Ultra-short baseline positioning method for solving phase ambiguity based on vector baseline fusion algorithm

Abstract

The invention relates to an ultra-short baseline positioning method for solving phase ambiguity based on a vector baseline fusion algorithm. The invention relates to the ultra-short baseline positioning method for solving the phase ambiguity based on the vector baseline fusion algorithm. The objective of the invention is to solve the problems of low ambiguity resolution success rate and high calculation overhead of the existing algorithm. The method comprises the following steps: step 1, in an N-element circular array, calculating a pseudo-fuzzy number combination set in each baseline combination through the phase of a received signal; step 2, obtaining a pseudo-fuzzy number combination of each baseline of the N-element array; 3, establishing a condition judgment loss function; calculating the error of the pseudo-fuzzy number combination; step 4, obtaining a combinatorial optimization model, and defining the combinatorial optimization model as a comprehensive loss function; obtaining a phase difference after ambiguity resolution of the corresponding baseline based on the comprehensive loss function; and step 5, calculating an azimuth function based on the obtained phase difference after ambiguity resolution of the corresponding base line, and solving the azimuth of the target based on the azimuth function. The method is applied to the field of ultra-short baseline positioning.

Description

Technical Field

[0001] The invention relates to an ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm. Background Art

[0002] Ultra-Short Baseline (USBL) technology is an acoustic measurement technology used for underwater positioning and navigation. It is widely used in marine exploration, marine engineering, scientific research and military fields. In the acoustic positioning system, the layout of the hydrophone array has a significant impact on the system performance. Common forms include Cross Linear Array (CLA) and Uniform Circular Array (UCA). Compared with CLA, UCA achieves 360° full coverage on the horizontal plane and avoids the blind spot problem caused by directional limitations. This makes UCA have significant advantages in application scenarios that require multi-directional and high-precision positioning.

[0003] Since narrowband signals have the advantages of strong resistance to broadband noise, high bandwidth resource utilization, low system complexity, and low power consumption compared to broadband signals, USBL systems currently use narrowband signals for positioning in practical applications. USBL systems can locate underwater targets by measuring the phase difference of the signal reaching each array element and the time delay of the signal reaching the base array. Using phase difference for direction finding has the advantages of high accuracy and simplicity, but in practical applications, the detected phase will be in the range of [-π,π]. When the spacing between array elements is greater than half the wavelength of the signal, the detected phase difference between array elements will differ from the actual phase difference by an integer multiple of 2π. This situation is called phase ambiguity. In engineering applications, a group of short baselines less than half a wavelength is usually constructed to combine with long baselines to eliminate phase ambiguity. However, when the signal frequency is too high, the short baseline distance is too short, which can easily cause signal coupling. Gong Xiangyi uses the multi-baseline ratio method to make the short baseline distance not strictly less than half a wavelength, but requires the lengths of each baseline to be mutually prime. The success rate of deambiguation is greatly affected by signal noise. Di Hui uses the multi-baseline ratio method to estimate the arrival time and reduces the baseline length requirement. However, the success rate of deambiguation depends on the accuracy of the estimated arrival time. Wang Yan uses the multi-classifier fusion idea to resolve phase ambiguity. The positioning deambiguation algorithm that fully utilizes the statistical characteristics of phase difference observation data no longer requires the lengths of each baseline to be mutually prime. The above algorithms are all based on the linear array model, and have poor scalability for the planar circular array model. For the deambiguation algorithm of the planar circular array, Wei Hewen proposed a correlation search method, but it needs to divide a sufficiently small grid to search for phase difference, and the algorithm has poor real-time performance. Chen Xin proposed a rotating array deambiguation algorithm, but the algorithm needs to perform phase registration on the array rotation before deambiguation, and the rotation angle is prone to errors, which affects the accuracy of deambiguation. Zhong Rongxing proposed dividing the sub-bands to resolve phase ambiguity, but this method is only applicable to broadband signals. Gui Xintao proposed a method based on parallel baselines to solve the arrival angle according to the ratio relationship of the linear array. The algorithm has low computational complexity, but has high requirements on the detection phase accuracy. The success rate of deambiguation is low under low signal-to-noise ratio conditions. Wang Qi clustered the directional functions to effectively improve the success rate of deambiguation, but the computational overhead is large. Summary of the invention

[0004] The purpose of the present invention is to solve the problems of low deambiguation success rate and high computational overhead of existing algorithms, and to propose an ultra-short baseline positioning method for deambiguating phase ambiguity based on a vector baseline fusion algorithm.

[0005] An ultra-short baseline positioning method based on vector baseline fusion algorithm to resolve phase ambiguity. The specific process is as follows:

[0006] Step 1: In an N-element circular array, the pseudo-fuzzy number combination set in each baseline combination is calculated by the phase of the received signal, and the pseudo-fuzzy number combination set in each baseline combination is set to i=1,2,…,N;

[0007] Step 2: Based on the error of the pseudo-fuzzy number combination set, select the pseudo-fuzzy number set that meets the constraint conditions and obtain the pseudo-fuzzy number combination x of each baseline of the N-element array. n ;

[0008] Step 3: Pseudo-fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function h(x n );

[0009] Calculate the pseudo-fuzzy number combination x n The error E(x n );

[0010] Step 4: Determine the loss function h(x) based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n );

[0011] Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline. Substitute the pseudo fuzzy number into Obtain the deblurred phase difference corresponding to the baseline;

[0012] Step 5: Calculate the orientation function f based on the obtained phase difference after deambiguation of the corresponding baseline, and find the orientation of the target based on the orientation function f.

[0013] The beneficial effects of the present invention are:

[0014] Based on the parallel baseline algorithm, this paper proposes a vector baseline fusion algorithm, which can effectively improve the algorithm's defuzzification success rate while reducing the computational overhead. The algorithm makes full use of the characteristics of the uniform circular array and the vector relationship between the phase differences of each baseline, establishes a comprehensive loss function, and finds the fuzzy number combination with the minimum comprehensive loss function, which is the optimal fuzzy number combination. Mathematically, the minimization of the comprehensive loss function is a combinatorial optimization problem, which can be solved by a step-by-step search method. The simulation and experimental results show that the defuzzification success rate of the proposed algorithm for N-element uniform circular arrays (N≥4) is better than other algorithms, and can be applied to real underwater environments.

