrix M₁With the 2nd peak value matrix M₂, wherein, M₁=[uu₁(t),…uu_i(t)…uu_n-m(t)], M₂=[uu_m+1(t)…uu_i(t)…uu_n(t)], m represents the 2nd peak value matrix M₂Relative to the first peak value matrix M₁The recurrence interval number postponed, then by M₁With M₂Conjugate multiplication, obtains phase difference matrix M_x;

(5b) conjugate multiplication matrix M is extracted_xThe phase place information of middle all elements, obtains phase place matrix:

Wherein, η_iIt it is Emitter pulse time of arrival;

(5c) Emitter pulse η time of arrival is utilized_iBuild time matrix:

$H=\left[\begin{array}{cc}1& {\mathrm{\η}}_1\\ 1& {\mathrm{\η}}_2\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\η}}_n\end{array}\right]$

(5d) phase place matrix Φ and time matrix H is utilized, calculated relationship matrix X:

X=(H^TH)^-1H^TΦ

(5e) matrix M after relation matrix X and peak value is utilized₂Matrix M before relative peak₁Delay pulse number of cycles m, estimate optimum frequency modulation rate

${\widehat{\mathrm{\μ}}}_2=X\[2\]/\left(2{\mathrm{\πmT}}_{pri}\right)$

Wherein, T_priFor the Emitter pulse repeat cycle;

(6) according to optimum frequency modulation rateObtain the signal matrix M after compensating_c:

(6a) optimum frequency modulation rate is utilizedBuild compensating signal matrix H=[h (η₁),h(η₂)…h(η_i)…h(η_n)], wherein, h (η_i) it is compensating signal;

(6b) compensating signal matrix H and peak value sampling complex signal matrix M are carried out dot product, eliminate the quadratic phase of peak value sampling complex signal about the time, the signal matrix after being compensated:

M_c=[uu₁(t)h(η₁),…uu_i(t)h(η_i)…uu_n(t)h(η_n)];

(7) to the signal matrix M after compensation_cCarry out fourier transformation and obtain Doppler frequencyCalculate the direction finding result of high precision

(8) the direction finding result of high precision is utilizedCalculate the distance of source of radiation and reconnaissance equipment

(9) the direction finding result of combined high precisionWith the distance of source of radiation and reconnaissance equipmentObtain radiation source positions.

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

The first, relative to traditional localization method, present invention utilizes the coherency of source of radiation, shorten setting time, it is possible to realize quick position;

2nd, the principle of synthetic-aperture radar is applied in radiolocation, by antenna array long for the synthesis of the signal-virtual of long time integration, it is achieved to the accurate measurement of angle of target;

3rd, utilize virtual vast of heaven linear array not meet far field condition, the characteristic that namely Received signal strength cannot be ignored about the quadratic phase of time, obtain distance parameter by phase difference method of least squares, it is to increase positioning precision.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention;

Fig. 2 is the positioning error figure of the present invention;

Fig. 3 is the setting time performance of the inventive method under different base line condition.

Embodiment

Below in conjunction with accompanying drawing, the present invention is done further detailed description.

With reference to Fig. 1, the specific implementation step of the present invention is as follows:

Step 1, acquisition baseband signal.

The present invention adopts the reconnaissance equipment doing linear uniform motion, carries out instantaneous frequency measurement and direction finding to received signal, obtains frequency measurement resultWith direction finding resultAnd utilize frequency measurement resultCarry out mixing and eliminate carrier frequency, obtain baseband signal u_rT (), frequency measurement error requirements is lower, is less than 1MHz.

Step 2, accumulation baseband signal.

To baseband signal u_rT () accumulates, namely often carry out the baseband signal that a mixing obtains and store, and accumulative obtains one group of baseband signal:

u_r1(t),u_r2(t),…u_ri(t)…u_rn(t), i=1,2,3 ... n

Wherein, n represents the accumulation total number of pulse.

Step 3, to accumulation baseband signal carry out matched filtering.

The baseband signal of accumulation is selected wherein any one as with reference to signal u_r0T (), by this reference signal u_r0The signal u of (t) and all accumulation_r1(t),u_r2(t),…u_ri(t)…u_rnT () does convolution respectively, obtain matched filtering result:

u₁(t),u₂(t),…u_i(t)…u_n(t)

Step 4, many times of interpolation, extract peak value sampling complex signal.

