CN109669178B - Satellite-borne three-array-element single-pulse two-dimensional direction finding method - Google Patents
Satellite-borne three-array-element single-pulse two-dimensional direction finding method Download PDFInfo
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- CN109669178B CN109669178B CN201811587949.0A CN201811587949A CN109669178B CN 109669178 B CN109669178 B CN 109669178B CN 201811587949 A CN201811587949 A CN 201811587949A CN 109669178 B CN109669178 B CN 109669178B
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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
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/886—Radar or analogous systems specially adapted for specific applications for alarm systems
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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
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/68—Radar-tracking systems; Analogous systems for angle tracking only
Abstract
The invention discloses a satellite-borne three-array element single-pulse two-dimensional direction finding method, which comprises the following steps: firstly, calculating the longest base line limit according to the shortest wavelength and amplitude comparison angle measurement precision of a received signal, calculating the shortest base line length requirement according to the required angle measurement precision and the longest wavelength of the received signal, comparing the longest base line requirement and the shortest base line requirement, and determining the base line length; calculating an amplitude difference table and a phase difference table corresponding to incident signals in different directions according to the antenna interval, the antenna beam pointing angle and the amplitude phase directional diagram; then, the amplitude difference of the same signal received by the three array elements is correlated with the amplitude difference table to obtain a rough measurement value of the incident direction of the signal; and finally, determining a search range of the signal incidence direction by using the rough measurement result of amplitude comparison direction finding and direction finding precision, and performing correlation and interpolation processing by using a three-channel phase difference and phase difference table to obtain a precise angle measurement result. The invention reduces the number of array elements, the number of system channels and the quantity of system equipment, and effectively improves the direction finding precision of the satellite-borne alarm system.
Description
Technical Field
The invention belongs to the field of electronic signal reconnaissance, and particularly relates to a satellite-borne three-array-element single-pulse two-dimensional direction-finding method.
Background
In order to deal with the threat of anti-satellite weapons and adapt to complex electromagnetic environments, the development of an effective satellite-borne broadband radar warning direction-finding system is urgently needed. The traditional radar warning system usually adopts amplitude comparison direction finding technology and is widely applied to airborne platforms. The traditional amplitude-comparison direction-finding technology utilizes the amplitude comparison of two channel received signals to carry out direction finding, the method is sensitive to the signal-to-noise ratio of the received signals, and the angle-finding precision is about one tenth of the beam width of 3 dB. For the radar warning antenna unit, because the range required to be instantaneously covered is large, the 3dB wave beam width is generally 90 degrees, and the corresponding amplitude-comparison angle measurement precision is about 10 degrees, the angle measurement precision can meet the requirement of aircraft warning, but for the satellite-borne platform, because the acting distance is far beyond the aircraft-borne platform, the positioning error caused by the same angle measurement error is large, and therefore, the satellite-borne radar warning system needs to adopt an angle measurement method with high angle measurement precision.
The main direction-finding technology of the radar alarm system is a broadband direction-finding principle, and the current common method can be divided into two systems, namely a comparison amplitude system and a comparison phase system. The amplitude comparison method mainly comprises a digital multi-beam amplitude comparison method and a traditional dual-channel amplitude comparison method. The digital multi-beam amplitude-comparison direction-finding method adopts a digital array antenna, the number of channels is large, and the equipment quantity is large. The phase comparison method is mainly an interferometer direction finding method, the angle finding precision is high, but the ambiguity resolving capability is improved by adopting multiple baselines, the number of antenna units is large, the size is large, and the equipment amount is large. For example, in the design and implementation of a combined direction-finding antenna system based on a multi-baseline interferometer and multi-beam amplitude comparison published by the leeward sea and the like, the number of array elements is more than ten, the equipment quantity is large, and the method is not suitable for satellite-borne radar alarm. The satellite-borne radar warning system is used as a part of a payload, and due to the particularity of a platform, the power, the size and the weight distributed to the radar warning system are limited, so that a direction-finding method with small equipment quantity and power consumption is needed. In conclusion, the direction finding method suitable for the satellite-borne platform is still the traditional two-channel amplitude comparison direction finding method, and the problem of improving the angle finding precision is urgently needed to be solved at present.
Disclosure of Invention
The invention aims to provide a satellite-borne three-array element single-pulse two-dimensional direction finding method, which solves the problem of low direction finding precision of a traditional radar warning system, integrates the advantages of specific amplitude direction finding and specific phase direction finding, makes up for the defect of low specific amplitude direction finding precision by utilizing the characteristic of high specific phase direction finding precision, and improves the direction finding precision of the system through long-baseline interference direction finding.
