A least squares improved interferometer recent projection point solution ambiguity method

Abstract

The application discloses a least square improved nearest projection point ambiguity resolution method, comprising the following steps: constructing a relationship model between ambiguity phase differences corresponding to each baseline of a double-long baseline phase interferometer; performing grid division on a field angle of the double-long baseline phase interferometer to construct a phase difference ambiguity graph; extending the relationship model of the double-long baseline phase interferometer to a multi-long baseline interferometer to construct a baseline vector, a theoretical ambiguity phase difference vector and an ambiguity number vector, and determining a hyperplane perpendicular to a phase line in the phase difference ambiguity graph; determining a start point ambiguity phase difference vector of all phase lines and a phase difference projection point of each phase line on the hyperplane based on the phase difference ambiguity graph; performing least square fitting on a measured ambiguity phase difference vector corresponding to a multi-shot target signal to find a fitting ambiguity phase difference vector with minimum variance, determine a nearest phase difference projection point, and obtain a corresponding ambiguity 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 interferometers offer the advantages of a simple structure, high direction-finding accuracy, and low computational complexity, playing a significant role in passive detection and reconnaissance, electronic countermeasures support, and other fields. However, with the increasing complexity of the electromagnetic environment, electronic warfare has expanded from low-frequency to ultra-high-frequency and even higher electromagnetic bands. However, when the phase error of a phase interferometer is determined, the baseline requirements for direction-finding accuracy and phase resolution are conflicting. A longer direction-finding baseline improves accuracy, while a shorter baseline reduces the ambiguity zone during phase resolution, making phase resolution easier. Furthermore, the size of the direction-finding antenna unit is limited by its minimum operating frequency and cannot be made sufficiently small. Therefore, phase ambiguity will occur when the system operates at higher frequencies. The longer the baseline, the greater the possible ambiguity. This conflict is even more acute over wide frequency bands.

[0003] Common interferometer deambiguation algorithms include the long-short baseline method, the remainder theorem, and the probability-based ergodic 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 employing axis transformation techniques and proposed an array spacing that improves the maximum phase error tolerance of the interferometer direction-finding system. However, this method is only applicable to interferometer models with fewer than four elements. When the number of interferometer elements exceeds four, visualization becomes difficult and phase deambiguation cannot be achieved. Chen et al. proposed a phase difference projection (PDP) method for direction finding, using hyperplanes to achieve phase deambiguation for linear arrays of arbitrary elements. However, under low signal-to-noise ratio (SNR) conditions, the success rate of deambiguation is low, resulting in poor direction-finding performance. Therefore, improving the universality and robustness of phase interferometer deambiguation algorithms and accurately deambiguating under low SNR conditions is a pressing technical challenge in this field. Summary of the Invention

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

[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, including:

[0007] A relationship model between the fuzzy phase differences corresponding to each baseline of a dual-long-baseline phase interferometer is constructed. The field of view of the dual-long-baseline phase interferometer is gridded, and the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids are calculated. Based on these, a phase difference fuzzy map is constructed.

[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. The baseline vector, theoretical ambiguity phase difference vector and ambiguity number vector of the multi-long-baseline interferometer are constructed, and based on this, a hyperplane perpendicular to the phase line in the phase difference ambiguity map is determined.

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

[0010] Determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane based on the starting point fuzzy phase difference vector;

[0011] Perform 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 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 method of constructing a relationship model between the fuzzy phase differences corresponding to each baseline of the dual-long-baseline phase interferometer; gridding the field of view angle of the dual-long-baseline phase interferometer, calculating the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids, and constructing a phase difference fuzzy map based on the calculated fuzzy phase differences and fuzzy number pairs, includes:

[0014] Assume that the two baselines of the double-long-baseline phase interferometer are d1 and d2, φ1 and φ2 are the true unambiguous phase differences corresponding to 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:

[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] Assume that the baseline ratio of the two baselines is d2 / d1=m2 / m1, where m1 and m2 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 recorded as θ grid ;

[0022] according to Calculate the field of view baselines d1 and d2 for all grids θ under noise-free conditions grid Theoretical fuzzy phase difference and fuzzy number pairs (k grid1 ,k grid2 ):

[0023]

[0024] And there are:

[0025]

[0026] The blurred phase difference corresponding to the baseline d1 Abscissa, fuzzy phase difference corresponding to baseline d2 Construct a coordinate system for the vertical coordinate and calculate the 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-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=(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,…,kM ), where m = 1, 2,…, M.