(4a) to each convolution results u_iT () carries out fourier transformation respectively, by convolution results u_iT () is transformed into frequency domain, and the heart inserts (K-1) N in a frequency domain_fIndividual zero, obtain the frequency domain signal after interpolation, wherein, N_fFor the data amount check after fourier transformation, K is interpolation multiple, and value is the integral number power of 2, and this example K gets 8;

(4b) the frequency domain signal after interpolation is carried out inverse Fourier transform, by signal recuperation to time domain, obtain sampled signal v_i(t); Record sampled result v_iTime t when () reaches peak value t_max, extraction time t_maxCorresponding peak value sampling complex signal uu_i(t)=v_i(t_max);

(4c) to all convolution results u₁(t),u₂(t),…u_i(t)…u_nT () carries out (4a)-(4b) process, obtain one group of peak value sampling complex signal: uu₁(t),uu₂(t),…uu_i(t)…uu_nT (), forms peak value sampling complex signal matrix M=[uu₁(t),uu₂(t),…uu_i(t)…uu_n(t)]。

Step 5, peak value sampling complex signal matrix M is carried out phase difference least square, estimate optimum frequency modulation rate

(5a) extract front n-m the element of peak value sampling complex signal matrix M and rear n-m element respectively, form the first peak value matrix M₁With the 2nd peak value matrix M₂, wherein, M₁=[uu₁(t),…uu_i(t)…uu_n-m(t)], M₂=[uu_m+1(t)…uu_i(t)…uu_n(t)], m represents the 2nd peak value matrix M₂Relative to the first peak value matrix M₁The recurrence interval number postponed, then by M₁With M₂Conjugate multiplication, obtains phase difference matrix M_x;

(5b) conjugate multiplication matrix M is extracted_xThe phase place information of middle all elements, obtains phase place matrix:

Wherein, η_iIt it is Emitter pulse time of arrival;

(5c) Emitter pulse η time of arrival is utilized_iBuild time matrix:

$H=\left[\begin{array}{cc}1& {\mathrm{\η}}_1\\ 1& {\mathrm{\η}}_2\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\η}}_n\end{array}\right]$

(5d) phase place matrix Φ and time matrix H is utilized, calculated relationship matrix X:

X=(H^TH)^-1H^TΦ

(5e) matrix M after relation matrix X and peak value is utilized₂Matrix M before relative peak₁Delay pulse number of cycles m, estimate optimum frequency modulation rate

${\widehat{\mathrm{\μ}}}_2=X\[2\]/\left(2{\mathrm{\πmT}}_{pri}\right)$

Wherein, T_priFor the Emitter pulse repeat cycle;

Step 6, according to optimum frequency modulation rateObtain the signal matrix M after compensating_c。

(6a) according to optimum frequency modulation rateWith Emitter pulse η time of arrival_i, construct compensating signal h (η according to the following formula_i):

$h\left({\mathrm{\η}}_i\right)=\exp \left(j\mathrm{\π}{\widehat{\mathrm{\μ}}}_2{\mathrm{\η}}_i^2\right),$

(6b) with n compensating signal h (η₁),h(η₂)…h(η_i)…h(η_n), form compensating signal matrix:

H=[h (η₁),h(η₂)…h(η_i)…h(η_n)];

(6c) compensating signal matrix H and peak value sampling complex signal matrix M are carried out dot product, eliminate the quadratic phase of all peak value sampling complex signals about the time, the signal matrix after being compensated:

M_c=[uu₁(t)h(η₁),…uu_i(t)h(η_i)…uu_n(t)h(η_n)]。

Step 7, carry out high-precision direction finding.

To the signal matrix M after compensation_cCarry out fourier transformation and obtain Doppler frequencyUtilize Doppler frequencyThe direction finding result obtaining high precision is:

${\widehat{\mathrm{\θ}}}_{new}=arccos\left(\frac{\mathrm{\λ}{\hat{f}}_d}{v}\right),$

Wherein, λ is the wavelength of Received signal strength, and v is reconnaissance equipment movement velocity.

If because the periodicity of cosine, when there is the situation of phase ambiguity, then the direction finding result that step 1 obtains can be utilizedAmbiguity solution.

Step 8, the distance calculated between source of radiation and reconnaissance equipment.

