An ultra-short baseline positioning method based on vector baseline fusion algorithm for resolving phase ambiguity

Abstract

The application relates to a super-short baseline positioning method based on a vector baseline fusion algorithm for solving phase ambiguity, and aims to solve the problems of low success rate of existing algorithm for solving ambiguity and large calculation cost. The process is as follows: step 1, in an N-element circular array, a pseudo-ambiguity combination set in each baseline combination is calculated through the phase of a received signal; step 2, pseudo-ambiguity combinations of each baseline of the N-element array are obtained; step 3, a conditional judgment loss function is established; the error of the pseudo-ambiguity combinations is calculated; step 4, a combination optimization model is obtained, the combination optimization model is defined as a comprehensive loss function, and the phase difference of the corresponding baseline after ambiguity solving is obtained based on the comprehensive loss function; step 5, a direction function is calculated based on the obtained phase difference of the corresponding baseline after ambiguity solving, and the direction of the target is solved based on the direction function. The application is used in the field of super-short baseline positioning.

Description

Technical Field

[0001] This invention relates to an ultra-short baseline positioning method based on a vector baseline fusion algorithm to resolve phase ambiguity. Background Technology

[0002] Ultra-short baseline (USBL) technology is an acoustic measurement technique used for underwater positioning and navigation, with wide applications in marine exploration, marine engineering, scientific research, and military fields. In acoustic positioning systems, the arrangement of the hydrophone array significantly impacts system performance. Common arrangements include cross-line arrays (CLA) and uniform circular arrays (UCA). Compared to CLA, UCA achieves 360° omnidirectional coverage in the horizontal plane, avoiding blind spots caused by directional limitations. This gives UCA a significant advantage in applications requiring multi-directional, high-precision positioning.

[0003] Because narrowband signals have advantages over wideband signals, such as strong resistance to wideband noise, high bandwidth resource utilization, low system complexity, and low power consumption, they are commonly used for positioning in USBL systems 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 to the array. Using phase difference for direction finding has the advantages of high accuracy and simplicity. However, 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 signal wavelength, the detected phase difference between array elements may differ from the actual phase difference by an integer multiple of 2π. This situation is called phase ambiguity. In engineering applications, a set of short baselines less than half a wavelength combined with long baselines is typically constructed 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 used a multi-baseline ratio method, which eliminates the need for the short baseline distance to be strictly less than half a wavelength, but requires that the lengths of each baseline be coprime. The success rate of deambiguation is greatly affected by signal noise. Di Hui combined the multi-baseline ratio method with arrival time estimation, reducing the baseline length requirement. However, the success rate of deambiguation at this point depends on the accuracy of the estimated arrival time. Wang Yan used a multi-classifier fusion approach to resolve phase ambiguity, and a positioning deambiguation algorithm that fully utilizes the statistical characteristics of phase difference observation data no longer requires that the lengths of each baseline be coprime. All of the above algorithms are based on linear array models. For planar circular array models, the scalability is poor. For deambiguation algorithms for planar circular arrays, Wei Hewen proposed a correlation search method, but it requires dividing the grid to a sufficiently small size to search for phase differences, resulting in poor real-time performance. Chen Xin proposed a rotating array deambiguation algorithm, but this algorithm requires phase registration of the array rotation before deambiguation, and the rotation angle is prone to errors, thus affecting the accuracy of deambiguation. Zhong Rongxing proposed dividing sub-frequency 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 angle of arrival, which has low computational cost but requires high phase detection accuracy and has a low success rate in resolving ambiguity under low signal-to-noise ratio conditions. Wang Qi used directional functions for clustering, which effectively improved the success rate of resolving ambiguity, but the computational cost was high. Summary of the Invention

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

[0005] The specific process of an ultra-short baseline localization method based on vector baseline fusion algorithm for resolving phase ambiguity is as follows:

[0006] Step 1: In an N-element circular array, calculate the set of pseudo-ambiguity number combinations for each baseline combination based on the phase of the received signal, and let the set of pseudo-ambiguity number combinations for each baseline combination be... 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 satisfies the constraints, and obtain the pseudo-fuzzy number combination x of each baseline of the N-element matrix. n ;

[0008] Step 3: Combination of pseudo-fuzzy numbers x based on each baseline of the N-element matrix n Establish a conditional loss function h(x) n );

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

[0010] Step 4: Based on the conditional decision loss function h(x) n ) and pseudo-fuzzy number combination x n Error E(x) n The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function G(x). n );

[0011] Find G(x) using the enumeration method n The pseudo-fuzzy number combination x corresponding to the minimum value min x min The value in the table is the pseudo-fuzzy number corresponding to the baseline. Substituting the pseudo-fuzzy number into the table... Obtain the phase difference after deblurring of the corresponding baseline;

[0012] Step 5: Calculate the azimuth function f based on the deblurred phase difference of the corresponding baseline, and determine the azimuth of the target based on the azimuth function f.

