Interferometer nearest projection point ambiguity resolution method based on least square improvement

Abstract

The invention discloses a least square improvement-based nearest projection point ambiguity resolution method. The method comprises the following steps of: constructing a relation model between ambiguity phase differences corresponding to various baselines of a double-long-baseline phase interferometer; grid division is carried out on the field angle of the double-long-baseline phase interferometer, and a phase difference fuzzy graph is constructed; expanding the relation model of the double-long-baseline phase interferometer to a multi-long-baseline interferometer, constructing a baseline vector, a theoretical fuzzy phase difference vector and a fuzzy number vector, and determining a hyperplane perpendicular to a phase line in the phase difference fuzzy graph; starting point fuzzy phase difference vectors of all phase lines and phase difference projection points of the phase lines on a hyperplane are determined based on the phase difference mode fuzzy graph; and performing least square fitting on an actually measured fuzzy phase difference vector corresponding to the actually measured multi-snapshot target signal, searching a fitted fuzzy phase difference vector with the minimum variance, determining the nearest phase difference projection point, and obtaining a corresponding fuzzy number vector to realize ambiguity resolution.

Description

Technical Field

[0001] The invention relates to the technical field of phase interferometer direction finding, and in particular to a nearest projection point deambiguation method based on least squares improvement. Background Art

[0002] Phase interferometer has the advantages of simple structure, high direction finding accuracy and low computational complexity, and has played a great role in the fields of passive detection and reconnaissance, electronic countermeasure support, etc. However, with the increasing complexity of the electromagnetic environment, electronic warfare has expanded from low frequency to ultra-high frequency and higher frequency electromagnetic bands. When the phase error of the phase interferometer direction finding is determined, the requirements for the baseline of direction finding accuracy and phase resolution are contradictory. The longer the direction finding baseline, the higher the direction finding accuracy. When the baseline is shorter, the ambiguity zone is smaller, and the phase resolution is easier. In addition, the size of the direction finding antenna unit is limited by its minimum operating frequency and cannot be made small enough. Therefore, when the system works at a higher frequency point, phase ambiguity will occur. The longer the baseline, the larger the possible ambiguity number. This contradiction is more acute in a wide bandwidth.

[0003] Common interferometer deambiguation algorithms include the long and short baseline method, the remainder theorem method, and the probability-based traversal solution method. Pace et al. proposed a method based on the optimal symmetric number system (OSNS) and the robust symmetric number system (RSNS), which requires that the antenna spacings are mutually prime. Lee et al. improved Jacob's phase space method by adopting the axis transformation technology, and proposed an array spacing that can improve the maximum phase error tolerance of the interferometer direction finding system. However, this method is only applicable to interferometer models with less than four elements. When the number of interferometer elements exceeds four, it is difficult to visualize and phase deambiguation cannot be achieved. Chen et al. proposed a phase difference projection (PDP) method for direction finding, using a hyperplane to achieve phase deambiguation of an arbitrary linear array of elements. However, under low signal-to-noise ratio (SNR) conditions, the success rate of deambiguation is low and the direction finding performance is poor. Therefore, how to improve the universality and robustness of the phase interferometer deambiguation algorithm and correctly deambiguate under low signal-to-noise ratio conditions is a technical problem that needs to be solved in this field. Summary of the invention

[0004] The purpose of the present invention is to provide an interferometer nearest projection point deambiguation method based on least squares improvement, which is used to solve the problem of low deambiguation probability of traditional phase interferometer deambiguation method under low signal-to-noise ratio conditions.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for defuzzifying the nearest projection point based on least squares improvement, comprising:

[0007] Construct a relationship model between the fuzzy phase differences corresponding to each baseline of the dual long baseline phase interferometer; divide the field of view of the dual long baseline phase interferometer into grids, calculate the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids, and construct a phase difference fuzzy map based on this;

[0008] The relationship model of the dual long baseline phase interferometer and the similarity of the phase difference ambiguity map are extended to the multi-long baseline interferometer, and the baseline vector, theoretical fuzzy phase difference vector and fuzzy number vector of the multi-long baseline interferometer are constructed, and the hyperplane perpendicular to the phase line in the phase difference ambiguity map is determined based on the baseline vector, theoretical fuzzy phase difference vector and fuzzy number vector of the multi-long baseline interferometer.

