CN102419430A - Parallel-baseline-based two-dimensional direction finding method of round array phase interferometer - Google Patents

Parallel-baseline-based two-dimensional direction finding method of round array phase interferometer Download PDF

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CN102419430A
CN102419430A CN2011102350237A CN201110235023A CN102419430A CN 102419430 A CN102419430 A CN 102419430A CN 2011102350237 A CN2011102350237 A CN 2011102350237A CN 201110235023 A CN201110235023 A CN 201110235023A CN 102419430 A CN102419430 A CN 102419430A
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phase difference
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phase
baselines
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CN102419430B (en
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吴奉微
贾可新
李亚星
程婷
何子述
蒲刚
蒋林鸿
张昕
郑攀
邹丁秋
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of radio monitoring technologies, and provides a parallel baseline based method for realizing two-dimensional wideband direction finding for a phase interferometer. The method comprises the steps of: figuring out a possible fuzzy number combination of a phase difference between two groups of parallel baselines by utilizing a linear relationship among fuzzy numbers of the phase difference between the two groups of parallel baselines in a uniform round array, thereby estimating the direction cosine of a possible incident signal; subsequently, calculating the corresponding phase differences among all the longest baselines; correlating actually measured phase difference vectors of all the longest baselines of the uniform round array; finding out a phase difference vector corresponding to the maximum correlation coefficient for estimation of a theoretical phase difference vector; and acquiring non-fuzzy phase difference vectors of all the longest baselines by resolving the phase ambiguity of all the longest baselines. According to the method provided by the invention, the deficiencies of other ambiguity resolving methods can be overcome; the estimation of the direction cosine approaches a CRLB (Cremer-Rao Lower Bound), so that the direction estimation of the incident signal achieves a very high direction finding precision; in addition, the calculation quantity in the invention is less.

Description

Two-dimensional direction finding method of circular array phase interferometer based on parallel baseline
Technical Field
The invention belongs to the technical field of radio monitoring, and particularly relates to a two-dimensional direction finding method for a wide-band phase interferometer in radio monitoring.
Background
The interferometer direction finding has the advantages of simple algorithm, high sensitivity, good real-time performance, various antenna array forms and the like, and is widely applied to a direction finding system in the field of electronic reconnaissance. In order to improve the direction finding accuracy and the capability of resisting the multipath effect, the antenna aperture is required to be large enough, however, the direction finding is necessary to be blurred. Therefore, in the direction finding of the phase interferometer, the multivalue of the phase, namely ambiguity, is a key problem influencing whether the direction finding is successful or not.
To solve the above problems, various methods of resolving ambiguity have been developed. The existing interferometer ambiguity resolution methods mainly comprise: the ambiguity is resolved by a long and short baseline combined method (see the literature: design research of circular arrays in a Cheng flag, Huang Gaoming, Song Shi Qiong. nine-element uniform circular array interferometer direction-finding system [ C ]. the Chinese electronics society electronic countermeasure group of the fourteenth academic society, the discourse corpus 2005 (1): 717) and phase difference ambiguity resolution based on the staggered distance (see the literature: Gong enjoys iridium, spring, grand Xiao. the ambiguity resolution method of phase difference change values based on the staggered distance research [ J ]. signal processing 2003, 19 (4): 308) and a multi-group clustering method (Zan, Cheng Shao, first besieged, five-element uniform circular array interferometer weighted direction-finding algorithm and phase ambiguity resolution conditions [ J ]. electronic countermeasure: 2004 (1): 8-12.). The long and short baseline combination method is simple and flexible, but requires the shortest baseline to be smaller than the half wavelength of the incident signal, which limits the highest operating frequency of the antenna. The phase difference ambiguity resolution method based on the staggered distance requires that the array element spacing meets a certain staggered relation and has certain limitation on the signal-to-noise ratio (Zhou Yao, Chen fly, Huangpu Kan, Suzhong kang. the multi-baseline phase interferometer ambiguity resolution algorithm [ J ] in the electronics and information report: 2005, 27 (2) 259 and 261 ]). The method for clustering multiple base line groups has large calculation amount, and cannot provide a definite clustering threshold, thus seriously influencing the fuzzy understanding performance.