Utilize the direction finding result of high precisionThe wavelength X of reconnaissance equipment movement velocity v, Received signal strength and optimum frequency modulation rateThe distance calculating source of radiation and reconnaissance equipment is:

$\hat{r}=\frac{v^2{\sin }^2{\widehat{\mathrm{\θ}}}_{new}}{\mathrm{\λ}{\widehat{\mathrm{\μ}}}_2}.$

Step 9, complete location.

The direction finding result of combined high precisionWith the distance of source of radiation and reconnaissance equipmentObtain radiation source positions, complete location.

The effect of the present invention is set forth further by following emulation.

1. simulated conditions:

Condition 1: emulation setting source of radiation is operated in X-band, and wavelength is 0.03m, and signal bandwidth is 10MHz, and pulse width is 10 μ s, and pulse repetition is 1KHz, source of radiation distance reconnaissance equipment 200km, the angle of arrival is 45 degree. Angle measurement precision is 0.01 degree, and frequency measurement precision is 1MHz. Reconnaissance equipment speed is 300m/s, and the scouting time is 0.5 second. Pulse time delay 200, namely 0.2 second.

Condition 2: emulation setting source of radiation is operated in X-band, and wavelength is 0.03m, and signal bandwidth is 10MHz, and pulse width is 10 μ s, and pulse repetition is 1KHz, source of radiation distance reconnaissance equipment 200km, the angle of arrival is 0 degree. Angle measurement precision is 0.01 degree, and frequency measurement precision is 1MHz. Reconnaissance equipment speed is 300m/s, and the scouting time is 0.5 second. Pulse time delay 200, namely 0.2 second.

2. emulate content:

Emulation 1: condition 1 time, adopts the present invention under different signal to noise ratio, the Distance positioning error of emulation reconnaissance equipment, carries out 100 Monte-Carlo Simulation tests under each signal to noise ratio, and result is as shown in Figure 2.

Emulation 2: condition 2 times, compares performance setting time of the present invention under different base line condition, and result is as shown in Figure 3.

3. simulation analysis:

As can be seen from Figure 2, with the lifting of signal to noise ratio, Distance positioning error declines. Scouting receiving end signal to noise ratio and be about 10dB, through 100 Monte-Carlo Simulation tests, Distance positioning error drops to about 0.04%. Modern radar signal to noise ratio can be improved to 10dB～20dB, through the test of 100 Monte-Carlo Simulation, Distance positioning error can drop to less than 0.04%, it is to increase positioning precision.

As can be seen from Figure 3, base length is more little, and the required accumulation time is more long. When base length reaches 30 meters, even if radiation source positions 300km, Measuring Time only needs about 2 seconds, meets the demand of quick position.

Claims (5)

1. the list based on phase difference method of least squares is stood passive method for rapidly positioning, it is characterised in that, it comprises the steps:

(1) reconnaissance equipment does linear uniform motion, carries out instantaneous frequency measurement and direction finding to received signal, obtains frequency measurement resultWith direction finding resultAnd utilize frequency measurement resultCarry out mixing and eliminate carrier frequency, obtain baseband signal u_r(t);

(2) to baseband signal u_rT () accumulates, obtain the baseband signal of one group of accumulation:

u_r1(t),u_r2(t),…u_ri(t)…u_rn(t), i=1,2,3 ... n,

Wherein, n represents the accumulation total number of pulse;

(3) baseband signal of accumulation is carried out matched filtering:

(3a) select one of them as with reference to signal u in the baseband signal of accumulation_r0(t);

(3b) Reference Signal u_r0T () and all accumulation pulse signals carry out convolution, obtain one group of convolution results u₁(t),u₂(t),…u_i(t)…u_n(t);

(4) to each convolution results u_iT () carries out many times of interpolation, obtain sampled signal v_iT (), extracts interpolation result v_iThe sampled complex uu at (t) peak value place_iT (), obtains peak value sampling complex signal matrix:

M=[uu₁(t),uu₂(t),…uu_i(t)…uu_n(t)];

(5) peak value sampling complex signal matrix M is carried out phase difference least square, estimate optimum frequency modulation rate

(5a) extract front n-m the element of peak value sampling complex signal matrix M and rear n-m element respectively, form the first peak value matrix M₁With the 2nd peak value matrix M₂, wherein, M₁=[uu₁(t),…uu_i(t)…uu_n-m(t)], M₂=[uu_m+1(t)…uu_i(t)…uu_n(t)], m represents the 2nd peak value matrix M₂Relative to the first peak value matrix M₁The recurrence interval number postponed, then by M₁With M₂Conjugate multiplication, obtains phase difference matrix M_x;