The technical solution for realizing the purpose of the invention is as follows: a satellite-borne three-array element single pulse two-dimensional direction finding method comprises the following steps:
step 1: calculating the longest base line limit according to the shortest wavelength and amplitude comparison angle measurement precision of the received signals; calculating the length requirement of the shortest base line according to the angle measurement precision required by the working frequency band and the longest wavelength of the received signal; comparing the longest base line requirement with the shortest base line requirement, if the longest base line requirement and the shortest base line requirement are contradictory, namely the longest base line is smaller than the shortest base line, under the working waveband width condition, a single base line amplitude ratio phase angle measurement cannot be adopted, the working frequency band width needs to be modified, or a double base line and multiple base line scheme is adopted;
and 2, step: according to the antenna beam pointing angle and the amplitude directional diagram, calculating the amplitude difference between the incident antennas of the signals in different directions to obtain an amplitude difference table; according to the antenna interval, the beam direction and the phase directional diagram, calculating the phase difference of the signal incident to the antenna in different directions to obtain a phase difference table;
and 3, step 3: utilizing three array elements to receive the amplitude difference of the same signal and an amplitude difference table for correlation processing to obtain a rough measurement value of the signal in the incident two-dimensional direction;
and 4, step 4: and determining a search range of the signal incidence direction by using the rough measurement result of amplitude-comparison direction finding and amplitude-comparison direction finding precision, and performing correlation processing and interpolation processing by using three groups of phase differences among three channels and a phase difference table to obtain a final angle measurement result.
Compared with the prior art, the invention has the remarkable advantages that:
(1) The algorithm principle is simple, the calculated amount is small, and the engineering implementation is easy.
(2) The number of channels is small, and the number of system equipment is small.
(3) The direction finding precision is high.
Drawings
FIG. 1 is a flow chart of system design and signal processing according to the present invention.
Fig. 2 is a scale direction finding principle diagram.
Fig. 3 is a phase comparison direction finding principle diagram.
FIG. 4 is a phase-to-phase direction-finding phase ambiguity diagram.
FIG. 5 is a schematic diagram of amplitude-to-amplitude ratio direction finding of the present invention.
FIG. 6 is a schematic diagram of a satellite-borne radar warning direction finding.
FIG. 7 is a schematic diagram of the two-dimensional direction finding of the amplitude-to-width ratio of the column sitting system.
Fig. 8 is a schematic view of beam pointing according to the present invention.
FIG. 9 is a schematic cross-sectional view of three beams according to the present invention.
FIG. 10 is a two-dimensional amplitude-contrast phase-ambiguity diagram of the present invention.
Fig. 11 is an amplitude gain diagram of an antenna pattern employed in the present invention, wherein (a) is a 2GHz antenna pattern amplitude gain diagram, (b) is a 4GHz antenna pattern amplitude gain diagram, and (c) is a 6GHz antenna pattern amplitude gain diagram.
FIG. 12 is a phase diagram of an antenna pattern for use with the present invention, wherein (a) is a 2GHz antenna pattern phase diagram, (b) is a 4GHz antenna pattern phase diagram, and (c) is a 6GHz antenna pattern phase diagram.
Fig. 13 is a graph of the superposition of the antenna pattern amplitudes of the present invention.
Figure 14 is an antenna pattern phase overlay.
Fig. 15 is a graph of the antenna pattern amplitude difference of the present invention.
Fig. 16 is a two-dimensional cross-sectional view of the amplitude difference diagram of the antenna directional diagram of the present invention, wherein (a) is a diagram showing the correspondence between the amplitude difference between the channels and the pitch angle, and (b) is a diagram showing the correspondence between the amplitude difference between the channels and the azimuth angle.
Fig. 17 is a two-dimensional cross-section of an amplitude difference plot for an antenna pattern of the present invention.
Fig. 18 is a two-dimensional cross-sectional view of a phase difference diagram between channels according to the present invention, in which (a) is a diagram showing a correspondence between a phase difference between channels and a pitch angle, and (b) is a diagram showing a correspondence between a phase difference between channels and an azimuth angle.
FIG. 19 is a two-dimensional amplitude-comparison phase-comparison direction-finding error diagram of the present invention, in which (a) is an azimuth dimension angle-finding error diagram, and (b) is a pitch dimension angle-finding error diagram.
Fig. 20 is a comparison graph of the amplitude-to-phase angle measurement errors of three frequency points according to the present invention, in which (a) is an azimuth angle measurement error graph, and (b) is a pitch angle measurement error graph.
FIG. 21 is a graph showing the variation of amplitude-to-amplitude ratio phase angle measurement error with the amplitude error between channels, in which (a) is an azimuth dimension angle measurement error graph and (b) is a pitch dimension angle measurement error graph.
FIG. 22 is a graph showing the variation of phase error between channels according to the amplitude-to-amplitude ratio of the present invention, wherein (a) is an azimuth angle error graph and (b) is a pitch angle error graph.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
With reference to fig. 1, the invention provides a two-dimensional direction finding method of satellite-borne three-array element single pulse, comprising the following steps:
step 1: according to the basic principle of amplitude comparison and direction finding, calculating the longest base line limit according to the shortest wavelength of the received signals and the accuracy requirement of amplitude comparison and angle measurement; and calculating the shortest base length requirement according to the longest wavelength of the received signal, the interference direction finding precision and the base length.