[0015] At present, most of the phase ambiguity resolution algorithms in ultra-short baseline positioning are only applicable to linear arrays, and there are few studies on uniform circular arrays. The fundamental reason is that the structure of the circular array does not form a linear relationship between its baselines, so it is impossible to use the linear relationship to resolve phase ambiguity. In response to this problem, this paper proposes a vector baseline fusion algorithm suitable for uniform circular arrays. The simulation results show that under a certain signal-to-noise ratio, the algorithm can resolve the correct phase ambiguity number for any uniform circular array with an array element number greater than 3. After lake test verification, in a real underwater environment, the algorithm's phase ambiguity resolution performance is better than the parallel baseline algorithm and the directional function clustering algorithm, indicating that the algorithm is suitable for complex underwater environments and provides a new idea for ultra-short baseline phase ambiguity resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of the present invention;

[0017] Figure 2 This is the principle diagram of uniform N-element circular array positioning;

[0018] Figure 3 This is the layout diagram of the uniform five-element circular array;

[0019] Figure 4 is the relationship diagram between signal-to-noise ratio and measured phase error;

[0020] Figure 5 This is a comparison chart of phase deambiguation performance under different weights and different signal-to-noise ratios;

[0021] Figure 6 The comparison chart of phase deambiguation performance of three algorithms under different signal-to-noise ratios;

[0022] Figure 7 This is a comparison chart of phase deambiguation performance under different signal-to-noise ratios with different numbers of array elements;

[0023] Figure 8 is the sound velocity profile;

[0024] Fig. 9 The phase difference diagram between each array element in the first 200 frames at a test distance of about 300m, (a) the phase difference between array element 1 and array element 2, (b) the phase difference between array element 2 and array element 3, (c) the phase difference between array element 3 and array element 4, (d) the phase difference between array element 4 and array element 5, (e) the phase difference between array element 5 and array element 1, (f) the error between the measured value and the true value of the phase difference between array elements;

[0025] Fig.10 This is the target's real position and calculated position diagram when the test distance is about 300m;

[0026] Fig.11The phase difference diagram between each array element in the first 200 frames when the test distance is about 700m, (a) the phase difference between array element 1 and array element 2, (b) the phase difference between array element 2 and array element 3, (c) the phase difference between array element 3 and array element 4, (d) the phase difference between array element 4 and array element 5, (e) the phase difference between array element 5 and array element 1, (f) the error between the measured value and the true value of the phase difference between array elements;

[0027] Fig.12 This is the target's actual position and calculated position diagram when the test distance is about 700m. DETAILED DESCRIPTION

[0028] Specific implementation method 1: This implementation method is an ultra-short baseline positioning method based on a vector baseline fusion algorithm to resolve phase ambiguity. The specific process is as follows:

[0029] Step 1: In an N-element circular array, the pseudo-fuzzy number combination set in each baseline combination is calculated by the phase of the received signal, and the pseudo-fuzzy number combination set in each baseline combination is set to i=1,2,…,N;

[0030] Step 2: Based on the error of the pseudo-fuzzy number combination set, select the pseudo-fuzzy number set that meets the constraint conditions and obtain the pseudo-fuzzy number combination x of each baseline of the N-element array. n ;

[0031] Step 3: Pseudo-fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function h(x n );

[0032] Calculate the pseudo-fuzzy number combination x n The error E(x n );

[0033] Step 4: Determine the loss function h(x) based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n );

[0034] Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline. Substitute the pseudo fuzzy number into Obtain the deblurred phase difference corresponding to the baseline;

[0035] Step 5: Calculate the orientation function f based on the obtained phase difference after deambiguation of the corresponding baseline, and find the orientation of the target based on the orientation function f.

[0036] Specific implementation method 2: The difference between this implementation method and specific implementation method 1 is that in step 1, in the N-element circular array, the pseudo-fuzzy number combination set in each baseline combination is calculated by the phase of the received signal, and the pseudo-fuzzy number combination set in each baseline combination is set to i=1,2,…,N; the specific process is:

[0037] Step 11, N array elements are evenly distributed on a circle with a radius of R and a center of the coordinate origin on the xoy plane of the spatial rectangular coordinate system. The array element serial numbers are 1 to N. Let the coordinates of the Nth array element be (Rcos(θ N ),Rsin(θ N ),0); where θ N represents the angle between the Nth array element and the x-axis;

[0038] In a uniform array of N elements, two adjacent elements form a baseline, and four adjacent elements form a parallel baseline. A parallel baseline includes a short baseline and a long baseline; N≥4

[0039] The short baseline is the baseline between two adjacent array elements, and the baseline parallel to the short baseline is called the long baseline;

[0040] Step 12: The relationship between the actual phase difference and the phase measurement value of any two adjacent array elements m and n is shown in the following formula:

[0041]

[0042] in, Represents the true phase difference between array element m and array element n; and Respectively represent the phase values ​​detected by array element m and array element n, δ m represents the detection error of array element m, δ n represents the detection error of array element n; Represents the pseudo fuzzy number of the detected phase difference; let The result is represents the detection phase difference between array elements m and n;

[0043] Step 13: The i-th pseudo-fuzzy number combination The pseudo-fuzzy number combination set for:

[0044]

[0045] in, represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline; represents the detection phase difference of the i-th short baseline, represents the detection phase difference of the i-th long baseline; represents the measurement error of the i-th long baseline; represents the measurement error of the i-th short baseline; represents the baseline length of the i-th long baseline; Indicates the baseline length of the i-th long baseline; round(·) means rounding to the nearest integer;

[0046] Step 14: Calculate the error of the pseudo-fuzzy number combination set. The expression is:

[0047]

[0048] in, Represents fuzzy number combination of error.

[0049] The other steps and parameters are the same as those in the first embodiment.

[0050] Specific implementation method three: This implementation method is different from specific implementation method one or two in that: in step 2, based on the error of the pseudo fuzzy number combination set, a pseudo fuzzy number set that meets the constraint conditions is selected to obtain the pseudo fuzzy number combination x of each baseline of the N-element array. n ; The specific process is:

[0051] Step 21: Select three pseudo-fuzzy number combinations with smaller errors based on the errors of the pseudo-fuzzy number combination set, and set the selected pseudo-fuzzy number combinations as the set have

[0052]

[0053] in, represents the pseudo fuzzy number combination with the minimum error in the i-th baseline calculated by the error expression of the pseudo fuzzy number combination set;

[0054] The error expression of the pseudo-fuzzy number combination set is

[0055]

[0056] It means that the pseudo fuzzy number combination with the second smallest error in the i-th baseline is calculated by the error expression of the pseudo fuzzy number combination set;

[0057] It means that the pseudo fuzzy number combination with the third smallest error in the i-th baseline is calculated by the error expression of the pseudo fuzzy number combination set;

[0058] represents the pseudo fuzzy number with the minimum error in the i-th long baseline; represents the pseudo fuzzy number with the minimum error in the i-th short baseline;

[0059] It represents the pseudo fuzzy number with the second smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the second smallest error in the i-th short baseline;

[0060] It represents the pseudo fuzzy number with the third smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the third smallest error in the i-th short baseline;

[0061] Step 22: N-element arrays can get N sets in total. The combination of the sets is F, and the total is N 3 Pseudo-fuzzy number combinations;

[0062]

[0063] Among them, combvec(·) is a combinatorial function, which means obtaining all possible combinations of the set;

[0064] Step 23: Set x n is an element in the set F, then x n represents a pseudo-fuzzy number combination, x n The form is

[0065]

[0066] in,

[0067] They represent the pseudo fuzzy numbers of the first short baseline and the first long baseline of the nth combination respectively;

[0068] They represent the pseudo fuzzy numbers of the second short baseline and the long baseline of the nth combination respectively;

[0069] They represent the pseudo fuzzy numbers of the Nth short baseline and the long baseline of the nth combination respectively.