In various direction finding methods in the prior art, the problems of limited use range or large calculation amount exist, and the direction finding precision is difficult to guarantee.
Disclosure of Invention
Aiming at the technical problems that the application range is limited or the calculated amount is large and the direction finding precision is difficult to guarantee in various direction finding methods in the prior art, the two-dimensional direction finding method of the circular array phase interferometer based on the parallel baseline is provided.
The invention discloses a two-dimensional direction finding method of a circular array phase interferometer based on a parallel baseline, which specifically comprises the following steps:
the first step is as follows: selecting two groups of parallel baselines in a planar array
Figure 2011102350237100002DEST_PATH_IMAGE002
And
Figure 2011102350237100002DEST_PATH_IMAGE004
the base length is respectively
Figure 2011102350237100002DEST_PATH_IMAGE006
And is and
Figure 2011102350237100002DEST_PATH_IMAGE008
the included angle between two groups of parallel baselines is；
The second step is that: calculating phase differences of a first set of parallel baselines
Figure 2011102350237100002DEST_PATH_IMAGE012
Phase difference with a second set of parallel base lines
Figure 2011102350237100002DEST_PATH_IMAGE014
And calculatePhase difference vector of root longest base line
Figure 2011102350237100002DEST_PATH_IMAGE018
Wherein
Figure 38906DEST_PATH_IMAGE016
The number of array elements;
the third step: using the phase difference obtained in the second step
Figure 956047DEST_PATH_IMAGE012
And
Figure 676397DEST_PATH_IMAGE014
calculating the number of possible ambiguities for two sets of parallel baselines、
Figure 2011102350237100002DEST_PATH_IMAGE022
、
Figure 2011102350237100002DEST_PATH_IMAGE024
、
Figure 2011102350237100002DEST_PATH_IMAGE026
：
Figure 2011102350237100002DEST_PATH_IMAGE028
；
Figure 2011102350237100002DEST_PATH_IMAGE030
；
Wherein
Figure 2011102350237100002DEST_PATH_IMAGE032
、
Figure 2011102350237100002DEST_PATH_IMAGE034
，
Figure 2011102350237100002DEST_PATH_IMAGE036
In order to be the wavelength of the incident signal,
Figure 2011102350237100002DEST_PATH_IMAGE038
it is meant to round-off the process,represents rounding down;
the fourth step: fuzzy number obtained from the third step
Figure 445507DEST_PATH_IMAGE020
、
Figure 259880DEST_PATH_IMAGE022
、、
Figure 224742DEST_PATH_IMAGE026
Is provided with
Figure 2011102350237100002DEST_PATH_IMAGE042
To pair
Figure 2011102350237100002DEST_PATH_IMAGE044
，
Figure 2011102350237100002DEST_PATH_IMAGE046
To pair
Figure 2011102350237100002DEST_PATH_IMAGE048
Namely:group ofRespectively calculating the direction cosines of the N groups of incident signals;
the fifth step: obtained according to the fourth step
Figure 2011102350237100002DEST_PATH_IMAGE054
The direction cosine of the incident signal is formed, and N groups are calculated
Figure 2072DEST_PATH_IMAGE016
Root longest baseline phase difference vector
Figure 2011102350237100002DEST_PATH_IMAGE056
；
And a sixth step: obtained in the fifth step
Figure 546317DEST_PATH_IMAGE056
Phase difference vector with M longest base lines measured
Figure 477364DEST_PATH_IMAGE018
Making correlation operation and selecting the phase difference vector corresponding to the maximum correlation coefficient and recording the phase difference vector as
Figure DEST_PATH_IMAGE058
；
The seventh step: according to the phase difference vector obtained in the sixth step
Figure 169376DEST_PATH_IMAGE058
To obtain
Figure 841141DEST_PATH_IMAGE016
Fuzzy number vector of root longest base line
Figure DEST_PATH_IMAGE060
；
Eighth step: obtaining the phase difference vector without ambiguity by using the ambiguity number vector obtained in the seventh step。
Preferably, the method further comprises:
the ninth step: and solving a least square solution of the direction cosine through the calculated unambiguous phase difference vector, and calculating the estimation of the direction cosine of the incident signal.