[0009] Based on the phase difference mode ambiguity map, the starting point ambiguity phase difference vector of all phase lines is determined;

[0010] Based on the starting point fuzzy phase difference vector, determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane;

[0011] Performing least square fitting on the measured blurred phase difference vector corresponding to the measured multi-snap target signal to find the fitted blurred phase difference vector with the minimum variance;

[0012] Find the phase difference projection point closest to the fitted fuzzy phase difference vector, obtain the corresponding fuzzy number vector, and achieve defuzzification.

[0013] Furthermore, the relationship model between the fuzzy phase differences corresponding to each baseline of the dual long baseline phase interferometer is constructed; the field of view angle of the dual long baseline phase interferometer is gridded, the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids are calculated, and a phase difference fuzzy map is constructed based on the fuzzy phase differences, including:

[0014] Assume that the two baselines of the double long baseline phase interferometer are d 1 and d 2 ,φ 1 ,φ 2 Baseline d 1 , d 2 The corresponding real unambiguous phase difference, θ is the target direction angle, λ is the wavelength corresponding to the target frequency, and the direction finding principle of the phase interferometer is:

[0015]

[0016] In practice, if the baseline length is greater than half a wavelength, phase ambiguity will occur, that is:

[0017]

[0018] in, Baseline d i The corresponding theoretical fuzzy phase difference, and Right now mod represents the modulo operation, then k i is the quotient, indicating the baseline d i The corresponding fuzzy number;

[0019] Let the baseline ratio of the two baselines be d 2 / d 1 =m 2 / m 1 , where m 1 and m 2 are relatively prime integers, then:

[0020]

[0021] Set the maximum field of view angle of the dual long baseline phase interferometer to θ max , then the angular range of the signal that the interferometer can receive is [-θ max ,θ max ],θ max <90°, for this range, follow θ step Perform sector meshing to obtain 2θ max / θ step grids, and the divided grid is denoted as θ grid ;

[0022] according to Calculate the field of view baseline d under noise-free conditions 1 and d 2 For all grids θ grid Theoretical fuzzy phase difference and fuzzy number pairs (k grid1 ,k grid2 ):

[0023]

[0024] And there are:

[0025]

[0026] Baseline d 1 The corresponding fuzzy phase difference Abscissa, baseline d 2 The corresponding fuzzy phase difference Construct a coordinate system for the ordinate and convert the calculated theoretical fuzzy phase difference Plotted in the coordinate system, the phase difference blur map is constructed, and these theoretical blur phase differences It forms multiple phase lines with the same slope.

[0027] Furthermore, the construction of the baseline vector, theoretical fuzzy phase difference vector and fuzzy number vector of the multi-long baseline interferometer includes:

[0028] For an N-element multi-baseline interferometer, taking the first element as the reference unit, M = N-1 baselines can be formed. m And the corresponding theoretical fuzzy phase difference and fuzzy number k m ; Construct baseline vector d = (d 1 ,…,d M ), theoretical fuzzy phase difference vector It can be regarded as a point in M-dimensional space, and the fuzzy number vector k=(k 1 ,…,k M ), where m = 1, 2,…, M.

[0029] Furthermore, the determining of the hyperplane perpendicular to the phase line in the phase difference ambiguity map is expressed as:

[0030]

[0031] in, is the theoretical fuzzy phase difference vector of the N-element multi-baseline interferometer, d is the baseline vector, and d 1 ,…,d M represents the M baselines in the baseline vector, Represents the M theoretical ambiguity phase differences in the theoretical ambiguity phase difference vector, m=1,2,…,M.

[0032] Further, the calculation determines the starting point fuzzy phase difference vectors of all phase lines based on the phase difference mode fuzzy map, including:

[0033] The first theoretical fuzzy phase difference vector of the lth phase line is: Denote as the starting point fuzzy phase difference vector, where Indicates the baseline d m The corresponding fuzzy phase difference; the calculation formula of the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line is as follows:

[0034]

[0035] where f 10 represents the unambiguous phase difference vector at the starting point of the first phase line, represents the fuzzy phase difference vector at the starting point of the first phase line, k 1 A fuzzy number vector representing the first phase line;

[0036] Find the index of the fuzzy phase difference vector at the starting point of the second phase line:

[0037]

[0038] in Indicates the i-th phase difference value of the fuzzy phase difference vector at the starting point of the first phase line, d i represents the i-th baseline, then the fuzzy phase difference vector and fuzzy number vector of the starting point of the second phase line are:

[0039]

[0040] k 2 (i) = k 2 (i)+1

[0041] in represents the fuzzy phase difference vector at the starting point of the second phase line, represents the i-th phase difference value of the fuzzy phase difference vector at the starting point of the second phase line, k 2 (i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line;

[0042] In this way, the fuzzy phase difference vectors and fuzzy number vectors of the starting points of all phase lines are calculated.