[0070] The other steps and parameters are the same as those in the first or second embodiment.

[0071] Specific implementation method 4: This implementation method is different from one of the specific implementation methods 1 to 3 in that: in step 3, the pseudo fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function h(x n );Calculate the pseudo fuzzy number combination x n The error E(x n ); the specific process is:

[0072] Step 31: Pseudo-fuzzy number combination x based on each baseline of the N-element matrixn Establish the conditional judgment loss function; expressed as:

[0073]

[0074] Among them, h(x n ) represents the conditional judgment loss function;

[0075] Cond i (x n ) represents the indicator function, which is expressed as:

[0076]

[0077] in, represents the delay difference of the i-th short baseline;

[0078] Step 32: Calculate the pseudo-fuzzy number combination x n The error E(x n ); expressed as:

[0079]

[0080] Among them, E(x n ) represents the pseudo-fuzzy number combination x n The error, Indicates error.

[0081] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0082] Specific implementation method 5: This implementation method is different from any one of the specific implementation methods 1 to 4 in that: in step 4, the loss function h(x) is determined based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n );

[0083] Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline. Substitute the pseudo fuzzy number into Obtain the deblurred phase difference corresponding to the baseline;

[0084] The specific process is:

[0085] Step 41: Determine the loss function h(x) based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n ); expressed as:

[0086] min G(x n )=E(x n )+ηh(x n )

[0087]

[0088] Among them, G(x n ) represents the comprehensive loss function;

[0089] represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the clockwise direction;

[0090] represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the counterclockwise direction;

[0091] represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline;

[0092] They represent the pseudo fuzzy numbers of the i-th short baseline and the long baseline of the n-th combination respectively;

[0093] η is the weight;

[0094] Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline;

[0095] Substituting the corresponding pseudo-fuzzy number into The deblurred phase difference corresponding to the baseline is obtained.

[0096] The other steps and parameters are the same as those in Specific Implementation 1 to 4-1.

[0097] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that: The acquisition process of i=1,2,…N is:

[0098] Since there is a vector relationship between the phase differences of each array element, we have

[0099]

[0100] in,

[0101] It represents the detection phase difference of the adjacent baselines of the i-th short baseline in the clockwise direction;

[0102] It represents the detection phase difference of the adjacent baselines of the i-th short baseline in the counterclockwise direction;

[0103] represents the detection phase difference of the i-th long baseline; represents the detection phase difference of the i-th short baseline;

[0104] represents the detection phase difference of the i-th short baseline, represents the detection phase difference of the i-th long baseline;

[0105] Will Substitution i=1,2,…N, and the relationship formula between the pseudo fuzzy number of the long baseline and the pseudo fuzzy number of the short baseline is obtained.

[0106]

[0107] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5-1.

[0108] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that: in step 5, the azimuth function f is calculated based on the obtained phase difference after deambiguation of the corresponding baseline, and the azimuth of the target is obtained based on the azimuth function f; the specific process is:

[0109] Step 41, calculate the phase difference between two adjacent array elements p and q; expressed as:

[0110]

[0111] make

[0112]

[0113] in, is the phase difference between array elements p and q, l pq is the distance between array elements p and q, φ pq is the inclination angle of the baseline formed by array elements p and q, is the sum of the baseline tilt angles, is the difference in the baseline tilt angle;

[0114] Step 42: Based on φ pq ,φ mn Solve the direction function f;

[0115] Step 43, calculating the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident based on the direction function f;

[0116] Step 44: Calculate the final target position based on the pitch angle α of the signal incidence and the horizontal azimuth angle β of the signal incidence.

[0117] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0118] Specific implementation eight: This implementation differs from any one of the specific implementations one to seven in that: the step 42 is based on φ pq ,φ mn Solve for the direction function f; expressed as:

[0119]

[0120] Where f is the direction function, j is the imaginary unit, and j 2 =-1.

[0121] The other steps and parameters are the same as those in Specific Implementation 1 to 7-1.

[0122] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that: in step 43, the pitch angle α and the horizontal azimuth angle β of the signal incident are calculated based on the direction function f; expressed as:

[0123] α=asin(|f|)

[0124] β=Arg(f)

[0125] Among them, Arg(·) is to find the principal value of the argument, and asin(·) is to find the inverse sine;

[0126] The other steps and parameters are the same as those in Specific Implementation 1 to 8-1.

[0127] Specific implementation method ten: This implementation method is different from any one of specific implementation methods one to nine in that: in step 44, the final target position is calculated based on the pitch angle α of the incident signal and the horizontal azimuth angle β of the incident signal; it is expressed as:

[0128]

[0129] Among them, Rs is the distance from the target to the center of the array, x s ,y s ,z s is the target position in the spatial rectangular coordinate system.

[0130] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 9.

[0131] The following examples are used to verify the beneficial effects of the present invention:

[0132] Embodiment 1:

[0133] 1. Ultra-short baseline positioning principle:

[0134] like Figure 1 As shown, N array elements are evenly distributed on a circle with a radius of R on the xoy plane and the origin of the coordinate system as the center. The array element numbers are distributed from 1 to N, α is the elevation angle of the signal incident, and β is the horizontal azimuth angle of the signal incident.