Preferably, the method further comprises:
the tenth step: and calculating the estimation of the azimuth angle and the pitch angle by using the estimation of the direction cosine obtained in the ninth step.
Preferably, the planar array is a uniform circular array.
Preferably, in the sixth step, the function of the correlation operation is:
。
preferably, the above 6 seventh step results in
Figure 177576DEST_PATH_IMAGE016
Fuzzy number vector of root longest base lineThe function is:
Figure DEST_PATH_IMAGE066
。
the invention has the beneficial effects that: a two-dimensional direction finding method for a circular array phase interferometer based on parallel baselines is provided, the method comprises the steps of selecting two groups of parallel baselines in a uniform circular array, calculating possible combination of fuzzy numbers by utilizing linear relation between fuzzy numbers of phase difference of the parallel baselines, calculating a phase difference vector corresponding to the fuzzy numbers according to the combination of the fuzzy numbers, then finding out estimation of theoretical phase difference by utilizing correlation operation, obtaining an unambiguous value of the phase difference vector of the longest base line by solving the phase ambiguity of the longest base line, and finally solving estimation of an incident signal azimuth angle and a pitch angle by utilizing a least square method. The invention not only can overcome the defects of other ambiguity resolution algorithms, but also can provide a high-precision direction estimation value of the incident signal, and the obtained direction cosine estimation can better approach the lower limit of the Cramer-Row. In addition, the method has small calculation amount, and ensures the real-time performance of the broadband direction finding.
Drawings
FIG. 1 is a flow chart of a two-dimensional direction finding method of a circular array phase interferometer based on a parallel baseline.
FIG. 2 is
Figure 724412DEST_PATH_IMAGE016
A uniform circular array model.
FIG. 3 shows two parallel baseline selection models.
FIG. 4 is a direction cosine
Figure DEST_PATH_IMAGE068
Is compared to the lower limit of cramer.
FIG. 5 is a direction cosineIs compared to the lower limit of cramer.
FIG. 6 is a standard deviation of azimuth direction finding according to the present invention.
Fig. 7 is a standard deviation of the pitch angle direction measurement of the present invention.
Detailed Description
The following detailed description of the embodiments of the present invention is provided in conjunction with the accompanying drawings.