[0043] Further, based on the starting point blurred phase difference vector, determining the phase difference projection point of each phase line in the phase difference blurred image on the hyperplane includes:

[0044] The hyperplane has a phase intersection point with each phase line, so the intersection point of the phase line and the hyperplane is recorded as the phase difference projection point, which can be expressed as:

[0045]

[0046] where p l represents the phase difference projection point between the lth phase line and the hyperplane, represents the first theoretical fuzzy phase difference vector of the lth phase line, represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane, ||·|| 2 Represents the L2 norm operation.

[0047] Further, performing least square fitting on the measured fuzzy phase difference vector corresponding to the measured multi-snap target signal to find the fitted fuzzy phase difference vector with the smallest variance includes:

[0048] For the K snapshot target signals x(t) received by the multi-baseline interferometer, t is the snapshot parameter, t = 1, ..., K; the K snapshot fuzzy phase difference vector can be obtained by the phase detector K snapshot blur phase difference vector Denote the measured fuzzy phase difference vector as , and perform the least squares fitting on it to find the fitted fuzzy phase difference vector with the smallest variance The objective function S is as follows:

[0049]

[0050] in represents the nth measured fuzzy phase difference in the measured fuzzy phase difference vector, where n=1, 2, …, N; ||·|| represents the Euclidean norm.

[0051] Furthermore, the step of finding the phase difference projection point closest to the fitted fuzzy phase difference vector, obtaining the corresponding fuzzy number vector, and realizing defuzzification includes:

[0052] Phase difference projection point Determined by the following formula:

[0053]

[0054] Each phase line has a phase difference projection point and a set of fuzzy numbers. Therefore, after finding the phase difference projection point closest to the fitted fuzzy phase difference vector, the fuzzy number vector corresponding to the phase difference projection point can be obtained.

[0055] According to the obtained fuzzy number vector, calculate the unambiguous phase difference vector This achieves defuzzification:

[0056]

[0057] Compared with the prior art, the present invention has the following technical features:

[0058] 1. The probability of correct deambiguation of the phase interferometer under low signal-to-noise ratio conditions is improved by fitting the blurred phase difference vector measured by multiple snapshots.

[0059] 2. By introducing the concept of hyperplane, the search for the nearest phase line is transformed into the search for the nearest projection point, so that the correct deambiguation of four or more coprime baselines and non-coprime baseline phase interferometers can be achieved, thereby improving the generalization ability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a flow chart of a method in one embodiment of the present invention;

[0061] Figure 2 is a schematic diagram of a double-baseline dry phase interferometer;

[0062] Figure 3 It is the dual mutually prime baseline phase difference fuzzy graph model of the present invention;

[0063] Figure 4(a) is a diagram showing the root mean square error effect of different signal-to-noise ratios in a scenario where the interferometer baseline lengths are mutually prime in an embodiment of the present invention; (b) is a diagram showing the correct deambiguation probability of different signal-to-noise ratios in a scenario where the interferometer baseline lengths are mutually prime in an embodiment of the present invention;

[0064] Figure 5 (a) is a diagram showing the root mean square error effect of different signal-to-noise ratios in a scenario where the interferometer baseline lengths are non-coprime in an implementation example of the present invention; (b) is a diagram showing the correct deambiguation probability of different signal-to-noise ratios in a scenario where the interferometer baseline lengths are non-coprime in an implementation example of the present invention. DETAILED DESCRIPTION

[0065] Referring to the accompanying drawings, the present invention provides a method for deblurring the nearest projection point based on least squares improvement. The basic idea of ​​the method is to first grid the field of view, calculate the theoretical fuzzy phase difference vectors of all grid points in the space, and establish a multi-baseline phase difference fuzzy graph model. Then, the least squares method is used to fit the measured multi-snap phase difference points to obtain the phase difference fitting points with smaller variance, and finally, the phase difference projection point closest to the fitted fuzzy phase difference vector is found to obtain the corresponding fuzzy number, thereby realizing phase deblurring. The specific implementation process of the present invention is further described in detail below.