[0135] Let the coordinates of the Nth array element be (Rcos(θ N ),Rsin(θ N ),0), where θ N represents the angle between the Nth array element and the x-axis. m and n are any two array elements. According to the vector projection method, the phase difference between array elements m and n is

[0136]

[0137] Where, λ is the wavelength of the received signal, l mn is the distance between array elements m and n, φ mn is the inclination angle of the baseline formed by array elements m and n, is the real phase difference between array elements m and n;

[0138] l mn With φ mn The expression is as follows:

[0139]

[0140] φ mn = atan2(sinθ n -sinθ m ,cosθ n -cosθ m ), (3)

[0141] Among them, θ n is the angle between the nth array element and the x-axis of the spatial rectangular coordinate system, θ m is the angle between the mth array element and the x-axis of the spatial rectangular coordinate system; atan2(·) is the inverse tangent of the four quadrants;

[0142] Without loss of generality, take another two array elements p and q, the phase difference between the two array elements can be expressed as

[0143]

[0144] make

[0145]

[0146] in, is the phase difference between array elements p and q, l pq is the distance between array elements p and q, φ pq is the inclination angle of the baseline formed by array elements p and q, is the sum of the baseline tilt angles, is the difference in the baseline tilt angle;

[0147] based on φ pq ,φ mn Solve the direction function f as shown below:

[0148]

[0149] Where f is the direction function, j is the imaginary unit, and j 2 =-1.

[0150] Calculate the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident based on the direction function f;

[0151] α=asin(|f|) (8)

[0152] β=Arg(f) (9)

[0153] Among them, Arg(·) is to find the principal value of the argument, and asin(·) is to find the inverse sine;

[0154] Through the direction function, we can know the target direction by knowing the phase difference between the two baselines, the array element position and the distance from the target to the array center.

[0155] Based on the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident, the final target position is calculated; the calculation is shown in formula (10):

[0156]

[0157] Among them, Rs is the distance from the target to the center of the array, x s ,y s ,z s is the target position in the spatial rectangular coordinate system.

[0158] 2. Phase ambiguity resolution method using uniform circular array

[0159] In actual situations, in order to avoid signal coupling caused by too small an array element spacing and to improve the positioning accuracy of the ultra-short baseline positioning system, the array element spacing is usually appropriately increased. When the spacing is greater than half the signal wavelength, the system will experience phase difference ambiguity.

[0160] The relationship between the actual phase difference and the phase measurement value of any two array elements m and n is shown in formula (11):

[0161]

[0162] in, is the real phase difference between array elements m and n; m=1,2,…,N,n=1,2,…,N, Indicates the phase difference measured by array elements m and n, δ mn To detect errors;

[0163] Integer k mn represents the true phase difference ambiguity number; where k mn The value set is

[0164]

[0165] Among them, d mn represents the distance between array elements m and n, Indicates rounding down. represents rounding up, λ is the wavelength of the received signal, C mn represents the true phase difference ambiguity number k mn Set, Z represents an integer;

[0166] Therefore, when solving the true phase difference, the problem of phase ambiguity needs to be solved.

[0167] 2.1 Parallel Baseline Algorithm

[0168] In an N (N≥4) element uniform array, four adjacent elements can form a parallel baseline. A parallel baseline includes a short baseline and a long baseline. The baseline between adjacent elements is called a short baseline, and the baseline parallel to the short baseline is called a long baseline. Taking a uniform five-element circular array as an example, the uniform five-element circular array layout is as follows: Figure 3 As shown in the figure, the array elements 5, 1, 2, and 3 can form a pair of parallel baselines, that is, the baseline formed by array element 1 and array element 2 is called the short baseline, and the baseline formed by array element 3 and array element 5 is called the long baseline. These two baselines satisfy the parallel relationship. Let the length of the baseline formed by array element 1 and 2 be d 12 , the phase difference is Similarly, the baseline length formed by array elements 5 and 3 is set to d 53 , the phase difference is In the far-field model (the target distance is much greater than the distance between array elements, which is considered a far-field model), there is a formula:

[0169]

[0170] Substituting equation (11) into equation (13), we get

[0171]

[0172] Among them, round(·) means rounding to the nearest integer;

[0173] According to equations (12) and (14), when the signal is the same, the range of the fuzzy number will increase with the increase of the baseline length, and a short baseline fuzzy number can correspond to a long baseline fuzzy number;

[0174] In order to reduce the amount of calculation, the parallel baseline algorithm traverses the real phase difference fuzzy number set C mn All the phase difference ambiguity numbers k in mn , we get a series of fuzzy number combinations, and the fuzzy number combinations are set as set D,

[0175]

[0176] in, represents the measured phase difference of the i-th short baseline, specifically, the detected phase difference between the i-th array element and the first array element in the counterclockwise direction based on the i-th array element;

[0177] and denote the baseline length, fuzzy number and measurement error of the i-th short baseline respectively;

[0178] like Figure 2 The detection phase difference of the baseline formed by array element 1 and array element 2 is This is called the phase difference of the first short baseline;

[0179] and They represent the baseline length, fuzzy number and measurement error of the first short baseline respectively; represents the measured phase difference of the i-th long baseline, specifically, the detected phase difference between the first array element in the clockwise direction and the second array element in the counterclockwise direction based on the i-th array element;

[0180] and denote the baseline length, fuzzy number and measurement error of the i-th long baseline respectively;

[0181] like Figure 2 The detection phase difference of the baseline formed by array element 3 and array element 5 is Will is called the phase difference of the first long baseline, and and They represent the baseline length, fuzzy number and detection error of the first long baseline respectively;

[0182] So D i represents the i-th fuzzy number combination

[0183] Each fuzzy number combination can form an error equation. The fuzzy number combination with the smallest error in each error equation is selected as the result of phase ambiguity resolution. In this way, the fuzzy numbers of all parallel baseline combinations can be obtained.

[0184] The error calculation formula is shown in formula (16):

[0185]

[0186] Among them, |·| means taking the absolute value. Each error equation selects the fuzzy number combination with the smallest error as the result of phase ambiguity resolution, so that the fuzzy numbers of all adjacent short baselines and corresponding long baselines can be obtained. In the case of low signal-to-noise ratio, the fuzzy number combination with the smallest error is usually not the correct fuzzy number combination, so the parallel baseline algorithm has a low success rate in ambiguity resolution under low signal-to-noise ratio conditions.