In step 1, the specific steps are as follows:
the amplitude-to-amplitude direction measurement utilizes the ratio of signal amplitude values received by two antennas to measure the angle, the schematic diagram is shown in fig. 2, two antenna beams which are partially overlapped with each other are adopted, and the field angles of the two antennas are theta under the condition of not considering the influence of the antenna beam side lobe a The signal axis phi deviating from two beams s The angle is incident, for two antenna directional diagrams, signals are incident from different angles, the amplitudes of two receiving channels are different, the farther a signal incident angle deviates from a signal axis, the larger the amplitude difference of the two channels is, therefore, the target deviation angle can be judged by comparing the amplitudes of the two channels, and the direction of a target signal is measured.
Under the condition of one-dimensional direction finding, an antenna directional diagram function is assumed to be F (theta), and the channel amplitude response is assumed to be A c (t), incident Signal amplitude A s (t), angle of incidence of signal φ s Then two channels output signal r 1 (t)、r 2 (t) are respectively:
wherein: a. The c1 、A c2 Amplitude response, θ, of the first channel 1 and the second channel 2, respectively a Two beam angles.
The amplitude ratio of the two-channel received signals is:
for the same time, expressed in decibels (dB), the two-channel amplitude ratio R 12 (t) is:
assuming that the two receive channels have the same amplitude response, i.e. A c1 (t)＝A c2 (t), then:
R 12 (t)＝F(θ a /2-φ s )-F(θ a /2+φ s )(dB) (4)
wherein, here, F (theta) a /2-φ s )、F(θ a /2+φ s ) Logarithmic decibel values are taken. Since F (theta) is in [ -theta [ - ] a ,θ a ]The range has monotonicity, so the ratio of the two channels has one-to-one correspondence with the incident angle of the signal.
Assuming the antenna pattern as a Gaussian function, i.e.
Assuming that its half-power beamwidth is θ b Defined in terms of half-power beamwidth, i.e.
The following can be obtained:
and (4) substituting, wherein the obtained two-channel amplitude ratio is as follows:
it can be seen that the amplitude ratio of the two channels corresponds to the signal incident angle one to one, and the incoming wave direction of the signal can be known as long as the amplitude ratio of the two channels is known.
For amplitude bearing, according to equation (6), one can obtain:
θ in the formula (7) a 、θ b 、R 12 And (5) performing full differentiation to obtain:
in the formula: delta phi s The angle measurement error is obtained; delta theta a Is the two beam field angle error; delta theta b A 3dB width error for the antenna beam; Δ R 12 Is the channel amplitude ratio error. It can be seen that: half power beamwidth θ of the beam b The smaller the beam, the narrower the beam, the smaller the angle measurement error; two beam field angle theta a The larger the angle measurement error is, the smaller the angle measurement error is; the smaller the specific amplitude of the two channels is, namely the closer the signal incidence direction is to the equal signal axis, the smaller the angle measurement error is; theta.theta. a 、θ b 、R 12 The variation of (b) has an effect on the angle measurement error. The derivation of the amplitude-to-amplitude precision does not consider the existence of the antenna beam side lobe, the antenna beam side lobe is inevitably increased while the antenna main beam is narrowed, if a signal enters from the side lobe, the signal incidence direction and the channel amplitude ratio have a non-monotonic relation, the amplitude-to-amplitude direction-finding result is influenced, and the direction cannot be found, so that the antenna main beam width cannot be infinitely small, and similarly, the two beam opening angles can also be too large. Therefore, the monotonicity of the channel amplitude ratio and the signal incidence direction cannot be destroyed by the change of the beam width and the beam opening angle, and otherwise, the direction finding ambiguity can be caused.
For a fixed antenna array, if the beam width and beam direction of the same frequency signal are fixed, the angle measurement error can be expressed as
Wherein: k = θ b /θ a And is constant. Theta a 、θ b 、R 12 Of the three error factors, Δ θ a 、Δθ b The method belongs to static errors, and can be corrected by methods such as meter calibration and the like in engineering implementation; Δ R 12 The dynamic error, namely the channel amplitude response changes along with the working environment, cannot be corrected in advance. The last term in equation (9) can be seen: at equal signal axes R 12 =0dB, the beam width and field angle have minimal effect on the amplitude angle measurement error, R in the beam pointing direction 12 The maximum is that the beam width and the field angle have the largest influence on the angle measurement error; the influence degree of the channel amplitude ratio error on the direction-finding error is mainly determined by the beam width, and the narrower the beam is, the smaller the error sensitivity of the angle-finding error on the channel amplitude ratio is, and the higher the direction-finding precision is.
The phase-to-phase direction is measured by using the phase differences between the echo signals received by the plurality of antennas, and a schematic diagram of the phase-to-phase direction is shown in fig. 3.
Under the assumption of far-field plane waves, due to the spacing d between the antennas, the time for signals to reach the two antennas is different, and the phase difference generated by the wave path difference Delta R is
As can be seen from fig. 3:
wherein: λ is the wavelength of the radiation source. If it can measure
Then the incoming wave direction phi of the signal can be determined s 。
For a phase direction finding, by differentiating equation (10), an expression of the direction finding error can be obtained, which is:
in the formula: delta phi s An angle measurement error;
phase discrimination errors for the two-channel phase difference; Δ d is a baseline length measurement error; Δ λ is the wavelength measurement error caused by the frequency measurement error.