Fig. 1 shows a flow chart of a two-dimensional direction finding method for a circular array phase interferometer based on parallel baselines, which specifically includes the following steps:
the first step is as follows: selecting two groups of parallel baselines in uniform circular array
Figure DEST_PATH_IMAGE072
And
Figure DEST_PATH_IMAGE074
the base length is respectively
Figure 753198DEST_PATH_IMAGE006
And is andthe included angle between two groups of parallel baselines is
Figure 607201DEST_PATH_IMAGE010
；
The second step is that: calculating phase differences of a first set of parallel baselines
Figure 273806DEST_PATH_IMAGE012
Phase difference with a second set of parallel base lines
Figure 352620DEST_PATH_IMAGE014
And calculatePhase difference vector of root longest base line
Figure 497611DEST_PATH_IMAGE018
Wherein
Figure 385933DEST_PATH_IMAGE016
The number of array elements;
the third step: using the phase difference obtained in the second step
Figure 203191DEST_PATH_IMAGE012
And
Figure 493358DEST_PATH_IMAGE014
and (3) calculating:
Figure 435907DEST_PATH_IMAGE028
（1）
Figure 811524DEST_PATH_IMAGE030
（2）
wherein
Figure 169824DEST_PATH_IMAGE032
、
Figure 580077DEST_PATH_IMAGE034
，
Figure 631210DEST_PATH_IMAGE036
In order to be the wavelength of the incident signal,
Figure 556440DEST_PATH_IMAGE038
it is meant to round-off the process,
Figure 718431DEST_PATH_IMAGE040
represents rounding down;
the fourth step: from the third step can be obtained
Figure 717611DEST_PATH_IMAGE042
To pair
Figure 930856DEST_PATH_IMAGE044
The same principle can be obtained
Figure 281066DEST_PATH_IMAGE046
To pair
Figure 309065DEST_PATH_IMAGE048
Thus can beTo obtain
Figure 428331DEST_PATH_IMAGE050
Group of
Figure DEST_PATH_IMAGE076
Or
Figure 493370DEST_PATH_IMAGE052
In combination with each other, is
Figure 330876DEST_PATH_IMAGE054
Group ofRespectively substituting:
Figure DEST_PATH_IMAGE078
（3）
thereby can obtain
Figure 74021DEST_PATH_IMAGE054
Direction cosine of group incident direction
Figure DEST_PATH_IMAGE080
Wherein
Figure DEST_PATH_IMAGE082
And is and
Figure DEST_PATH_IMAGE084
is an integer;
the fifth step: obtained according to the fourth stepThe direction cosine of the group incident signal is substituted into a theoretical calculation formula for calculating the phase difference to obtain
Figure 569517DEST_PATH_IMAGE054
Group of
Figure 877002DEST_PATH_IMAGE016
Root longest baseline phase difference vector
Figure 705280DEST_PATH_IMAGE056
；
And a sixth step: obtained in the fifth step
Figure 440018DEST_PATH_IMAGE056
Substituting:
Figure 986537DEST_PATH_IMAGE064
（4）
the phase difference vector corresponding to the maximum of the formula (4) is taken as the estimation of the theoretical phase difference vector；
The seventh step: estimating the theoretical phase difference obtained in the sixth stepSubstituting:
Figure 16963DEST_PATH_IMAGE066
（5）
solution (II)
Figure 50778DEST_PATH_IMAGE016
Obtaining fuzzy number vector according to the fuzzy of phase difference of the longest base line；
Eighth step: substituting the fuzzy number into:
Figure DEST_PATH_IMAGE086
（6）
thereby obtaining a phase difference vector without ambiguity
Figure 502936DEST_PATH_IMAGE062
；
The ninth step: solving a least squares solution of the direction cosine through the calculated unambiguous phase difference vector, wherein the solution is as follows:
Figure DEST_PATH_IMAGE088
（7）
wherein，
Figure DEST_PATH_IMAGE092
Is oneEach row of the matrix corresponds to a selection combination of array elements corresponding to a longest base line, and a certain row is assumed to correspond to an array element
Figure DEST_PATH_IMAGE096
And array element
Figure DEST_PATH_IMAGE098
In combination, then the 1 st element of the row is
Figure DEST_PATH_IMAGE100
2 nd elementIs composed of
Figure DEST_PATH_IMAGE102
， In combination ofIn the method for preparing the seed coating,
Figure 723756DEST_PATH_IMAGE016
the number of array elements;
the tenth step: and calculating the estimation of the azimuth angle and the pitch angle by using the estimation of the direction cosine obtained in the ninth step:
（8）
the working principle of the invention is as follows:
consider an M-element uniform circular array as shown in FIG. 2, with array elements of radius
Figure DEST_PATH_IMAGE108
The center of the circle is used as a reference point. Let the incident signal direction be
Figure DEST_PATH_IMAGE110
At a frequency of