[0187] 2.2 Vector baseline fusion algorithm

[0188] In order to improve the success rate of the system in deambiguation under low signal-to-noise ratio conditions, this paper proposes a vector baseline fusion algorithm based on the parallel baseline algorithm according to the vector relationship between the array element baselines. This algorithm takes into account the relationship between the fuzzy numbers between the baselines. Compared with the parallel baseline algorithm, it can provide more information for deambiguation. Since the phase difference is obtained by subtracting the phase values ​​measured by each array element in actual situations, equation (11) can be rewritten as

[0189]

[0190] in, Represents the actual phase difference between array element m and array element n;

[0191] and Respectively represent the phase values ​​detected by array element m and array element n;

[0192] δ m represents the detection error of array element m, δ n represents the detection error of array element n;

[0193] Pseudo-fuzzy number representing the detected phase difference;

[0194] make The result is represents the detection phase difference between array elements m and n;

[0195] Since the phase difference between array elements may produce an ambiguous period, all and The relationship is

[0196]

[0197] With k mn The relationship is

[0198]

[0199] in, Indicates the phase difference measured by array elements m and n, k mn represents the phase difference ambiguity number;

[0200] at this time It is not a fuzzy number in the traditional sense, and is called a pseudo-fuzzy number;

[0201] If known and the corresponding The correct phase after deblurring can also be obtained, so the correct It also means that the defuzzification is successful;

[0202] at this time is not a fuzzy number in the traditional sense, and is called a pseudo-fuzzy number. and the corresponding The correct phase after deblurring can also be obtained, so the correct It also means that the defuzzification is successful.

[0203] The pseudo-fuzzy number combination set Formula (15) can be rewritten as

[0204]

[0205] in,

[0206] represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline;

[0207] represents the detection phase difference of the i-th short baseline, represents the detection phase difference of the i-th long baseline;

[0208] represents the measurement error of the i-th long baseline; represents the measurement error of the i-th short baseline;

[0209] represents the baseline length of the i-th long baseline; represents the baseline length of the i-th long baseline;

[0210] round(·) means rounding to the nearest integer;

[0211] The error calculation formula is rewritten from equation (16) as

[0212] Calculate the error of the pseudo-fuzzy number combination set, the expression is:

[0213]

[0214] in, Represents fuzzy number combination The error of

[0215] Since there is a vector relationship between the phase differences of each array element, taking the baseline 51, 12, 23, 53 as an example, we have

[0216]

[0217] Substituting equation (17) into the equation, if the baseline phase ambiguity solution is correct, we have

[0218]

[0219] By analogy, we can get the existence formula of N-dimensional circular array

[0220]

[0221] in represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the clockwise direction;

[0222] represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the counterclockwise direction;

[0223] represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline;

[0224] At this point, the problem becomes a combinatorial optimization problem. Formula (23) can be used as a constraint condition. All pseudo-fuzzy number combinations in formula (20) can be substituted into formula (21) to calculate the error of each baseline fuzzy number combination, calculate all pseudo-fuzzy number combinations of all baselines, and select the pseudo-fuzzy number combination with the smallest error for each baseline that meets the constraint conditions. In order to reduce the amount of calculation, a step-by-step search method can be used to first screen and select candidate solutions for each baseline, and then use the relationship between the pseudo-fuzzy numbers between the baselines to perform combined screening to obtain the final solution. The specific implementation is to first calculate the error of the pseudo-fuzzy number combination of each baseline within the pseudo-fuzzy number range, and select several pseudo-fuzzy number combinations with the smallest error;

[0225] Based on pseudo-fuzzy number combination set The error selects three pseudo-fuzzy number combinations with smaller errors, and sets the selected pseudo-fuzzy number combinations as the set have

[0226]

[0227] in, represents the pseudo fuzzy number combination with the minimum error in the i-th baseline calculated by equation (21);

[0228] It means the pseudo fuzzy number combination with the second smallest error in the i-th baseline calculated by equation (21);

[0229] It means the pseudo fuzzy number combination with the third smallest error in the i-th baseline calculated by equation (21);

[0230] represents the pseudo fuzzy number with the minimum error in the i-th long baseline; represents the pseudo fuzzy number with the minimum error in the i-th short baseline;

[0231] It represents the pseudo fuzzy number with the second smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the second smallest error in the i-th short baseline;

[0232] It represents the pseudo fuzzy number with the third smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the third smallest error in the i-th short baseline;

[0233] N-element arrays can get N sets in total. By using formula (26), all The total number of combinations is N. 3 Pseudo-fuzzy number combinations;

[0234]

[0235] Among them, combvec(·) is a combinatorial function, which means obtaining all possible combinations of the set;

[0236] Let x n is an element in the set F, then x n represents a pseudo-fuzzy number combination, x n The form is

[0237]

[0238] in,

[0239] They represent the pseudo fuzzy numbers of the first short baseline and the first long baseline of the nth combination respectively;

[0240] They represent the pseudo fuzzy numbers of the second short baseline and the long baseline of the nth combination respectively;

[0241] They represent the pseudo fuzzy numbers of the Nth short baseline and the long baseline of the nth combination respectively.

[0242] At this time, a series of different pseudo-fuzzy number combinations with different baselines are obtained. It is necessary to select the best one from these pseudo-fuzzy number combinations. In order to further improve the success rate of defuzzification, the time delay difference information of the signal reaching different array elements can be used. and is an integer, and a true pseudo-fuzzy number can be obtained The delay difference has the same sign as the baseline or The pseudo-fuzzy number combination x based on each baseline of the N-element matrix n Establish a conditional judgment loss function;

[0243]

[0244] Among them, h(x n ) represents the loss function for N conditions with the same priority;

[0245] Cond i (x n ) represents the indicator function of whether the pseudo fuzzy number of the i-th short baseline in the input pseudo fuzzy number combination satisfies the condition that the sign is the same as the delay difference or the pseudo fuzzy number is zero. The indicator function is expressed as

[0246]

[0247] in, represents the delay difference of the i-th short baseline;

[0248] Calculate the pseudo-fuzzy number combination x n The error E(x n ); expressed by formula (30):

[0249]

[0250] Among them, E(x n ) represents the pseudo-fuzzy number combination x n The error, Indicates error;

[0251] Based on the conditional judgment loss function h(x n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n ), as shown in formula (31)

[0252]

[0253] Among them, G(x n 0 represents the comprehensive loss function; represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the clockwise direction; represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the counterclockwise direction; represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline; They represent the pseudo fuzzy numbers of the i-th short baseline and long baseline of the n-th combination respectively; η is the weight, which is used to adjust the importance of the loss function;

[0254] Since some pseudo-fuzzy number combinations have been eliminated by equation (25), we only need to use the enumeration method to find G(x n ) The pseudo-fuzzy number combination x with the smallest result value min , at this time x min The value in is the pseudo-fuzzy number corresponding to the baseline defuzzification;

[0255] Finally, substitute the corresponding pseudo fuzzy number into formula (17): The deblurred phase difference corresponding to the baseline can be obtained.

[0256] 2.3 Algorithm Error Tolerance

[0257] After the initial screening of equation (25), when it is ensured that there are correct pseudo-fuzzy numbers in it, the maximum measured error is regarded as the error tolerance. The error tolerance is actually the phase difference between each pseudo-fuzzy number combination, which is affected by the number of array elements and the signal wavelength. Since the error concept of each baseline combination is the same, only one baseline combination is analyzed when calculating the error tolerance.