[0029] Furthermore, the determining of a 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, 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, where m = 1, 2, …, M.

[0032] Furthermore, the calculation is based on the phase difference mode ambiguity map to determine the starting point ambiguity phase difference vectors of all phase lines, 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 of the starting point of the first phase line, k1 represents the fuzzy number vector of 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] k2(i)=k2(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, k2(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] Furthermore, 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:

[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, and ||·||2 represents the L2 norm operation.

[0047] Furthermore, 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 minimum 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 blurred phase difference vector Denote it as the measured fuzzy phase difference vector, perform least square fitting on it, and find the fitted fuzzy phase difference vector with the minimum variance The objective function S is as follows:

[0049]

[0050] in represents the nth measured ambiguity phase difference in the measured ambiguity 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 achieving 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. By fitting the blurred phase difference vector measured by multiple snapshots, the probability of correct deambiguation of the phase interferometer under low signal-to-noise ratio conditions is improved.

[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, which enables the correct deambiguation of four or more coprime baselines and non-coprime baseline phase interferometers, 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 coprime baseline phase difference ambiguity graph model of the present invention;

[0063] Figure 4 (a) is a diagram showing the root mean square error 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 of different signal-to-noise ratios in a scenario where the interferometer baseline lengths are non-coprime 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 non-coprime in an embodiment 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 an improvement in least squares. The basic idea of ​​this method is to first grid the field of view, calculate the theoretical fuzzy phase difference vectors for all spatial grid points, and establish a multi-baseline phase difference fuzzy map model. The least squares method is then used to fit the measured multiple snapshot phase difference points to obtain phase difference fitting points with a small variance. Finally, the phase difference projection point closest to the fitted fuzzy phase difference vector is found to obtain the corresponding fuzzy number, thereby achieving phase deblurring. The specific implementation process of the present invention is further explained below.

[0066] Step 1: 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 angle 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.

[0067] 1.1 Assume that the two baselines of the double-long-baseline phase interferometer are d1 and d2, φ1 and φ2 are the true unambiguous phase differences corresponding to 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:

[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 d i The corresponding fuzzy number.

[0072] Assume that the baseline ratio of the two baselines is d2 / d1=m2 / m1, where m1 and m2 are relatively prime integers, then:

[0073]

[0074] 1.2 Set the maximum field 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°, in this range, a certain step θ is used step Perform sector meshing to obtain 2θ max / θ stepgrids, and the divided grid is recorded as θ grid .

[0075] Follow the steps in step 1.1 Calculate the field of view baselines d1 and d2 for all grids θ under noise-free conditions grid Theoretical fuzzy phase difference And the fuzzy number pair (kgrid1, kgrid2):

[0076]

[0077] And there are:

[0078]

[0079] The blurred phase difference corresponding to the baseline d1 Abscissa, fuzzy phase difference corresponding to baseline d2 Construct a coordinate system for the vertical coordinate and use the theoretical fuzzy phase difference calculated by the above formula 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, construct the baseline vector, theoretical ambiguity phase difference vector and ambiguity 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=(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.

[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 fuzzy 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 decreases to -θ max In the process, until it is reduced to a certain value, one of the fuzzy numbers is reduced 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 ambiguity number corresponding to each phase line; since the phase line is composed of a series of theoretical ambiguity phase differences, that is, the theoretical ambiguity phase difference vector after expansion to the N-element multi-baseline interferometer. Assume that the first theoretical ambiguity phase difference vector of the l-th 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 of the starting point of the first phase line, and k1 represents the fuzzy number vector of 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] k2(i)=k2(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, and k2(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: Determine the phase difference projection points of each phase line in the phase difference fuzzy map on the hyperplane based on the starting point fuzzy phase difference vector.