[0066] Step 1, construct a relationship model between the fuzzy phase differences corresponding to each baseline of the dual long baseline phase interferometer; grid the field of view angle of the dual long baseline phase interferometer, calculate the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids, and construct a phase difference fuzzy map based on this.

[0067] 1.1 Assume that the two baselines of the double long baseline phase interferometer are d 1 and d 2 ,φ 1 ,φ 2 Baseline d 1 , d 2 The corresponding real unambiguous phase difference, θ is the target direction angle, λ is the wavelength corresponding to the target frequency, and the direction finding principle of the phase interferometer is:

[0068]

[0069] In practice, if the baseline length is greater than half a wavelength, phase ambiguity will occur, that is:

[0070]

[0071] in, Baseline d i The corresponding theoretical fuzzy phase difference, and Right now mod represents the modulo operation, then k i is the quotient, indicating the baseline di The corresponding fuzzy number.

[0072] Let the baseline ratio of the two baselines be d 2 / d 1 =m 2 / m 1 , where m 1 and m 2 are relatively prime integers, then:

[0073]

[0074] 1.2 Set the maximum field of view angle of the dual long baseline phase interferometer to θ max , that is, the angular range of the signal that the interferometer can receive is [-θ max ,θ max ],θ max <90°, for this range, follow a certain step θ step Perform sector meshing to obtain 2θ max / θ step grids, and the divided grid is denoted as θ grid .

[0075] Follow the steps in step 1.1 Calculate the field of view baseline d under noise-free conditions 1 and d 2 For all grids θ grid Theoretical fuzzy phase difference and fuzzy number pairs (kgrid 1 ,kgrid 2 ):

[0076]

[0077] And there are:

[0078]

[0079] Baseline d 1 The corresponding fuzzy phase difference Abscissa, baseline d 2 The corresponding fuzzy phase difference Construct a coordinate system for the ordinate, and convert the theoretical fuzzy phase difference calculated by the above formula into Plotted in the coordinate system, the phase difference blur map is constructed, and these theoretical blur phase differences It forms multiple phase lines with the same slope.

[0080] Step 2, extend the relationship model of the dual long baseline phase interferometer and the similarity of the phase difference ambiguity map to the multi-long baseline interferometer, and construct the baseline vector, theoretical fuzzy phase difference vector and fuzzy number vector of the multi-long baseline interferometer, and determine the hyperplane perpendicular to the phase line in the phase difference ambiguity map.

[0081] 2.1 Extending the double long baseline interferometer to the N-element multi-long baseline interferometer; taking the first element as the reference unit, M = N-1 baselines can be formed. m And the corresponding theoretical fuzzy phase difference and fuzzy number k m ; Construct baseline vector d = (d 1 ,…,d M ), theoretical fuzzy phase difference vector It can be regarded as a point in M-dimensional space, and the fuzzy number vector k=(k 1 ,…,k M ), where m = 1, 2,…, M.

[0082] 2.2 Determine the hyperplane perpendicular to the phase line, expressed as follows:

[0083]

[0084] The parameter superscript T represents the transposition operation, the same below.

[0085] Step 3: Determine the starting point blurred phase difference vector of all phase lines based on the phase difference mode fuzzy map.

[0086] For the phase difference blur map, when θ grid =0°, k grid1 =k grid2 =0; when θ grid Gradually increase to θ max In the process, the fuzzy number pair (k grid1 ,k grid2 ) remains unchanged until θ grid When it increases to a certain value, one of the fuzzy numbers increases by 1; similarly, when θ grid Gradually decrease to -θ max In the process, until it decreases to a certain value, one of the fuzzy numbers decreases by 1; so a set of fuzzy number pairs (k grid1 ,k grid2 ) corresponds to a phase line with a constant slope.

[0087] Calculate the fuzzy number corresponding to each phase line; since the phase line is composed of a series of theoretical fuzzy phase differences, that is, the theoretical fuzzy phase difference vector after being extended to the N-element multi-baseline interferometer. Assume that the first theoretical fuzzy phase difference vector of the lth phase line is Denote as the starting point fuzzy phase difference vector, where Indicates the baseline d m The corresponding fuzzy phase difference; the calculation formula of the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line is as follows:

[0088]

[0089] where f 10 represents the unambiguous phase difference vector at the starting point of the first phase line, represents the fuzzy phase difference vector at the starting point of the first phase line, k 1 Vector of fuzzy numbers representing the first phase line.