[0258] When calculating the error tolerance, since the true value of the phase difference is not a priori information, it is necessary to traverse all pseudo-fuzzy number combinations and set all the traversed pseudo-fuzzy number combinations as set S. Since it is within a certain range and d short / d long When it is an irrational number, different pseudo-fuzzy number combinations correspond to a phase value, so a pseudo-fuzzy phase function y is established. m ,have

[0259]

[0260] in, and represents the mth combination of short baseline and long baseline pseudo fuzzy numbers, and M is the cardinality of set S.

[0261] To calculate the error tolerance between pseudo-fuzzy number combinations, we need to first m All the results are sorted, and Y = [y1, y2, ..., y M ],Y sort = sort(Y), where sort(·) means sorting the input array from small to large. Let Y sort [j], 0≤j≤M represents the phase value of the jth pseudo-fuzzy number combination sorted from small to large. The error tolerance Δy(j) of each pseudo-fuzzy number combination is expressed as

[0262]

[0263] Where min(·) is the minimum value, and Δy(j) represents the error tolerance of the initial screening of the three fuzzy number combinations with the minimum errors.

[0264] Let δ max is the maximum measurement error, in formula (21) we have And it can be concluded

[0265]

[0266] Therefore, according to equations (34) and (35), the relationship between the maximum measurement error and the error tolerance of each pseudo-fuzzy number combination can be obtained as follows:

[0267]

[0268] The measurement error tolerance calculated at this time is the maximum phase error of the single array element detection, which means that within this phase error range, it can ensure that x n There are correct pseudo-fuzzy number combinations in all of them, and from x n The correct pseudo-fuzzy number combination needs to be calculated through formula (31).

[0269] It is worth noting that since the formation is a uniform circular formation, it is easy to have d short / d long =1 / (1+2cos(360 / N)), where N is the number of array elements. For example, when N is 4 or 6, d short / d longis a rational number. At this time, there may be some angles that make the phase error between the pseudo-fuzzy number combinations zero, resulting in the inability to select the pseudo-fuzzy number combination with the smallest error. At this time, it is necessary to substitute all possible pseudo-fuzzy number combinations into formula (31) to calculate the comprehensive loss degree, and select a pseudo-fuzzy number combination with the smallest loss degree as the defuzzification result. Therefore, in actual situations, the algorithm should avoid using uniform four-element circular arrays and uniform six-element circular arrays for defuzzification. When the number of array elements increases, since the signals detected by each array element can be regarded as independent of each other, if the three combinations with the smallest error are selected in formula (25), the defuzzification performance of multiple array elements may be lower than that of fewer array elements. Therefore, when the number of array elements increases, the number of pseudo-fuzzy number combinations with the smallest error should also increase.

[0270] 3 Simulation Analysis

[0271] In order to verify the performance of the algorithm, numerical simulation analysis is required. If no special instructions are given, the conditions are as follows: set the radius of the circular array R = 0.2m, the speed of sound in water c = 1500m / s, and the signal frequency The Notch filter is used to estimate the time delay and phase information of the CW signal reaching the array element for the detection and estimation of narrowband signals.

[20] The signal incident elevation angle α is set to take random values ​​from 0° to 90°, and the horizontal azimuth angle β is set to take random values ​​from 0° to 360°. Each simulation experiment uses 1000 Monte Carlo tests, and successful deambiguation is defined as the phase difference under which all baselines have solved the correct ambiguity number.

[0272] (1) Simulate and analyze the relationship between signal-to-noise ratio and measured phase error.

[0273] Since in actual engineering, it is necessary to detect and estimate the signal to obtain the arrival time and phase value of the signal, the signal-to-noise ratio is generally used to measure the signal quality. The relationship between the signal-to-noise ratio and the measured phase error is as follows: Figure 4 As shown, it can be seen that as the signal-to-noise ratio decreases, the measured phase error continues to increase, which is consistent with the actual situation. Therefore, in subsequent simulations, the signal-to-noise ratio is used instead of the measured phase error.

[0274] (2) Simulate and analyze the impact of different weights η on the probability of successful defuzzification under different signal-to-noise ratios.

[0275] The base array is a five-element circular array, with each element evenly distributed on the circumference. As can be seen from equation (12), different weights will lead to different degrees of loss, which will affect the probability of correct deambiguation. Therefore, four sets of weights are set to 0, 1, 2, and 5. The three combinations with the smallest error are initially selected in equation (25). The probability of successful deambiguation under different signal-to-noise ratio conditions is observed, and the signal-to-noise ratio range is set to -16dB to -4dB. Figure 4It can be seen that when the signal-to-noise ratio is less than -6dB, adding a loss function composed of delay information can effectively increase the probability of successful deambiguation. As the signal-to-noise ratio continues to decrease, the effect of improving the probability of successful deambiguation is more obvious, and the greater the weight, the greater the degree of improvement in the probability of successful deambiguation. In this figure, the probability of successful deambiguation is the same when η is equal to 2 and 5 because the algorithm does not require high accuracy in delay estimation, and it only needs to satisfy the same positive and negative relationship between the estimated delay difference and the actual delay difference.

[0276] (3) Simulate and analyze the deblurring performance of different algorithms under different signal-to-noise ratios.

[0277] The base array is a five-element circular array, and the signal-to-noise ratio range is set to -16dB to 0dB. The parallel baseline algorithm, directional function clustering algorithm, and vector baseline fusion algorithm are compared in different signal-to-noise ratio conditions. The clustering baseline selected by the directional function clustering algorithm is all adjacent short baselines, that is, the phase difference combination is According to the literature, different directional functions are constructed for clustering. The weight η in the vector baseline fusion algorithm is set to 2, and the three combinations with the smallest error are initially selected in formula (25). Figure 6 It can be seen that the traditional parallel baseline algorithm is greatly affected by the signal-to-noise ratio. When the signal-to-noise ratio is -2dB, the parallel baseline algorithm has a success rate of less than 100% in defuzzification, and as the signal-to-noise ratio decreases, the success rate of defuzzification decreases significantly. When the signal-to-noise ratio is -6dB, the success rate of defuzzification of the directional function clustering algorithm is less than 100%. One reason for its failure in defuzzification is that the directional function clustering algorithm only looks for the fuzzy number combination with the smallest direction error when solving the fuzzy number combination of each baseline. However, the smallest direction error can only prove that the azimuth calculated by each baseline phase difference combination is the same, and it cannot be ruled out that this azimuth is not the true target azimuth. Under the condition of -10dB signal-to-noise ratio, the vector baseline fusion algorithm has a 44.7% improvement in defuzzification success rate compared with the parallel baseline algorithm, and a 6.3% improvement in defuzzification success rate compared with the directional function clustering algorithm. As the signal-to-noise ratio decreases, the success rate of defuzzification of the vector baseline fusion algorithm decreases more slowly than the other two algorithms, and the algorithm can make the success rate of defuzzification the highest under the signal-to-noise ratio of the simulation conditions, indicating that the algorithm in this paper has stability and accuracy in defuzzification of phase.