Of three measurement errors of delta d and delta lambda, the delta d is a static error, and can be measured and corrected before the equipment works in the engineering realization,
Δ λ is a dynamic error and cannot be corrected in advance.
For a direction-finding error Δ φ λ caused by a wavelength measurement error, it can be expressed as:
assuming the frequency measurement error is Δ f, then:
wherein: f. of 0 A real carrier frequency of the signal; and c is the speed of light. Therefore, Δ φ λ may be further expressed as:
since Δ f is relative to the center frequency f 0 Smaller, can reach less than one percent, and measured phi s The range is usually limited to + -pi/4, so that the corresponding angle measurement error delta phi λ Smaller and negligible, so the angle measurement error is mainly determined by the phase difference phase discrimination error between channels, namely:
in the formula (15), λ, φ s Determined by the characteristics of the radiation source signal, d is the length of a phase comparison base line and is set by the antenna arrangement, and as can be seen from the formula (15), the larger d is, the higher the angle measurement precision is, and the way of obtaining the high angle measurement precision is, however, the larger d is, the measured angle measurement precision is
The larger, when
In time, phase ambiguity exists in the phase difference measurement value between channels, and the ambiguity must be solved first to measure the direction.
A phase-to-phase direction-finding phase-ambiguity diagram is shown in FIG. 4, where φ a For the period of the direction-finding blur, only in phi a Measuring phase difference between channels over a wide range of angles
Angle of incidence with the signal phi s One-to-one correspondence, no ambiguity exists. As can be seen from the equation (10), when d > λ/2, there is phase ambiguity in the channel phase difference, λ/2 corresponds to the unambiguous incident angle range, and d corresponds to all incident angle possibilities of 180 °, φ a Comprises the following steps:
if the phase ambiguity of the phase angle is solved by using the amplitude comparison angle measurement method, the amplitude comparison direction measurement result must be ensured not to exceed the ambiguity range of the phase angle measurement, and the uniqueness of the subsequent phase angle measurement result can be ensured. Suppose the true incident angle of the signal is phi s0 And amplitude comparison angle measurement precision is delta phi ae The principle of amplitude versus direction finding is shown in fig. 5.
As can be seen from FIG. 5, the solution of phase ambiguity of phase measurement angle by amplitude measurement method must satisfy 2 Δ φ ae ≤φ a And (4) condition. Neglecting the static error factor according to equation (9), then
Then, the base length condition that the amplitude-to-phase direction finding can solve the phase ambiguity is:
suppose that the angle measurement precision required by the system design is delta phi s0 From equation (15), the antenna baseline length d is obtained as:
by combining formula (18) and formula (19), the limitation range of the antenna base length d of the available amplitude-to-amplitude ratio phase direction finding method is as follows:
for a broadband radar detection system, the working frequency range is wide, the corresponding wavelength variation is large, the ratio of the longest wavelength to the shortest wavelength can reach more than 3 times, and the wavelength variation range of a received signal is assumed to be [ lambda ] min ,λ max ]Because the condition of the formula (20) is the limit for a single frequency point, for the whole system, in order to ensure the direction-finding precision, the shortest working baseline should select the maximum value, and in the same way, in order to ensure that the phase-comparison direction-finding can be deblurred, the longest working baseline should select the minimum value, so the limit range of the antenna baseline length d in the phase-comparison direction-finding method with the amplitude-comparison ratio can be modified as follows:
step 2: according to the antenna beam pointing angle and the amplitude directional diagram, calculating the amplitude difference between the signals incident to the antenna in different directions to obtain an amplitude difference table; and calculating the phase difference of the signals incident to the antenna in different directions according to the antenna interval, the beam direction and the phase directional diagram to obtain a phase difference table.
And 3, step 3: and (3) receiving the amplitude difference of the same signal by using the three array elements and carrying out correlation processing on the amplitude difference table to obtain a rough measurement value of the signal in the incident two-dimensional direction.
The space-borne radar warning system needs to measure the space two-dimensional angle information of a radiation source and needs to carry out two-dimensional direction measurement. The schematic diagram of warning direction finding of the satellite-borne radar is shown in fig. 6, the radiation source is positioned in the visible area of the satellite, and the angle information of the radiation source to be measured is (alpha) 1 ,β 1 ) Wherein α is 1 Is an azimuth angle, beta 1 Is a pitch angle. Fig. 6 shows the azimuth and pitch angles of the radiation source defined under the satellite carrier coordinate system, in practical implementation, a cylindrical coordinate system is usually used to define the azimuth and pitch angles of the radiation source, and the relationship between the azimuth and pitch angles of the radiation source and the satellite carrier coordinate system is shown in fig. 7, where the azimuth and pitch angles of the radiation source are (α, β).