[0013] The beneficial effects of this invention are as follows:

[0014] This paper proposes a vector baseline fusion algorithm based on the parallel baseline algorithm, which can effectively improve the defuzzification success rate while reducing computational overhead. The algorithm fully utilizes the characteristics of a uniform circular array and the vector relationship of the phase differences between baselines to establish a comprehensive loss function. The optimal fuzzy number combination is the one that minimizes the comprehensive loss function. Mathematically, minimizing the comprehensive loss function is a combinatorial optimization problem, which can be solved using a step-by-step search method. Simulation and experimental results show that the proposed algorithm outperforms other algorithms in defuzzification success rate for N-ary uniform circular arrays (N≥4) and is applicable to real underwater environments.

[0015] Currently, most phase ambiguity resolution algorithms in ultra-short baseline positioning are only applicable to linear arrays, with limited research on uniform circular arrays. The fundamental reason is that the structure of a circular array prevents the baselines from forming a linear relationship, making it impossible to resolve phase ambiguity using linear relationships. This paper proposes a vector baseline fusion algorithm suitable for uniform circular arrays. Simulation results show that, under a certain signal-to-noise ratio, this algorithm can correctly resolve the phase ambiguity number for any uniform circular array with a pair of elements greater than 3. Lake experiments have verified that, in a real underwater environment, the phase ambiguity resolution performance of this algorithm is superior to both parallel baseline algorithms and directional function clustering algorithms, indicating that this algorithm is suitable for complex underwater environments and provides a new approach for phase ambiguity resolution in ultra-short baseline positioning. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention;

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

[0018] Figure 3 A diagram showing the arrangement of a uniform five-element circular array;

[0019] Figure 4 This is a graph showing the relationship between signal-to-noise ratio and measurement phase error.

[0020] Figure 5 A comparison chart of phase defuzzification performance under different weights and signal-to-noise ratios;

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

[0022] Figure 7 Comparison of phase deambiguation performance for different numbers of array elements under different signal-to-noise ratios;

[0023] Figure 8 This is a profile of the speed of sound.

[0024] Figure 9 The phase difference diagrams between array elements in the first 200 frames at a test distance of approximately 300m are shown in the following figures: (a) Phase difference between array element 1 and array element 2, (b) Phase difference between array element 2 and array element 3, (c) Phase difference between array element 3 and array element 4, (d) Phase difference between array element 4 and array element 5, (e) Phase difference between array element 5 and array element 1, and (f) Error between the measured and true values ​​of the phase difference between array elements.

[0025] Figure 10 This is a diagram showing the actual and calculated positions of the target at a test distance of approximately 300m.

[0026] Figure 11The phase difference diagrams between array elements in the first 200 frames when the test distance is about 700m are shown. (a) Phase difference between array element 1 and array element 2, (b) Phase difference between array element 2 and array element 3, (c) Phase difference between array element 3 and array element 4, (d) Phase difference between array element 4 and array element 5, (e) Phase difference between array element 5 and array element 1, (f) Error between the measured value and the true value of the phase difference between array elements.

[0027] Figure 12 This is a diagram showing the actual and calculated positions of the target at a test distance of approximately 700m. Detailed Implementation

[0028] Specific Implementation Method 1: The specific process of this implementation method for ultra-short baseline positioning based on vector baseline fusion algorithm to resolve phase ambiguity is as follows:

[0029] Step 1: In an N-element circular array, calculate the set of pseudo-ambiguity number combinations for each baseline combination based on the phase of the received signal, and let the set of pseudo-ambiguity number combinations for each baseline combination be... 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 satisfies the constraints, and obtain the pseudo-fuzzy number combination x of each baseline of the N-element matrix. n ;

[0031] Step 3: Combination of pseudo-fuzzy numbers x based on each baseline of the N-element matrix n Establish a conditional loss function h(x) n );

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

[0033] Step 4: Based on the conditional decision loss function h(x) n ) and pseudo-fuzzy number combination x n Error E(x) n The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function G(x). n );

[0034] Find G(x) using the enumeration method n The pseudo-fuzzy number combination x corresponding to the minimum value min x min The value in the table is the pseudo-fuzzy number corresponding to the baseline. Substituting the pseudo-fuzzy number into the table... Obtain the phase difference after deblurring of the corresponding baseline;

[0035] Step 5: Calculate the azimuth function f based on the deblurred phase difference of the corresponding baseline, and determine the azimuth of the target based on the azimuth function f.