Figure DEST_PATH_IMAGE112
At a wavelength of
Figure DEST_PATH_IMAGE114
Wherein
Figure DEST_PATH_IMAGE116
at the speed of light, the first
Figure DEST_PATH_IMAGE118
The phase of each array element relative to the reference point is:
Figure DEST_PATH_IMAGE120
（9）
thus it is first
Figure DEST_PATH_IMAGE122
Array element and the firstThe phase difference between the individual array elements can be expressed as:
Figure DEST_PATH_IMAGE126
（10）
order to
Figure DEST_PATH_IMAGE128
，
Figure DEST_PATH_IMAGE130
Is as follows
Figure 115135DEST_PATH_IMAGE124
Array element and the first
Figure 35162DEST_PATH_IMAGE122
The length of the base line between the array elements is shown in FIG. 3, wherein the center of the circle is the origin of coordinates and the north direction is
Figure DEST_PATH_IMAGE132
Axis parallel to
Figure DEST_PATH_IMAGE134
The base line direction is
Figure DEST_PATH_IMAGE136
A shaft. Thus, formula(10) Can be written as:
Figure DEST_PATH_IMAGE138
（11）
wherein,
Figure DEST_PATH_IMAGE140
. So that the theoretical phase difference of two groups of baselines can be obtainedWherein
Figure DEST_PATH_IMAGE144
Two sets of parallel baseline numbers. When the ratio of the longest base length to the signal wavelength (base wavelength ratio) is large, phase ambiguity occurs, so:
the phase difference of the first set of parallel baselines can be expressed as:
Figure DEST_PATH_IMAGE146
（12）
the phase difference of the second set of parallel baselines can be expressed as:
（13）
wherein
Figure DEST_PATH_IMAGE150
For the purpose of the phase difference measurement,
Figure DEST_PATH_IMAGE152
in order to be a fuzzy number,
Figure DEST_PATH_IMAGE154
the included angle of the two groups of parallel baselines.
For the first set of baselines, ideally:
Figure DEST_PATH_IMAGE156
（14）
finishing to obtain:
Figure DEST_PATH_IMAGE158
（15）
it can be seen that
Figure 600047DEST_PATH_IMAGE044
In a linear relationship wherein
Figure DEST_PATH_IMAGE160
Are all known to be used in the prior art,
Figure 608455DEST_PATH_IMAGE032
，is the wavelength of the incident signal. Obtainable from formula (15)
Figure 377007DEST_PATH_IMAGE022
Corresponding toThe noise is generated, due to the influence of noise,possibly not an integer, the following is done:
Figure DEST_PATH_IMAGE162
（16）
in the same way, can obtain
Figure 817326DEST_PATH_IMAGE026
Corresponding to
Figure 449295DEST_PATH_IMAGE024
。
Is obtained by the formula (16)
Figure 38540DEST_PATH_IMAGE042
To pair
Figure 21539DEST_PATH_IMAGE044
The same principle can be obtained
Figure 354431DEST_PATH_IMAGE046
To pair
Figure 840908DEST_PATH_IMAGE048
Thus can obtain
Figure 928949DEST_PATH_IMAGE050
Group of
Figure 124877DEST_PATH_IMAGE076
Or
Figure DEST_PATH_IMAGE164
Combinations of (a) and (b). The second expression of the formula (12) and the second expression of the formula (13) can be used to estimateSet the direction cosine of the incident signal
Figure 540126DEST_PATH_IMAGE054
Direction cosine substitution formula (11) to
Figure 799069DEST_PATH_IMAGE054
Group of
Figure 491081DEST_PATH_IMAGE016
Root longest baseline phase difference
Figure DEST_PATH_IMAGE166
Wherein
Figure 103459DEST_PATH_IMAGE082
And is and
Figure 564527DEST_PATH_IMAGE084
are integers. Wherein there is and only one set of phase difference vectors androot longest baseline phase differencePhase difference
Figure DEST_PATH_IMAGE168
Integer multiple relation, to find the set of phase difference vectors, we will
Figure 321240DEST_PATH_IMAGE166
Andperforming a correlation operation as shown in the formula (4), and selecting the phase difference vector corresponding to the maximum value of the formula (4) as the estimation of the theoretical phase difference vector
Figure 237561DEST_PATH_IMAGE058
. Will be provided with
Figure 904166DEST_PATH_IMAGE058
Substitution formula (5) solutionObtaining fuzzy number vector according to the fuzzy of phase difference of the longest base line
Figure 356324DEST_PATH_IMAGE060
Substituting the fuzzy number into:
Figure 800074DEST_PATH_IMAGE086
（17）
thereby obtaining
Figure 956905DEST_PATH_IMAGE016
Root longest base line unambiguous phase difference vector
Figure 777093DEST_PATH_IMAGE062
. Obtaining a least squares estimate of the directional cosine using equation (7)Using equation (8) to calculate the estimation of azimuth and pitch angles
Figure DEST_PATH_IMAGE172
And thus, estimation of the incident signal azimuth angle and the pitch angle is completed.