In order to reduce the equipment amount and the number of channels, the system adopts a three-element antenna array, as shown in fig. 7, the directional diagrams of the three-element antenna are the same, but the beam directions are different, and the three antenna beams are uniformly distributed in the space by taking the Z axis as a central axis, as shown in fig. 8, the azimuth angles α of the first antenna 1, the second antenna 2 and the third antenna 3 are 225 °, 0 ° and 90 ° respectively, the beam directions of the three antenna beams are the same as the included angle of the Z axis, that is, the elevation angles β of the beam directions are the same, at this time, the geometric relationships of the second antenna 2 and the third antenna 3 relative to the first antenna 1 are equivalent, that is, if the antenna directional diagrams are completely symmetrical about the central line of the beam in the three-dimensional space, the angle measuring capabilities of the antenna array in the X axis direction and the Y axis direction are the same.
Under the condition that the antenna beam of fig. 8 is directed, the cross section of the beam along the XOZ plane is as shown in fig. 9, unlike the case of one-dimensional direction finding, in which the beam of the third antenna 3 is not symmetrical to the beam of the first antenna 1 and the beam of the second antenna 2, the antenna beams are overlapped in space.
Because the antenna gain and the beam direction are known, the beam amplitude gain difference is fixed, and therefore, the ratio can still be adoptedThe web method performs direction finding. Three antenna beams can form three groups of amplitude-comparing angle-measuring antenna pairs, namely, every two days can obtain a group of antenna amplitude gain differences delta F, and three amplitude differences in a certain direction form a vector X (alpha, beta), wherein X (alpha, beta) = [ delta F ] 12 ；ΔF 13 ；ΔF 23 ]Wherein, Δ F 12 For the antenna amplitude gain difference between the first antenna 1 and the second antenna 2, Δ F can be obtained similarly 13 、ΔF 23 Of the three amplitude difference variables,. DELTA.F 12 ，ΔF 13 The angles of the radiation sources are judged by the correlation coefficient of Y and X, and the angle corresponding to the vector X with the maximum correlation coefficient is the incident angle of the radiation source. Assuming that the number of spatial samples of the incident angle of the signal is N, the two-dimensional amplitude-comparison angle measurement can be expressed as:
(α,β)←max{Cov(Y,X 1 ),…,Cov(Y,X N )} (22)
in a certain angle, because the two-dimensional ratio amplitude measurement angle has one more independent variable relative to the one-dimensional angle measurement, the angle measurement robustness is stronger, namely, the sensitivity of the angle measurement error to the inter-channel amplitude error is lower than that of the one-dimensional ratio amplitude measurement angle.
And 4, step 4: and determining a search range of the signal incidence direction by using the rough measurement result of amplitude-comparison direction finding and amplitude-comparison direction finding precision, and performing correlation processing and interpolation processing by using three groups of phase differences among three channels and a phase difference table to obtain a final angle measurement result.
For the two-dimensional phase comparison angle measurement of the three array elements of the system, the angle measurement process is different from that of the one-dimensional phase comparison angle measurement. In the one-dimensional phase comparison measurement angle, the directions of the two antenna beams are the same, and under the assumption that an incident signal is a plane wave, the signal is incident from the same angle of the two antenna beams, so that the phases of the two antenna beams have the same influence on the signal, namely the signals received by the two channels are superposed with the same phase, when the phase difference between the channels is measured, the influence of the antenna phases on the signal phases can be eliminated, and only the phase difference between the channels caused by the antenna base line is remained. In the phase comparison two-dimensional direction finding of the system, the three antenna beams have different directions, as shown in fig. 9, when receiving signals, the same signal is incident from different angles of the antenna beams, so that the same signal is superposed with different phase information in each channel, and when taking phase difference between the channels, the influence of the phase characteristic of an antenna directional diagram on the signal phase cannot be removed, so that the phase difference between the same signal channels comprises the difference between the phase generated by an antenna base line and the phase of the antenna directional diagram corresponding to the two channels, and therefore, the incident angle of a radiation source cannot be calculated simply by the formula (10).
For signals incident in a certain direction, the phase difference of corresponding antenna beams is fixed, and the phase caused by the wave path difference is also fixed, so that a signal incident phase table can be established by referring to a comparative ranging method, namely a channel phase difference lookup table is established for all possibilities of spatial incident angles.
Unlike the phase ambiguity period of one-dimensional direction finding, the three-array element ambiguity period is longer due to the combination of the phase differences among the three groups of channels, and the two-dimensional amplitude ratio phase ambiguity diagram is shown in fig. 10.
In the three-element antenna system, three groups of element combinations exist, that is, three direction-finding baselines exist, the same signal is incident from different spatial angles, the fuzzy periods of the three baselines are different, and the three groups of element combinations are shown in fig. 10. The three groups of phase differences have respective fuzzy periods, the two-dimensional phase comparison angle measurement simultaneously utilizes the three groups of phase differences to measure the angle, even if one group or two groups have phase ambiguity, as long as one group is monotonous in the whole search interval and is in one-to-one correspondence with the angle, the incoming wave direction can be determined, and the angle measurement is completed. Therefore, the period of ambiguity of the two-dimensional phase ratio angle measurement is the maximum of the three sets of phase difference ambiguity periods, as shown in fig. 10.