[0036] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step 1, within the N-element circular array, the set of pseudo-fuzzy number combinations in each baseline combination is calculated based on the phase of the received signal, and the set of pseudo-fuzzy number combinations in each baseline combination is set as follows: i = 1, 2, ..., N; The specific process is as follows:

[0037] Step 11: N array elements are uniformly distributed on a circle with radius R centered at the origin on the xoy plane of a spatial rectangular coordinate system. The array element numbers are denoted as 1 to N. Let the coordinates of the Nth array element be (Rcos(θ)). N ),Rsin(θ N ),0); where θ N This 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 consists of 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 true 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, This represents the true phase difference between array element m and array element n; and δ represents the phase values ​​detected by array elements m and n, respectively. m δ represents the detection error of array element m. n This represents the detection error of array element n; Let represent the pseudo-fuzzy number indicating the detected phase difference; The result is This represents the detection phase difference between array elements m and n;

[0043] Step 13, Combination of the i-th pseudo-fuzzy number The set of pseudo-fuzzy number combinations for:

[0044]

[0045] in, Let represent the pseudo-fuzzy number of the i-th long baseline; Let represent the pseudo-fuzzy number of the i-th short baseline; This represents the detection phase difference of the i-th short baseline. This represents the detection phase difference of the i-th long baseline; This represents the measurement error of the i-th long baseline; This represents the measurement error of the i-th short baseline; This represents the baseline length of the i-th long baseline; This represents the baseline length of the i-th long baseline; round(·) rounds to the nearest integer.

[0046] Step 14: Calculate the error of the pseudo-fuzzy number combination set, expressed as:

[0047]

[0048] in, Representing fuzzy number combinations The error.

[0049] The other steps and parameters are the same as in Specific Implementation Method 1.

[0050] Specific Implementation Method Three: This implementation method differs 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 satisfies the constraints is selected, and the pseudo-fuzzy number combination x of each baseline of the N-element matrix is ​​obtained. n The specific process is as follows:

[0051] Step 21: Based on the error of the pseudo-fuzzy number combination set, select three pseudo-fuzzy number combinations with smaller errors, and set the selected pseudo-fuzzy number combinations as a set. have

[0052]

[0053] in, This represents the pseudo-fuzzy number combination with the smallest error among the i-th baselines calculated from the error expression of the pseudo-fuzzy number combination set;

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

[0055]

[0056] This represents the second smallest pseudo-fuzzy number combination with error calculated from the error expression of the pseudo-fuzzy number combination set for the i-th baseline;

[0057] This represents the pseudo-fuzzy number combination with the third smallest error among the i-th baselines, calculated from the error expression of the pseudo-fuzzy number combination set.

[0058] Let represent the pseudo-fuzzy number with the smallest error in the i-th long baseline; Let represent the pseudo-fuzzy number with the smallest error in the i-th short baseline;

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

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

[0061] Step 22: An N-element matrix can yield N sets. [The remaining text appears to be incomplete and requires further context.] Combining sets yields F, and a total of N can be obtained. 3 Combinations of pseudo-fuzzy numbers;

[0062]

[0063] Here, combvec(·) is a combination function that represents obtaining all possible combinations of the set;

[0064] Step 23, let x n If x is an element in set F, then n Let x represent a pseudo-fuzzy number combination. n The form is

[0065]

[0066] in,

[0067] Let represent the pseudo-fuzziness numbers of the first short baseline and the first long baseline of the nth combination, respectively;

[0068] Let represent the pseudo-fuzziness numbers of the second short baseline and the second long baseline in the nth combination, respectively;

[0069] Let represent the pseudo-fuzziness numbers of the Nth short baseline and the long baseline of the nth combination, respectively.

[0070] Other steps and parameters are the same as in specific implementation method one or two.

[0071] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: in step 3, the pseudo-fuzzy number combination x based on each baseline of the N-element matrix... n Establish a conditional loss function h(x) n ); Calculate the pseudo-fuzzy number combination x n Error E(x) n The specific process is as follows:

[0072] Step 31: Combination of pseudo-fuzzy numbers x based on each baseline of the N-element matrixn Establish a conditional loss function; expressed as:

[0073]

[0074] Where h(x) n () represents the conditional decision loss function;

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

[0076]

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

[0078] Step 32: Calculate the pseudo-fuzzy number combination x n Error E(x) n ); is represented as:

[0079]

[0080] Wherein, 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 one of the specific implementation methods one to three.