[0090] Find the index of the fuzzy phase difference vector at the starting point of the second phase line:

[0091]

[0092] in Indicates the i-th phase difference value of the fuzzy phase difference vector at the starting point of the first phase line, d i represents the i-th baseline, then the fuzzy phase difference vector and fuzzy number vector of the starting point of the second phase line are:

[0093]

[0094]

[0095] k 2 (i) = k 2 (i)+1

[0096] in represents the fuzzy phase difference vector at the starting point of the second phase line, represents the i-th phase difference value of the fuzzy phase difference vector at the starting point of the second phase line, k 2 (i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line.

[0097] By analogy, the fuzzy phase difference vector and fuzzy number vector of the starting point of all phase lines are calculated until It represents the fuzzy phase difference vector of the starting point of the last phase line, so there are L phase lines in total.

[0098] Step 4: Based on the starting point blurred phase difference vector, determine the phase difference projection point of each phase line in the phase difference blurred image on the hyperplane.

[0099] Since the hyperplane has a phase intersection point with each phase line, the intersection point of the phase line and the hyperplane is recorded as the phase difference projection point, which can be expressed as:

[0100]

[0101] where p l represents the phase difference projection point between the lth phase line and the hyperplane, represents the first theoretical fuzzy phase difference vector of the lth phase line, represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane, ||·|| 2 Represents the L2 norm operation.

[0102] Step 5: Perform a least squares fit on the measured blurred phase difference vector corresponding to the measured multi-snap target signal to find the fitted blurred phase difference vector with the smallest variance.

[0103] For the K snapshot target signals x(t) received by the multi-baseline interferometer, t is the snapshot parameter, t = 1, ..., K; the K snapshot fuzzy phase difference vector can be obtained by the phase detector Due to the influence of system noise, K snapshot blur phase difference vector It does not fall on the phase line in the phase difference blur map, and is recorded as the measured blur phase difference vector. Therefore, the distance The nearest phase line is used for deambiguation.

[0104] First, the measured fuzzy phase difference vector corresponding to the K snapshot target signals is Perform least squares fitting to find the fitted fuzzy phase difference vector with the smallest variance The objective function S is as follows:

[0105]

[0106] in represents the nth measured fuzzy phase difference in the measured fuzzy phase difference vector, n=1,2,…,N; ||·|| represents the Euclidean norm, The fitted fuzzy phase difference vector is the one that minimizes the above objective function value.

[0107] Step 6: Find and fit the fuzzy phase difference vector The nearest phase difference projection point Obtain the corresponding fuzzy number vector to achieve defuzzification.

[0108] Among them, the phase difference projection point Determined by the following formula:

[0109]

[0110] According to the above, each phase line has a phase difference projection point and a set of fuzzy numbers. Therefore, after finding the phase difference projection point closest to the fitted fuzzy phase difference vector, the fuzzy number vector corresponding to the phase difference projection point can be obtained.

[0111] According to the obtained fuzzy number vector, calculate the unambiguous phase difference vector This achieves defuzzification:

[0112]

[0113] Example:

[0114] The present invention establishes a phase difference fuzzy graph model of dual coprime baselines, such as Figure 3 As shown. Assume that the radiation source signal frequency is f = 8GHz, the corresponding wavelength is λ = 37.5mm, and Figure 2 The double long baseline phase interferometer shown has a baseline of d 1 =62mm, d 2 =107mm,d 2 / d 1 =m 2 / m 1 =107 / 62. Then the direction finding principle of phase interferometer is:

[0115]

[0116] where k 1 and k 2 Baseline d 1 and d 2 fuzzy number.

[0117] Establish the phase difference blur graph model. max ,θ max ],θ max = 90°, and divide the grid into 1801 grid points in 0.1° increments. Calculate all grid points θ in the field of view under noise-free conditions. grid Theoretical fuzzy phase difference point and fuzzy number pairs (k gird1 ,k grid2 ), a set of fuzzy number pairs (k gird1 ,k grid2 ) corresponds to a phase line with a fixed slope, and the phase difference fuzzy graph model is obtained. Figure 3 The blue line in the middle is the phase line formed by the theoretical phase points, and its slope is μ=d 2 / d 1=107 / 62, which is related to the baseline ratio. The red points are the measured phase points with phase errors, and the green straight line is perpendicular to all phase lines with a slope of -1 / μ=-62 / 107.