As described above, in the two-dimensional ratio, since there is a phase difference due to the incidence of the antenna beam in different directions in addition to the inter-channel phase difference due to the baseline, the actual period result is different from fig. 10, and the inter-channel phase differences corresponding to different angular positions include different beam phase differences, which causes the periodicity of each channel phase difference to change, or even lose the periodicity. However, because three-channel phase difference direction finding is adopted, two-dimensional phase comparison direction finding can be completed as long as three groups of phase differences have one-to-one phase difference with angles in a search interval.
In summary, for the two-dimensional amplitude-comparison phase ratio, the base length d in the equation (21) not only follows the limit of the angle measured by the one-dimensional amplitude-comparison phase ratio, but also needs to be reasonably adjusted according to the actual antenna gain, pointing direction and arrangement condition.
To further illustrate the effectiveness of the method of the present invention, the method was analyzed in simulation. The simulation system adopts a three-array-element L-shaped layout, an antenna array layout geometric model is shown in figure 7, the three array elements are completely the same, the working waveband of the antenna is 2 GHz-6 GHz, the beam width is 90 degrees, the beam-oriented directions of the three antennas are 225 degrees, 0 degrees and 90 degrees respectively, the pitch angle is 40 degrees under a cylindrical coordinate system, the spatial positions are shown in figures 7 and 8, the phase error between channels is assumed to be 15 degrees, the amplitude error between the channels is 1dB, d is more than or equal to 0.08m and less than or equal to 0.57m according to the calculation of a formula (21), and the distance between a first antenna 1 and a second antenna 2 as well as between a third antenna 3 is set to be 0.14m according to the actual situation.
Selecting three frequency points of 2GHz, 4GHz and 6GHz for simulation experiment, and transforming the azimuth angle and the pitch angle of the antenna beam to a satellite carrier coordinate system, namely transforming the (alpha, beta) coordinate into the (alpha, beta) coordinate 1 ,β 1 ) The amplitude diagram of the antenna pattern corresponding to three frequency points is shown in fig. 11, and the phase of the antenna pattern is shown in fig. 12. Comparing the three graphs in fig. 11, it can be found that the beam width of the high frequency point is narrower than the lower frequency point, i.e. θ b The gain of the main beam lobe at the high frequency point is smaller than that at the low frequency point, and the instantaneous coverage area of the antenna of the detection system is determined by the beam width theta of the high frequency point b It is determined that changes in antenna beam width and gain affect the accuracy of radial direction finding. From FIG. 12The phase ambiguity of the antenna directional diagram of the three frequency points is seen, namely the phase difference of the same antenna directional diagram in different directions exceeds 2 pi, and the ambiguity of the three frequency points is compared, so that the ambiguity of the phase of the antenna beam of 6GHz is seen to be the most serious. This phase ambiguity, which is detrimental to the subsequent phase comparison angle measurement, leads to a complication of the phase differences between the different channels at the same spatial angle due to the different pointing directions of the three beams.
Because the three frequency point beam patterns are similar, the 4GHz frequency point beam pattern is taken as an example for simulation analysis. And according to the set beam direction, performing rotation transformation on the same beam to obtain three beams with different directions, wherein a spatial superposition diagram of amplitude gains of the three antenna beams is shown in fig. 13, and a phase superposition diagram is shown in fig. 14. As can be seen from fig. 13, the three beams are overlapped in a crossed manner in space, and the corresponding amplitude gains of the three beams are different in the same spatial angle, so that two-dimensional direction finding can be realized by using the gain difference. As shown in fig. 14, because the phases of the three antenna beams have a phase ambiguity, the three beam phase diagrams are complex after being overlapped, but it can be found that the phases of the three beams corresponding to the same spatial angle are different, and a phase comparison direction measurement can be realized by using the phase difference.
The amplitude gain differences among the beams of the first antenna 1, the second antenna 2 and the third antenna 3 are respectively obtained according to the amplitude gain values corresponding to the same spatial angle, and the obtained result is shown in fig. 15. As can be seen from fig. 15, the three sets of amplitude gain differences are relatively smooth in space and have no large fluctuation, that is, the amplitude gain differences have monotonicity in space, and the combinations of the three sets of amplitude gain differences correspond to the spatial angles one to one, and can be used for two-dimensional direction finding.
In order to observe the principle of amplitude difference direction finding more clearly, profile analysis was performed on the amplitude difference along the pitch angle 0 ° plane and the azimuth angle 0 ° plane, respectively, and the obtained results are shown in fig. 16. As shown in fig. 16, the amplitude differences among the three channels have monotonicity in the whole angle measurement range [ -45 °,45 ° ] and correspond to the signal angles one to one, and it can be seen that the amplitude differences among the three channels have different values, and the three amplitude difference values corresponding to any angle have uniqueness, which is beneficial to the subsequent correlation amplitude-versus-direction measurement processing.