[0099] Since the hyperplane has a phase intersection with each phase line, the intersection 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, and ||·||2 represents the L2 norm operation.

[0102] Step 5: Perform 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.

[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 blurred phase difference vector It does not fall on the phase line in the phase difference ambiguity diagram, and is recorded as the measured ambiguity phase difference vector, so the distance is found 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 minimum 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 fuzzy phase difference vector is fitted to minimize the value of the objective function.

[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 mutually prime 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 baselines of the double-long-baseline phase interferometer shown are d1=62mm, d2=107mm, and d2 / d1=m2 / m1=107 / 62. The direction-finding principle of the phase interferometer is:

[0115]

[0116] where k1 and k2 are the fuzzy numbers of baselines d1 and d2 respectively.

[0117] Establish a phase difference blur map 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. gridTheoretical 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 ambiguity map model is obtained. Figure 3 The blue line in the middle represents the phase line formed by the theoretical phase points, with a slope of μ = d2 / d1 = 107 / 62, which is related to the baseline ratio. The red points are measured phase points with phase errors. The green straight line is perpendicular to all phase lines and has a slope of -1 / μ = -62 / 107.

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

[0119] Step 1: Extend the phase difference ambiguity model to the case of a five-element mutually prime baseline interferometer. Take the first element as the reference unit and construct the baseline vector d = (d1, d2, d3, d4) = (62, 103, 371, 521) mm. The baseline lengths are mutually prime. For the 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 and the corresponding fuzzy number vector of the phase line. 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. 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.

[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 fuzzy phase difference vector at the starting point of the first phase line, then the fuzzy phase difference vector and fuzzy number vector at the starting point of the second phase line are:

[0129]

[0130] k2(i)=k2(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, and k2(i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line.

[0132] By the above formula, we can calculate k2=(-4,-6,-20,-30). And so on, calculate the starting point fuzzy phase difference vector and fuzzy number vector of all phase lines until Indicates the fuzzy 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 true incoming angle is θ = 30°, the interferometer receives K = 64 snapshot signals, and obtains the 64 snapshot measured fuzzy phase difference vector Due to the influence of system noise, the measured fuzzy phase difference vector does not fall on the phase line, so the phase line closest to the measured fuzzy phase difference vector is found for deambiguation.

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

[0138]

[0139] where ||·|| represents the Euclidean norm, The fuzzy phase difference vector is fitted to minimize the value of the objective function.

[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 based on the fuzzy number vector obtained in step 6:

[0144]

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

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

[0147] Step 1: Extend the phase difference ambiguity model to the case of a five-element non-coprime baseline interferometer. Take the first element as the reference unit and construct the baseline vector d = (d1, d2, d3, d4) = (60, 180, 420, 520) mm. The baseline lengths are mutually prime. For the grid point θ grid , fuzzy 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 and the corresponding fuzzy number vector of the phase line. 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. 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.

[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 fuzzy phase difference vector at the starting point of the first phase line, then the fuzzy phase difference vector and fuzzy number vector at the starting point of the second phase line are:

[0157]

[0158] k2(i)=k2(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, and k2(i) represents the i-th fuzzy number of the fuzzy number vector of the second phase line.

[0160] Calculate k2=(-2,-5,-12,-14). And so on, 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 fuzzy phase difference vectors Due to the influence of system noise, the measured fuzzy phase difference vector does not fall on the phase line, so the phase line closest to the measured fuzzy phase difference vector is found for deambiguation.

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

[0166]

[0167] where ||·|| represents the Euclidean norm, The fuzzy phase difference vector is fitted to minimize the value of the objective function.