[0118] In the implementation example, the present invention considers two usage scenarios, namely, a five-element mutual prime baseline phase interferometer and a five-element non-mutual prime baseline phase interferometer. The first is a five-element mutual prime baseline phase interferometer scenario, and the specific steps are as follows:

[0119] Step 1: Extend the phase difference ambiguity graph model to the case of a five-element mutual prime baseline interferometer. Take the first element as the reference unit and construct the baseline vector d = (d 1 ,d 2 ,d 3 ,d 4 )=(62,103,371,521)mm, the baseline lengths are mutually prime. For grid point θ grid , the theoretical fuzzy phase difference vector is It can be regarded as a point in four-dimensional space. Fuzzy number vector k grid =(k grid1 ,…,k grid4 ).

[0120] Step 2: Calculate the hyperplane perpendicular to the phase line according to the following formula:

[0121]

[0122] Step 3, find the starting point fuzzy phase difference vector of the phase line and the corresponding fuzzy number vector. The calculation formula of the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line is as follows:

[0123] f 10 =2πdsin(-π) / λ

[0124]

[0125] where f 10 The unambiguous phase difference vector representing the starting point of the first phase line. k represents the fuzzy phase difference vector at the starting point of the first phase line. 1 Vector of fuzzy numbers representing the first phase line.

[0126] Find the index of the fuzzy phase difference vector at the starting point of the second phase line:

[0127]

[0128] in represents the i-th phase difference value of the starting point fuzzy phase difference vector of the first phase line, then the starting point fuzzy phase difference vector and fuzzy number vector of the second phase line are:

[0129]

[0130] k 2 (i) = k 2 (i)+1

[0131] in represents the fuzzy phase difference vector at the starting point of the second phase line, represents the i-th phase difference value of the fuzzy phase difference vector at the starting point of the second phase line, k 2 (i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line.

[0132] By using the above formula, we can calculate k 2 =(-4,-6,-20,-30). By analogy, calculate the starting point fuzzy phase difference vector and fuzzy number vector of all phase lines until Indicates the blurred phase difference vector of the starting point of the last phase line.

[0133] Step 4, calculate the phase difference projection point:

[0134]

[0135] where p l Represents the phase difference projection point between the lth phase line and the hyperplane. Represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane.

[0136] Step 5: Assume that the real direction angle is θ = 30°, the interferometer receives K = 64 snapshot signals, and obtains 64 snapshot measured fuzzy phase difference vectors Due to the influence of system noise, the measured ambiguous phase difference vector does not fall on the phase line, so the phase line closest to the measured ambiguous phase difference vector is found for deambiguation.

[0137] First, the blur phase difference vector of these 64 snapshots is measured. Perform least squares fitting to find the phase difference point with the smallest variance. The objective function S is as follows:

[0138]

[0139] where ||·|| represents the Euclidean norm, The fitted fuzzy phase difference vector is the one that minimizes the above objective function value.

[0140] Step 6: Find the distance fitting fuzzy phase difference vector The nearest phase difference projection point

[0141]

[0142] Get the fuzzy number vector corresponding to the phase line

[0143] Step 7, calculate the unambiguous phase difference vector according to the fuzzy number vector obtained in step 6:

[0144]

[0145] Step 8: Repeat steps 5 to 7 for 1000 times of Monte Carlo experiments to calculate the root mean square error of the angle measurement results and the probability of correct resolution.

[0146] Secondly, the present invention is used in a five-element non-coprime baseline phase interferometer scenario, and the specific steps are as follows:

[0147] Step 1: Extend the phase difference ambiguity graph model to the case of a five-element non-mutually prime baseline interferometer. Take the first element as the reference unit and construct the baseline vector d = (d 1 ,d 2 ,d 3 ,d 4 )=(60,180,420,520)mm, the baseline lengths are mutually prime. For grid point θ grid , the blurred phase difference vector It can be regarded as a point in four-dimensional space. Fuzzy number vector k grid =(k grid1 ,…,k grid4 ).

[0148] Step 2: Calculate the hyperplane perpendicular to the phase line according to the following formula:

[0149]

[0150] Step 3, find the starting point fuzzy phase difference vector of the phase line and the corresponding fuzzy number vector. The calculation formula of the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line is as follows:

[0151] f 10 =2πdsin(-π) / λ

[0152]

[0153] where f 10 The unambiguous phase difference vector representing the starting point of the first phase line. k represents the fuzzy phase difference vector at the starting point of the first phase line. 1 Vector of fuzzy numbers representing the first phase line.