The following exemplifies the specific effects of the present invention: the two-dimensional direction finding method of the circular array phase interferometer based on the parallel base lines comprises the steps of firstly selecting two groups of parallel base lines in a uniform circular array to carry out rough measurement, solving the phase ambiguity of all the longest base lines after finding out the ambiguity number, then carrying out direction cosine estimation by using the phase difference vector of the longest base lines after ambiguity resolution through a least square method, and further solving the estimation of an azimuth angle and a pitch angle.
Considering a 9-element uniform circular array, two groups of parallel baselines of 81, 72, 67 and 40 are selected, and the included angle between the two groups of parallel baselines is
Figure DEST_PATH_IMAGE174
. The radius of the array is 50 meters, the signal source is a single-frequency signal, and the signal is incidentIn the direction of
Figure DEST_PATH_IMAGE176
Simulation experiments were performed with the longest baseline length to wavelength ratio (baseline wavelength ratio) varying from 0.5 to 13, with signal-to-noise ratios of 10dB, 20dB, 30dB, respectively, with 1000 monte carlo experiments performed at each baseline wavelength ratio. Fig. 4 and 5 show plots of the direction cosine estimates and cramer-perot lower limit as a function of baseline wavelength ratio for different signal-to-noise ratios. Fig. 6 and 7 are plots of the direction-finding standard deviation versus the baseline wavelength ratio for different signal-to-noise ratios. As can be seen from fig. 4 and 5, under different selected signal-to-noise ratios and baseline wavelength ratios, the estimation of the direction cosine of the method provided by the present invention approaches the cramer-circle lower limit, thereby ensuring the accuracy of the estimation of the azimuth angle and the pitch angle of the incident signal, as shown in fig. 6 and 7, when the baseline wavelength ratio is greater than 1, the direction-finding errors of the azimuth angle and the pitch angle can be ensured within 1 °.
The algorithm provided by the invention is not only suitable for the uniform circular array of the practical application of the interferometer direction-finding system, but also suitable for other planar arrays. Only two groups of parallel baselines need to be found out in other planar arrays, and no special requirements are required for antenna arrangement.
The invention extends to any novel feature or any combination of features disclosed in this specification and to any method or process step or any combination of steps disclosed.