Similar to the amplitude direction finding, the phase differences among the channels corresponding to the first antenna 1, the second antenna 2, and the third antenna 3 are respectively obtained according to the phase of each antenna beam corresponding to the same spatial angle and the phase difference caused by the geometric position of each antenna, and the obtained result is shown in fig. 17. As shown in fig. 17, the phase difference between the antennas is complex, but still exhibits a blurring characteristic, such as the phase difference between the second antenna 2 and the third antenna 3 in fig. 17, a significant periodicity can be observed, and such phase blurring causes phase differences corresponding to the same spatial angle to be not unique, and needs to be corrected by a deblurring method.
Similarly, in order to observe the law of phase difference change between channels more clearly, the results of profile analysis of the inter-channel phase difference map along the pitch angle 0 ° plane and the azimuth angle 0 ° plane are shown in fig. 18. As can be seen from fig. 18, there is a certain periodicity in the phase difference between the three groups of channels, but the repetition period is not fixed and varies, because the inter-channel phase includes not only the phase caused by the distance difference from the signal to the antenna, but also the phase difference between the beams of the two antennas. As the regularity of the phase difference between the two antenna beams is poor, the final phase difference has no fixed period and only shows a certain periodicity, but as can be seen from fig. 18, in a repeating period, at least two groups of phase differences have monotonicity, and three groups of phase differences corresponding to the same angle have uniqueness, so that the phase difference can be used for direction finding.
According to the simulation model, under a cylindrical coordinate system, simulation points are arranged in a range from 0 degrees to 360 degrees in an azimuth dimension at intervals of 10 degrees, simulation points are arranged in a range from 0 degrees to 45 degrees in a pitch dimension at intervals of 5 degrees, 100 Monte Carlo simulations are carried out on each point, and direction-finding errors corresponding to different frequencies are simulated. Taking a 4GHz frequency point as an example, assuming that a phase error between system channels is 15 degrees, an amplitude error between the channels is 1dB, a phase ratio fuzzy range is set to be 10 degrees, all angle measurement results of all simulation points are sequenced from small to large according to angle measurement errors, and an obtained two-dimensional phase ratio amplitude ratio direction measurement error is shown in fig. 19.
In fig. 19, the amplitude comparison error curve is an error result obtained by only using amplitude comparison angle measurement, and the phase comparison error curve is an error obtained by using an amplitude comparison method, it can be seen that the first half section of the amplitude comparison angle measurement is obviously smaller than the amplitude comparison error, and the second half section of the amplitude comparison error is overlapped with the phase comparison error curve, because the phase comparison angle measurement is performed on the basis of the amplitude comparison angle measurement, the phase comparison angle measurement result needs to be searched according to the amplitude comparison angle measurement result, the search range is a fuzzy interval, when the amplitude comparison angle measurement error is larger, the deviation signal is larger in the true direction, and at this time, the search region does not contain a true angle, so that the angle obtained by phase comparison angle measurement is a fuzzy angle, and the angle measurement error may become larger, and therefore, the result of fig. 19 may appear. The first intersection of the amplitude versus error curve and the amplitude versus phase error curve in fig. 19 is essentially the variance value of the angle measurement error, conforming to the 3 σ criterion of normal distribution, being the first σ point. It can also be seen that the azimuth and elevation angle error curves are slightly different, which is caused by the antenna pattern not being completely symmetrical through 360 °.
In order to compare the difference of the angle measurement performance of each frequency point, the angle measurement error of the amplitude ratio of the 2GHz frequency point and the 6GHz frequency point is simulated and compared with the 4GHz frequency point, and the result is shown in figure 20. It can be seen from fig. 20 that the direction-finding accuracy of three frequency points is highest at 6GHz and lowest at 2GHz, because the 3dB beam of the antenna at the high frequency point is narrower, which is beneficial to direction-finding with a specific amplitude, so that the direction-finding accuracy is higher than the phase direction-finding accuracy with a specific amplitude.
In order to study the influence of the inter-channel amplitude measurement error on the amplitude-to-phase ratio angle measurement error, the section also simulates the amplitude-to-phase ratio angle measurement error under the condition of different amplitude measurement errors, the inter-channel amplitude measurement error is from 0.3dB to 1.5dB, and the simulation result is shown in FIG. 21. As can be seen from fig. 21, the amplitude-to-amplitude ratio phase angle measurement error increases with an increase in the amplitude error, and the speed increase increases with an increase in the amplitude error.
Similarly, under the condition that the inter-channel amplitude measurement error is 0.9dB, the simulation in this section analyzes the influence of the inter-channel phase error on the amplitude-to-phase direction-finding error, and the inter-channel phase error changes from 0 ° to 16 °, and the obtained simulation result is shown in fig. 22. As shown in fig. 22, the amplitude-to-amplitude phase angle measurement error increases with the increase of the inter-channel phase error, but is significantly reduced compared with the single amplitude-to-amplitude angle measurement result, and compared with fig. 21, the amplitude-to-amplitude phase direction measurement error result changes slowly with the phase, which shows that the method has less influence on phase error and stable angle measurement error.
Simulation results show that the two-dimensional amplitude comparison method has feasibility, the direction finding precision of the traditional amplitude comparison direction finding can be obviously improved, and the warning capability of the satellite-borne warning radar is enhanced. The related technology can be applied to various satellite platforms, is used for monitoring and alarming threats, and has wide military application prospects.