[0154] Find the index of the fuzzy phase difference vector at the starting point of the second phase line:

[0155]

[0156] in represents the i-th phase difference value of the starting point fuzzy phase difference vector of the first phase line, then the starting point fuzzy phase difference vector and fuzzy number vector of the second phase line are:

[0157]

[0158] k 2 (i) = k 2 (i)+1

[0159] in represents the fuzzy phase difference vector at the starting point of the second phase line, represents the i-th phase difference value of the fuzzy phase difference vector at the starting point of the second phase line, k 2 (i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line.

[0160] Calculate k 2 =(-2,-5,-12,-14). By analogy, calculate the starting point fuzzy phase difference vector and fuzzy number vector of all phase lines until

[0161] Step 4, calculate the phase difference projection point:

[0162]

[0163] where p l Represents the phase difference projection point between the lth phase line and the hyperplane. Represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane.

[0164] Step 5: The interferometer receives K=64 snapshot signals and obtains 64 snapshot measured blur phase difference vectors Due to the influence of system noise, the measured ambiguous phase difference vector does not fall on the phase line, so the phase line closest to the measured ambiguous phase difference vector is found for deambiguation.

[0165] First, the blur phase difference vector of these 64 snapshots is measured. Perform least squares fitting to find the phase difference point with the smallest variance. The objective function S is as follows:

[0166]

[0167] where ||·|| represents the Euclidean norm, The fitted fuzzy phase difference vector is the one that minimizes the above objective function value.

[0168] Step 6: Find the distance fitting fuzzy phase difference vector The nearest phase difference projection point

[0169]

[0170] The fuzzy number vector corresponding to the phase line is obtained as

[0171] Step 7, calculate the unambiguous phase difference vector according to the fuzzy number obtained in step 6:

[0172]

[0173] Step 8: Repeat steps 5 to 7 for 1000 times of Monte Carlo experiments to calculate the root mean square error of the angle measurement results and the probability of correct resolution.

[0174] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for defuzzifying the nearest projection point based on least squares improvement, characterized in that: include: Construct a relationship model between the fuzzy phase differences corresponding to each baseline of the dual long baseline phase interferometer; The field of view of the dual long baseline phase interferometer is gridded, the theoretical fuzzy phase difference and fuzzy number pairs corresponding to all grids are calculated, and the phase difference fuzzy map is constructed based on this; The relationship model of the dual long baseline phase interferometer and the similarity of the phase difference ambiguity map are extended to the multi-long baseline interferometer, and the baseline vector, theoretical fuzzy phase difference vector and fuzzy number vector of the multi-long baseline interferometer are constructed, based on which the hyperplane perpendicular to the phase line in the phase difference ambiguity map is determined; Based on the phase difference mode ambiguity map, the starting point ambiguity phase difference vector of all phase lines is determined; Based on the starting point fuzzy phase difference vector, determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane; Performing least square fitting on the measured blurred phase difference vector corresponding to the measured multi-snap target signal to find the fitted blurred phase difference vector with the smallest variance; Find the phase difference projection point closest to the fitted fuzzy phase difference vector, obtain the corresponding fuzzy number vector, and achieve defuzzification.

2. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The relationship model between the fuzzy phase differences corresponding to the baselines of the dual long baseline phase interferometer is constructed; The field of view of the dual long baseline phase interferometer is gridded, the theoretical fuzzy phase difference and fuzzy number pairs corresponding to all grids are calculated, and the phase difference fuzzy map is constructed based on this, including: Assume that the two baselines of the double long baseline phase interferometer are d1 and d2, φ1 and φ2 are the corresponding real unambiguous phase differences of baselines d1 and d2, θ is the target direction angle, and λ is the wavelength corresponding to the target frequency. Then the direction finding principle of the phase interferometer is: In practice, if the baseline length is greater than half a wavelength, phase ambiguity will occur, that is: in, Baseline d i The corresponding theoretical fuzzy phase difference, and Right now mod represents the modulo operation, then k i is the quotient, indicating the baseline d i The corresponding fuzzy number; Assume that the baseline ratio of the two baselines is d2 / d1=m2 / m1, where m1 and m2 are relatively prime integers, then: Set the maximum field of view angle of the dual long baseline phase interferometer to θ max , then the angular range of the signal that the interferometer can receive is [-θ max ,θ max ],θ max <90°, for this range, follow θ step Perform sector meshing to obtain 2θ max / θ step grids, and the divided grid is denoted as θ grid ; according to Calculate the field of view baselines d1 and d2 under noise-free conditions for all grids θ grid Theoretical fuzzy phase difference and fuzzy number pairs (k grid1 ,k grid2 ): And there are: The blurred phase difference corresponding to the baseline d1 Abscissa, blurred phase difference corresponding to baseline d2 Construct a coordinate system for the ordinate and convert the calculated theoretical fuzzy phase difference Plotted in the coordinate system, the phase difference blur map is constructed, and these theoretical blur phase differences It forms multiple phase lines with the same slope.

3. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The method of constructing a baseline vector, a theoretical fuzzy phase difference vector and a fuzzy number vector of a multi-long baseline interferometer includes: For an N-element multi-baseline interferometer, taking the first element as the reference unit, M = N-1 baselines can be formed. m And the corresponding theoretical fuzzy phase difference and fuzzy number k m ; Construct baseline vector d = (d1,…,d M ), theoretical fuzzy phase difference vector It can be regarded as a point in M-dimensional space, and the fuzzy number vector k=(k1,…,k M ), where m = 1, 2,…, M.

4. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The determining of the hyperplane perpendicular to the phase line in the phase difference ambiguity map is expressed as: in, is the theoretical fuzzy phase difference vector of the N-element multi-baseline interferometer, d is the baseline vector, d1,…,d M represents the M baselines in the baseline vector, Represents the M theoretical ambiguity phase differences in the theoretical ambiguity phase difference vector, m=1,2,…,M.

5. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The calculation is based on the phase difference mode ambiguity map to determine the starting point ambiguity phase difference vector of all phase lines, including: The first theoretical fuzzy phase difference vector of the lth phase line is: Denote as the starting point fuzzy phase difference vector, where Indicates the baseline d m The corresponding fuzzy phase difference; the calculation formula of the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line is as follows: where f 10 represents the unambiguous phase difference vector at the starting point of the first phase line, represents the fuzzy phase difference vector of the starting point of the first phase line, k1 represents the fuzzy number vector of the first phase line; Find the index of the fuzzy phase difference vector at the starting point of the second phase line: in Indicates the i-th phase difference value of the fuzzy phase difference vector at the starting point of the first phase line, d i represents the i-th baseline, then the fuzzy phase difference vector and fuzzy number vector of the starting point of the second phase line are: k2(i)=k2(i)+1 in represents the fuzzy phase difference vector at the starting point of the second phase line, represents the i-th phase difference value of the fuzzy phase difference vector of the starting point of the second phase line, k2(i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line; In this way, the fuzzy phase difference vectors and fuzzy number vectors of the starting points of all phase lines are calculated.

6. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: Based on the starting point fuzzy phase difference vector, determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane includes: The hyperplane has a phase intersection point with each phase line, so the intersection point of the phase line and the hyperplane is recorded as the phase difference projection point, which can be expressed as: where p l represents the phase difference projection point between the lth phase line and the hyperplane, represents the first theoretical fuzzy phase difference vector of the lth phase line, represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane, and ||·||2 represents the L2 norm operation.

7. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The least squares fitting is performed on the measured fuzzy phase difference vector corresponding to the measured multi-snap target signal to find the fitted fuzzy phase difference vector with the smallest variance, including: For the K snapshot target signals x(t) received by the multi-baseline interferometer, t is the snapshot parameter, t = 1, ..., K; the K snapshot fuzzy phase difference vector can be obtained by the phase detector K snapshot blur phase difference vector Denote the measured fuzzy phase difference vector as , and perform the least squares fitting on it to find the fitted fuzzy phase difference vector with the smallest variance The objective function S is as follows: in represents the nth measured fuzzy phase difference in the measured fuzzy phase difference vector, where n=1, 2, …, N; ||·|| represents the Euclidean norm.

8. The method for defuzzifying the nearest projection point based on least squares improvement according to claim 1, characterized in that: The step of finding the phase difference projection point closest to the fitted fuzzy phase difference vector, obtaining the corresponding fuzzy number vector, and realizing defuzzification includes: Phase difference projection point Pass Determine by the following formula: Each phase line has a phase difference projection point and a set of fuzzy numbers. Therefore, after finding the phase difference projection point closest to the fitted fuzzy phase difference vector, the fuzzy number vector corresponding to the phase difference projection point can be obtained. According to the obtained fuzzy number vector, calculate the unambiguous phase difference vector This achieves defuzzification:

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