Claims (6)

1. A two-dimensional direction finding method of a circular array phase interferometer based on a parallel baseline specifically comprises the following steps:
the first step is as follows: selecting two groups of parallel baselines in a planar array
Figure DEST_PATH_IMAGE002
And
Figure DEST_PATH_IMAGE004
the base length is respectively
Figure DEST_PATH_IMAGE006
And is and
Figure DEST_PATH_IMAGE008
the included angle between two groups of parallel baselines is
Figure DEST_PATH_IMAGE010
；
The second step is that: calculating phase differences of a first set of parallel baselines
Figure DEST_PATH_IMAGE012
Phase difference with a second set of parallel base lines
Figure DEST_PATH_IMAGE014
And calculate
Figure DEST_PATH_IMAGE016
Phase difference of root longest base lineVector of wherein
Figure 846234DEST_PATH_IMAGE016
The number of array elements;
the third step: using the phase difference obtained in the second step
Figure 701057DEST_PATH_IMAGE012
And
Figure 418477DEST_PATH_IMAGE014
calculating the possible fuzzy numbers of two groups of parallel baselines
Figure DEST_PATH_IMAGE020
、
Figure DEST_PATH_IMAGE022
、、
Figure DEST_PATH_IMAGE026
：
Figure DEST_PATH_IMAGE028
；
Figure DEST_PATH_IMAGE030
；
Wherein
Figure DEST_PATH_IMAGE032
、
Figure DEST_PATH_IMAGE034
，
Figure DEST_PATH_IMAGE036
In order to be the wavelength of the incident signal,
Figure DEST_PATH_IMAGE038
it is meant to round-off the process,
Figure DEST_PATH_IMAGE040
represents rounding down;
the fourth step: fuzzy number obtained from the third step
Figure 187588DEST_PATH_IMAGE020
、
Figure 939643DEST_PATH_IMAGE022
、
Figure 702719DEST_PATH_IMAGE024
、
Figure 969752DEST_PATH_IMAGE026
Calculating the direction cosines of N possible incident signals respectively, wherein
Figure DEST_PATH_IMAGE042
；
The fifth step: obtained according to the fourth step
Figure DEST_PATH_IMAGE044
The direction cosine of the incident signal is calculated
Figure 981701DEST_PATH_IMAGE044
Group of
Figure 588263DEST_PATH_IMAGE016
Root longest baseline phase difference vector；
And a sixth step: obtained in the fifth step
Figure 456993DEST_PATH_IMAGE044
Group ofRoot longest baseline phase difference vector
Figure 886018DEST_PATH_IMAGE046
And measured
Figure 344156DEST_PATH_IMAGE016
Phase difference vector of root longest base lineMaking correlation operation and selecting the phase difference vector corresponding to the maximum correlation coefficient and recording the phase difference vector as
Figure DEST_PATH_IMAGE048
；
The seventh step: according to the phase difference vector obtained in the sixth stepTo obtain
Figure 41482DEST_PATH_IMAGE016
Fuzzy number vector of root longest base line
Figure DEST_PATH_IMAGE050
；
Eighth step: obtaining the phase difference vector without ambiguity by using the ambiguity number vector obtained in the seventh step
Figure DEST_PATH_IMAGE052
。
2. The two-dimensional direction finding method for the parallel-baseline-based circular array phase interferometer according to claim 1, wherein the method further comprises:
the ninth step: and solving a least square solution of the direction cosine through the calculated unambiguous phase difference vector, and calculating the estimation of the direction cosine of the incident signal.
3. The two-dimensional direction finding method for the parallel-baseline-based circular array phase interferometer according to claim 2, wherein the method further comprises:
the tenth step: and calculating the estimation of the azimuth angle and the pitch angle by using the estimation of the direction cosine obtained in the ninth step.
4. The parallel-baseline based two-dimensional direction finding method for circular array phase interferometers according to claim 1, wherein the planar array is a uniform circular array.
5. The two-dimensional direction finding method of the parallel-baseline-based circular array phase interferometer according to claim 1, wherein in the sixth step, the function of the correlation operation is:
Figure DEST_PATH_IMAGE054
。
6. the two-dimensional direction finding method for the parallel-baseline-based circular array phase interferometer of claim 1, wherein the seventh step is performed to obtain
Figure 498002DEST_PATH_IMAGE016
Fuzzy number vector of root longest base lineThe function is:
Figure DEST_PATH_IMAGE056
。
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