[0278] (4) Simulate and analyze the algorithm defuzzification performance with different numbers of array elements.

[0279] The defuzzification performance of the uniform five-element, seven-element, and nine-element circular array algorithms is compared, and the signal-to-noise ratio range is set to -16dB to -6dB. Since the maximum number of array elements is nine, if the smallest three pseudo-fuzzy number combinations are selected, the correct pseudo-fuzzy number combinations may be eliminated. Therefore, at this time, the three arrays are initially screened in formula (25) to select the five pseudo-fuzzy number combinations with the smallest errors.

[0280] from Figure 7 It can be seen that the algorithms used have a high deambiguation success rate in different arrays, and when the signal-to-noise ratio is -10dB, the deambiguation success rates of the three arrays can reach 100%. When the signal-to-noise ratio is lower than -10dB, the more array elements there are, the higher the probability of successful deambiguation. This means that the more array elements there are, the more constraint information can be used, and it is easier to successfully deambiguate.

[0281] 4 Experimental analysis

[0282] The performance of the algorithm in this paper is verified by using the ultra-short baseline positioning test conducted in Songhua Lake, Jilin Province in November 2023. | The average water depth in the test is 62m. The test equipment is the ultra-short baseline system developed by Harbin Engineering University. The array is a uniform five-element plane array with a circular array radius of 0.1625m. The transmitted signal is a CW signal with a frequency of 25kHz. The output coordinates of the positioning result are based on the dock as the origin, the north direction as the y-axis, and the east direction as the x-axis. The target is placed on the bottom of the lake. Figure 8 As shown in the figure, the lake bottom depth is about 62m. The coordinates of the target are obtained by the long baseline intersection algorithm, which is regarded as the real target position. The effectiveness of the algorithm's defuzzification is judged by analyzing the target position information calculated by the algorithm in this paper. During the experiment, the receiving and sending distance is about 200m to 400m. Fig. 9 The relationship between the measured phase difference and the true phase difference in this experiment. Due to the influence of the speed of sound, the true phase value of each array element at the time of arrival is difficult to obtain, but the relatively accurate phase difference value can be inferred from the true target position. This phase difference is regarded as the true phase difference, and the measured phase difference and the true phase difference are limited to the range [-π,π]. Therefore, in this experiment, the relationship between the phase difference and the true phase difference is used to reflect the relationship between the phase of the arrival time measured by the array element and the true phase. The phase difference error is calculated by subtracting the measured phase difference from the true phase difference. The positioning results of the three algorithms are shown in Figure 1. Fig.10 As shown in the figure, it can be seen that the final target positioning result is divided into piles. This is because there are strong multipath effects and low signal-to-noise ratio in the Songhua Lake test, which leads to large phase estimation errors, making the defuzzification algorithm wrong. The number of wrong ambiguities solved eventually leads to positioning errors. Because the final positioning result will obviously deviate from the true position of the target if the defuzzification is wrong, the performance of the defuzzification algorithm can be verified based on whether the final positioning result is near the true position of the target. It can be seen that the parallel baseline algorithm has the largest number of piles, while the vector baseline fusion algorithm has the least number of piles. The positioning results within a circle with a radius of 20m near the real target are regarded as successful defuzzification. The probability of successful defuzzification of different algorithms is statistically calculated, and the statistical results are shown in Table 1. From Table 1, it can be found that the vector baseline fusion algorithm has the highest defuzzification success rate, and the performance is consistent with the simulation results, which proves the effectiveness of the algorithm.

[0283] Table 1 Statistical results of success probability of defuzzification by different algorithms when the test distance is about 300m

[0284]

[0285] In order to test a more complex underwater environment, the ship was driven to a position about 700m away from the target to observe the positioning situation at this time. Fig.11 As shown in the figure, it can be seen that the measured phase difference error becomes larger as the distance increases, which is consistent with the real underwater environment. Fig.12 As can be seen from Table 2, the defuzzification success rates of the three algorithms have all decreased, but the performance of the proposed algorithm has decreased the least, and can still achieve a defuzzification success rate of 92.6%, indicating that the algorithm can also perform excellent performance in a real and complex underwater environment.

[0286] Table 2 Statistical results of success probability of defuzzification by different algorithms when the test distance is about 700m

[0287]

[0288] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. An ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm, characterized by: The specific process of the method is: Step 1: In an N-element circular array, the pseudo-fuzzy number combination set in each baseline combination is calculated by the phase of the received signal, and the pseudo-fuzzy number combination set in each baseline combination is set to Step 2: Based on the error of the pseudo fuzzy number combination set, select the pseudo fuzzy number set that meets the constraint conditions to obtain the pseudo fuzzy number combination xn of each baseline of the N-element array; Step 3: Pseudo-fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function h(x n ); Calculate the pseudo-fuzzy number combination x n The error E(x n ); Step 4: Determine the loss function h(x) based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n ); Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline. Substitute the pseudo fuzzy number into Obtain the deblurred phase difference corresponding to the baseline; Step 5: Calculate the orientation function f based on the obtained phase difference after deambiguation of the corresponding baseline, and find the orientation of the target based on the orientation function f.

2. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 1, characterized in that: In step 1, in the N-element circular array, the pseudo-fuzzy number combination set in each baseline combination is calculated by the phase of the received signal, and the pseudo-fuzzy number combination set in each baseline combination is set to The specific process is: Step 11, N array elements are evenly distributed on a circle with a radius of R and a center at the origin of the coordinate system on the xoy plane of the spatial rectangular coordinate system, and the array element serial numbers are recorded as 1 to N; Let the coordinates of the Nth array element be (Rcos(θ N ),Rsin(θ N ),0); Among them, θ N represents the angle between the Nth array element and the x-axis; In a uniform array of N elements, two adjacent elements form a baseline, and four adjacent elements form a parallel baseline. A parallel baseline includes a short baseline and a long baseline; N≥4 The short baseline is the baseline between two adjacent array elements, and the baseline parallel to the short baseline is called the long baseline; Step 12: The relationship between the actual phase difference and the phase measurement value of any two adjacent array elements m and n is shown in the following formula: in, Represents the true phase difference between array element m and array element n; and They represent the phase values ​​detected by array element m and array element n respectively, δ m represents the detection error of array element m, δ n represents the detection error of array element n; Pseudo-fuzzy number representing the detected phase difference; make The result is represents the detection phase difference between array elements m and n; Step 13: The i-th pseudo-fuzzy number combination The pseudo-fuzzy number combination set for: in, represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline; represents the detection phase difference of the i-th short baseline, represents the detection phase difference of the i-th long baseline; represents the measurement error of the i-th long baseline; represents the measurement error of the i-th short baseline; represents the baseline length of the i-th long baseline; represents the baseline length of the i-th long baseline; round(·) means rounding to the nearest integer; Step 14: Calculate the error of the pseudo-fuzzy number combination set. The expression is: in, Represents fuzzy number combination of error.

3. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 2, characterized in that: In step 2, based on the error of the pseudo fuzzy number combination set, a pseudo fuzzy number set that satisfies the constraint condition is selected to obtain the pseudo fuzzy number combination x of each baseline of the N-element matrix. n ; The specific process is: Step 21: Select three pseudo-fuzzy number combinations with smaller errors based on the errors of the pseudo-fuzzy number combination set, and set the selected pseudo-fuzzy number combinations as the set have in, represents the pseudo fuzzy number combination with the minimum error in the i-th baseline calculated by the error expression of the pseudo fuzzy number combination set; It means that the pseudo fuzzy number combination with the second smallest error in the i-th baseline is calculated by the error expression of the pseudo fuzzy number combination set; It means that the pseudo fuzzy number combination with the third smallest error in the i-th baseline is calculated by the error expression of the pseudo fuzzy number combination set; represents the pseudo fuzzy number with the minimum error in the i-th long baseline; represents the pseudo fuzzy number with the minimum error in the i-th short baseline; It represents the pseudo fuzzy number with the second smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the second smallest error in the i-th short baseline; It represents the pseudo fuzzy number with the third smallest error in the i-th long baseline; It represents the pseudo fuzzy number with the third smallest error in the i-th short baseline; Step 22: N-element arrays can get N sets in total. The combination of the sets is F, and the total is N 3 Pseudo-fuzzy number combinations; Among them, combvec(·) is a combinatorial function, which means obtaining all possible combinations of the set; Step 23: Set x n is an element in the set F, then x n represents a pseudo-fuzzy number combination, x n The form is in, They represent the pseudo fuzzy numbers of the first short baseline and the first long baseline of the nth combination respectively; They represent the pseudo fuzzy numbers of the second short baseline and the long baseline of the nth combination respectively; They represent the pseudo fuzzy numbers of the Nth short baseline and the long baseline of the nth combination respectively.

4. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 3, characterized in that: In step 3, the pseudo fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function h(x n );Calculate the pseudo fuzzy number combination x n The error E(x n ); the specific process is: Step 31: Pseudo-fuzzy number combination x based on each baseline of the N-element matrix n Establish the conditional judgment loss function; expressed as: Among them, h(x n ) represents the conditional judgment loss function; Cond i (x n ) represents the indicator function, which is expressed as: in, represents the delay difference of the i-th short baseline; Step 32: Calculate the pseudo-fuzzy number combination x n The error E(x n ); expressed as: Among them, E(x n ) represents the pseudo-fuzzy number combination x n The error, Indicates error.

5. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 4, characterized in that: In step 4, the loss function h(x) is determined based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n ); Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline. Substitute the pseudo fuzzy number into Obtain the deblurred phase difference corresponding to the baseline; The specific process is: Step 41: Determine the loss function h(x) based on the condition n ) and pseudo-fuzzy number combination x n The error E(x n ) to obtain the combined optimization model, which is defined as the comprehensive loss function G(x n ); expressed as: Among them, G(x n ) represents the comprehensive loss function; represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the clockwise direction; represents the pseudo fuzzy number of the adjacent baselines of the i-th short baseline in the counterclockwise direction; represents the pseudo fuzzy number of the i-th long baseline; represents the pseudo fuzzy number of the i-th short baseline; They represent the pseudo fuzzy numbers of the i-th short baseline and the long baseline of the n-th combination respectively; η is the weight; Use enumeration method to find G(x n ) takes the minimum value corresponding to the pseudo-fuzzy number combination x min , x min The value in is the pseudo fuzzy number corresponding to the baseline; Substituting the corresponding pseudo-fuzzy number into The deblurred phase difference corresponding to the baseline is obtained.

6. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 5, characterized in that: Said The acquisition process is: Since there is a vector relationship between the phase differences of each array element, we have in, It represents the detection phase difference of the adjacent baselines of the i-th short baseline in the clockwise direction; It represents the detection phase difference of the adjacent baselines of the i-th short baseline in the counterclockwise direction; represents the detection phase difference of the i-th long baseline; represents the detection phase difference of the i-th short baseline; represents the detection phase difference of the i-th short baseline, represents the detection phase difference of the i-th long baseline; Will Substitution The relationship formula between the pseudo fuzzy number of the long baseline and the pseudo fuzzy number of the short baseline is obtained 7. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 6, characterized in that: In step 5, the azimuth function f is calculated based on the obtained phase difference after deambiguation of the corresponding baseline, and the azimuth of the target is obtained based on the azimuth function f; the specific process is: Step 41, calculate the phase difference between two adjacent array elements p and q; expressed as: make in, is the phase difference between array elements p and q, l pq is the distance between array elements p and q, φ pq is the inclination angle of the baseline formed by array elements p and q, is the sum of the baseline tilt angles, is the difference in the baseline tilt angle; Step 42: Based on φ pq ,φ mn Solve the direction function f; Step 43, calculating the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident based on the direction function f; Step 44: Calculate the final target position based on the pitch angle α of the signal incidence and the horizontal azimuth angle β of the signal incidence.

8. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 7, characterized in that: In step 42, based on φ pq ,φ mn Solve for the direction function f; expressed as: Where f is the direction function, j is the imaginary unit, and j 2 =-1.

9. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 8, characterized in that: In step 43, the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident are calculated based on the direction function f; they are expressed as: α=asin(|f|) β=Arg(f) Where Arg(·) is used to find the principal value of the angle, and asin(·) is used to find the inverse sine.

10. The ultra-short baseline positioning method for resolving phase ambiguity based on a vector baseline fusion algorithm according to claim 9, characterized in that: In step 44, the final target position is calculated based on the pitch angle α of the signal incident and the horizontal azimuth angle β of the signal incident; it is expressed as: Among them, Rs is the distance from the target to the center of the array, x s ,y s ,z s is the target position in the spatial rectangular coordinate system.

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