Claims (3)
1. A satellite-borne three-array element single-pulse two-dimensional direction finding method is characterized by comprising the following steps:
step 1: calculating the longest base line limit according to the shortest wavelength and amplitude comparison angle measurement precision of the received signals; calculating the length requirement of the shortest base line according to the angle measurement precision required by the working frequency band and the longest wavelength of the received signal; comparing the longest base line requirement with the shortest base line requirement, if the two requirements are contradictory, namely the longest base line is smaller than the shortest base line, under the working waveband width condition, a single base line amplitude ratio phase angle measurement cannot be adopted, the working frequency band width needs to be modified, or a double base line and multiple base line scheme is adopted; the method comprises the following specific steps:
for direction finding of amplitude comparison
Wherein phi s Is the incident angle of the signal; theta.theta. a Two beam angles; two-channel amplitude ratio R 12 ；θ b Is a half-power beamwidth;
theta in pair formula (7) a 、θ b 、R 12 And (5) performing full differentiation to obtain:
wherein, is s The angle measurement error is obtained; delta theta a Is the two beam field angle error; delta theta b A 3dB width error for the antenna beam; Δ R 12 Is the channel amplitude ratio error; for a fixed antenna array, if the beam width and beam direction of a signal with the same frequency are fixed, the angle measurement error is expressed as
Wherein k = θ b /θ a Is a constant; theta a 、θ b 、R 12 Of the three error factors, Δ θ a 、Δθ b Pertaining to static error, Δ R 12 Is a dynamic error;
for comparative direction finding, the expression for the direction finding error is:
assuming that the wavelength of the received signal varies within a range of [ lambda ] min ,λ max ]The limitation range of the antenna base length d of the amplitude-to-phase ratio direction finding method is as follows:
step 2: according to the antenna beam pointing angle and the amplitude directional diagram, calculating the amplitude difference between the signals incident to the antenna in different directions to obtain an amplitude difference table; according to the antenna interval, the beam direction and the phase directional diagram, calculating the phase difference of the signal incident to the antenna in different directions to obtain a phase difference table;
and step 3: utilizing three array elements to receive the amplitude difference of the same signal and an amplitude difference table for correlation processing to obtain a rough measurement value of the signal in the incident two-dimensional direction;
and 4, step 4: and determining a search range of the signal incidence direction by using the rough measurement result of amplitude-comparison direction finding and amplitude-comparison direction finding precision, and performing correlation processing and interpolation processing by using three groups of phase differences among three channels and a phase difference table to obtain a final angle measurement result.
2. The two-dimensional direction finding method of the satellite-borne three-array element single pulse according to claim 1, characterized in that: the specific steps of step 2 and step 3 are as follows:
three antenna beams form three groups of amplitude-comparing angle-measuring antenna pairs, namely, every two antenna beams obtain a group of antenna amplitude gain differences delta F, and the three amplitude differences in a certain direction form a vector X (alpha, beta), X (alpha, beta) = [ delta F ], (alpha, beta) 12 ；ΔF 13 ；ΔF 23 ]Wherein, Δ F 12 The antenna amplitude gain difference of the first antenna (1) and the second antenna (2) is obtained to obtain delta F 13 、ΔF 23 Of the three amplitude difference variables,. DELTA.F 12 ，ΔF 13 The angles of the radiation sources correspond to three-channel amplitude difference vectors one by one, the phase difference between the three measured channels is assumed to be Y, the angles of the radiation sources are judged through the correlation coefficients of Y and X, and the angle corresponding to the vector X with the maximum correlation coefficient is the incident angle of the radiation sources; assuming that the number of spatial samples of the incident angle of the signal is N, the two-dimensional amplitude-comparison angle measurement is expressed as:
(α,β)←max{Cov(Y,X 1 ),…,Cov(Y,X N )} (22)。
3. the satellite-borne three-array-element single-pulse two-dimensional direction finding method according to claim 1, characterized in that: the specific steps of step 4 are as follows:
in the three-array-element antenna system, three groups of array element combinations exist, namely three direction-finding baselines exist, the same signal is incident from different space angles, and the fuzzy periods of the three baselines are different; the three groups of phase differences have respective fuzzy periods, the two-dimensional phase comparison angle measurement simultaneously utilizes the three groups of phase differences to measure the angle, even if one group or two groups have phase ambiguity, as long as one group is monotonous in the whole search interval and is in one-to-one correspondence with the angle, the incoming wave direction can be determined, the angle measurement is completed, and the fuzzy period of the two-dimensional phase comparison angle measurement is the maximum value of the fuzzy periods of the three groups of phase differences.
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| CN112596022B (en) * | 2020-11-24 | 2023-09-22 | 中国科学院微小卫星创新研究院 | Wave arrival angle estimation method of low-orbit satellite-borne multi-beam regular hexagonal phased array antenna |
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| CN113203979A (en) * | 2021-04-14 | 2021-08-03 | 北京睿信丰科技有限公司 | Phase comparison method angle measurement method after smoothing |
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