(5b) conjugate multiplication matrix M is extracted_xThe phase place information of middle all elements, obtains phase place matrix:

Wherein, η_iIt it is Emitter pulse time of arrival;

(5c) Emitter pulse η time of arrival is utilized_iBuild time matrix:

$H=\left[\begin{array}{cc}1& {\mathrm{\η}}_1\\ 1& {\mathrm{\η}}_2\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\η}}_n\end{array}\right]$

(5d) phase place matrix Φ and time matrix H is utilized, calculated relationship matrix X:

X=(H^TH)^-1H^TΦ

(5e) matrix M after relation matrix X and peak value is utilized₂Matrix M before relative peak₁Delay pulse number of cycles m, estimate optimum frequency modulation rate

${\widehat{\mathrm{\μ}}}_2=X\[2\]/\left(2{\mathrm{\πmT}}_{pri}\right)$

Wherein, T_priFor the Emitter pulse repeat cycle;

(6) according to optimum frequency modulation rateObtain the signal matrix M after compensating_c:

(6a) optimum frequency modulation rate is utilizedBuild compensating signal matrix H=[h (η₁),h(η₂)…h(η_i)…h(η_n)], wherein, h (η_i) it is compensating signal;

(6b) compensating signal matrix H and peak value sampling complex signal matrix M are carried out dot product, eliminate the quadratic phase of peak value sampling complex signal about the time, the signal matrix after being compensated:

M_c=[uu₁(t)h(η₁),…uu_i(t)h(η_i)…uu_n(t)h(η_n)];

(7) to the signal matrix M after compensation_cCarry out fourier transformation and obtain Doppler frequencyCalculate the direction finding result of high precision

(8) the direction finding result of high precision is utilizedCalculate the distance of source of radiation and reconnaissance equipment

(9) the direction finding result of combined high precisionWith the distance of source of radiation and reconnaissance equipmentObtain radiation source positions.

2. the list based on phase difference method of least squares according to claim 1 is stood passive method for rapidly positioning, it is characterised in that, to each convolution results u in described step (4)_iT () carries out many times of interpolation, carry out as follows:

(4a) to convolution results u_iT () carries out fourier transformation, by convolution results u_iT () is transformed into frequency domain;

(4b) heart inserts (K-1) N in a frequency domain_fIndividual zero, obtain the frequency domain signal after interpolation, wherein N_fFor the data amount check after fourier transformation, K is interpolation multiple, and value is the integral number power of 2;

(4c) the frequency domain signal after interpolation is carried out inverse Fourier transform, by signal recuperation to time domain, obtain sampled signal v_i(t)。

3. the list based on phase difference method of least squares according to claim 1 is stood passive method for rapidly positioning, it is characterised in that, described step (6a) utilizes optimum frequency modulation rateBuild compensating signal matrix H, carry out as follows:

(6a1) according to optimum frequency modulation rateWith Emitter pulse η time of arrival_i, construct compensating signal h (η according to the following formula_i):

$h\left({\mathrm{\η}}_i\right)=\exp \left(j\mathrm{\π}{\widehat{\mathrm{\μ}}}_2{\mathrm{\η}}_i^2\right);$

(6a2) with n compensating signal h (η₁),h(η₂)…h(η_i)…h(η_n), build compensating signal matrix:

H=[h (η₁),h(η₂)…h(η_i)…h(η_n)]。

4. the list based on phase difference method of least squares according to claim 1 is stood passive method for rapidly positioning, it is characterised in that, described step utilizes Doppler frequency in (7)Calculate the direction finding result of high precisionCalculated by following formula:

${\widehat{\mathrm{\θ}}}_{new}=arccos\left(\frac{\mathrm{\λ}{\hat{f}}_d}{v}\right),$

Wherein, λ is the wavelength of Received signal strength, and v is reconnaissance equipment movement velocity.

5. the list based on phase difference method of least squares according to claim 1 is stood passive method for rapidly positioning, it is characterised in that, described step (8) utilizes the direction finding result of high precisionThe wavelength X of reconnaissance equipment movement velocity v, Received signal strength and optimum frequency modulation rateCalculate the distance of source of radiation and reconnaissance equipment, calculated by following formula:

$\hat{r}=\frac{v^2{\sin }^2{\widehat{\mathrm{\θ}}}_{new}}{\mathrm{\λ}{\widehat{\mathrm{\μ}}}_2}.$