[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 based on the fuzzy number obtained in step 6:

[0172]

[0173] Step 8: Repeat steps 5 to 7 1000 times for the Monte Carlo experiment, and 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 various embodiments of the present application, and should all be included in the scope of protection 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 a dual-long-baseline phase interferometer; The field of view of the dual-long-baseline phase interferometer is divided into grids, 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 them; 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. The baseline vector, theoretical ambiguity phase difference vector and ambiguity number vector of the multi-long-baseline interferometer are constructed, and based on this, a 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; Determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane based on the starting point fuzzy phase difference vector; Perform 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 minimum 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, and the theoretical fuzzy phase differences and fuzzy number pairs corresponding to all grids are calculated. Based on this, a phase difference fuzzy map is constructed, including: Assume that the two baselines of the double-long-baseline phase interferometer are and , , Baseline , The corresponding true unambiguous phase difference is, The target angle is 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 The corresponding theoretical fuzzy phase difference, and ,Right now , represents the modulo operation, then is the quotient, indicating the baseline The corresponding fuzzy number; Set the baseline ratio of the two baselines ,in and are relatively prime integers, then: Set the maximum field of view of the dual long baseline phase interferometer to , then the angular range of the signal that the interferometer can receive is , for this range according to Perform sector mesh division to obtain grids, and the divided grids are recorded as ; according to , calculate the field of view baseline under noise-free conditions and For all meshes Theoretical fuzzy phase difference and fuzzy number pairs : And there are: Baseline Corresponding fuzzy phase difference horizontal axis, baseline Corresponding fuzzy phase difference Construct a coordinate system for the vertical coordinate and calculate the 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-baseline interferometer includes: for The multi-element long baseline interferometer can be composed of the first element as the reference unit. Baseline And the corresponding theoretical fuzzy phase difference and fuzzy numbers ;Build baseline vector , theoretical fuzzy phase difference vector , Can be seen as Point in dimensional space, fuzzy number vector , 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, for Theoretical fuzzy phase difference vector of the array element multi-long baseline interferometer, is the baseline vector, represents the M baselines in the baseline vector, represents the M theoretical ambiguity phase differences in the theoretical ambiguity phase difference vector, where 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 method is based on the phase difference mode ambiguity map to determine the starting point ambiguity phase difference vectors of all phase lines, including: No. The first theoretical fuzzy phase difference vector of the phase line is , recorded as the starting point fuzzy phase difference vector, where Indicates baseline The corresponding fuzzy phase difference, represents the number of theoretical fuzzy phase differences; the calculation formulas for the starting point fuzzy phase difference vector and its fuzzy number vector of the first phase line are as follows: in is the maximum field of view of the dual long baseline phase interferometer, is the baseline vector, is the wavelength corresponding to the target frequency; represents the unambiguous phase difference vector at the starting point of the first phase line, Indicates the fuzzy phase difference vector at the starting point of the first phase line, A fuzzy number vector representing the first phase line; Find the index of the fuzzy phase difference vector at the starting point of the second phase line: in The first phase line is the starting point of the fuzzy phase difference vector Phase difference, 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: in represents the fuzzy phase difference vector at the starting point of the second phase line, The first fuzzy phase difference vector representing the starting point of the second phase line Phase difference, The fuzzy number vector representing the second phase line fuzzy numbers; 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: Determining the phase difference projection point of each phase line in the phase difference fuzzy map on the hyperplane based on the starting point fuzzy phase difference vector 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: in Indicates the The phase line and the hyperplane phase difference projection point, Indicates the The first theoretical fuzzy phase difference vector of the phase line, is the baseline vector, Represents the distance from the fuzzy phase difference vector at the starting point of the phase line to the hyperplane, Indicates L2 norm operation, parameter superscript T indicates transposition operation, is the number of phase lines.

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 minimum variance, including: For the multi-baseline interferometer Snapshot target signal , t is the snapshot parameter, ; can be obtained through the phase detector Snapshot Blur Phase Difference Vector ; Snapshot Blur Phase Difference Vector Denote it as the measured fuzzy phase difference vector, perform least square fitting on it, and find the fitted fuzzy phase difference vector with the minimum variance , the objective function as follows: in represents the nth measured ambiguity phase difference in the measured ambiguity phase difference vector, n=1,2,…,N; represents the Euclidean norm, is the number of array elements.

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 implementing defuzzification includes: Phase difference projection point Determined by the following formula: in Indicates the Phase lines, is the number of phase lines; is the fitted fuzzy phase difference vector with the minimum variance, Indicates the Phase lines and the phase difference projection point of the hyperplane; 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 , thus achieving defuzzification: in is the baseline vector, and the superscript T in the parameter indicates the transpose operation.

Images