[0082] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: in step 4, the conditional decision loss function h(x) is used... n ) and pseudo-fuzzy number combination x n Error E(x) n The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function G(x). n );

[0083] Find G(x) using the enumeration method n The pseudo-fuzzy number combination x corresponding to the minimum value min x min The value in the table is the pseudo-fuzzy number corresponding to the baseline. Substituting the pseudo-fuzzy number into the table... Obtain the phase difference after deblurring of the corresponding baseline;

[0084] The specific process is as follows:

[0085] Step 41: Based on the conditional decision loss function h(x) n ) and pseudo-fuzzy number combination x n Error E(x) nThe combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function G(x). n ); is represented as:

[0086] min G(x n )=E(x n )+ηh(x n )

[0087]

[0088] Wherein G(x) n ) represents the comprehensive loss function;

[0089] This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the clockwise direction;

[0090] This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the counterclockwise direction;

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

[0092] Let represent the pseudo-fuzziness numbers of the i-th short baseline and long baseline in the n-th combination, respectively;

[0093] η is the weight;

[0094] Find G(x) using the enumeration method n The pseudo-fuzzy number combination x corresponding to the minimum value min x min The value in the value is the pseudo-fuzzy number of the corresponding baseline;

[0095] Substitute the corresponding pseudofuzzy numbers The phase difference after deblurring of the corresponding baseline is obtained.

[0096] The other steps and parameters are the same as those in specific implementation methods one through four.

[0097] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that: the... The process of obtaining i = 1, 2, ... N is as follows:

[0098] Since there is a vector relationship between the phase differences between the array elements, then we have

[0099]

[0100] in,

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

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

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

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

[0105] Will Substitution For i = 1, 2, ..., N, the formula relating the pseudo-fuzzy numbers of long baselines to those of short baselines is obtained.

[0106]

[0107] The other steps and parameters are the same as those in specific implementation methods one through five.

[0108] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step 5, the azimuth function f is calculated based on the de-blurred phase difference of the corresponding baseline, and the azimuth of the target is determined based on the azimuth function f; the specific process is as follows:

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

[0110]

[0111] make

[0112]

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

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

[0115] Step 43: Calculate the pitch angle α and 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 and the horizontal azimuth angle β of the signal incident.

[0117] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0118] Specific Implementation Method Eight: This implementation method differs from one of Specific Implementation Methods One to Seven in that: in step 42, 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 methods one through seven.

[0122] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that: in step 43, the elevation 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] Where Arg(·) is used to find the principal value of the argument, and asin(·) is used to find the arcsine;

[0126] The other steps and parameters are the same as those in specific implementation methods one through eight.

[0127] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that: in step 44, the final target position is calculated based on the pitch angle α and the horizontal azimuth angle β of the signal incidence; expressed as:

[0128]

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

[0130] The other steps and parameters are the same as those in specific implementation methods one through nine.

[0131] The beneficial effects of the present invention are verified using the following embodiments:

[0132] Example 1:

[0133] 1. Principle of ultra-short baseline positioning:

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

[0135] Let the coordinates of the Nth element be (Rcos(θ)). N ),Rsin(θ N ),0), where θ N Let m and n be 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 φ is the distance between array elements m and n. mn Let be the tilt angle of the baseline formed by array elements m and n. The actual 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] Where, θ n Let θ be the angle between the nth element and the x-axis of the Cartesian coordinate system. m Let be the angle between the m-th array element and the x-axis of the spatial rectangular coordinate system; atan2(·) is used to find the arctangent in the four quadrants;

[0142] Without loss of generality, consider two other array elements p and q. The phase difference between the two elements can be expressed as:

[0143]

[0144] make

[0145]

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

[0147] based on φ pq φ mn The direction function f is solved as shown in the following equation:

[0148]

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

[0150] The elevation angle α and the horizontal azimuth angle β of the signal incident are calculated based on the direction function f.

[0151] α=asin(|f|) (8)

[0152] β=Arg(f) (9)

[0153] Where Arg(·) is used to find the principal value of the argument, and asin(·) is used to find the arcsine;

[0154] According to the direction function, the target's azimuth can be determined by knowing only the phase difference between the two baselines, the position of the array elements, and the distance from the target to the center of the array.

[0155] The final target position is calculated based on the pitch angle α and the horizontal azimuth angle β of the signal incident; the calculation is shown in equation (10).

[0156]

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

[0158] 2. Uniform Circular Array Phase Blur Resolving Method

[0159] In practice, to avoid signal coupling caused by excessively small element spacing and to improve the positioning accuracy of ultra-short baseline positioning systems, the element spacing is usually appropriately increased. When the spacing is greater than half the signal wavelength, the system will experience phase ambiguity.

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

[0161]

[0162] in, Let m be the true phase difference between array elements m and n; m = 1, 2, ..., N, n = 1, 2, ..., N. This indicates that the phase difference between array elements m and n is measured. δ mn For detection error;

[0163] Integer k mn Represents the true phase difference ambiguity number; where k mn The set of values ​​is

[0164]

[0165] Where, d mn This represents the distance between array elements m and n. This indicates rounding down. This indicates rounding up, where λ is the wavelength of the received signal, and C... mn The ambiguity number k represents the true phase difference. mn A set, where Z represents integers;

[0166] Therefore, when solving for the true phase difference, it is necessary to address the issue of phase ambiguity.

[0167] 2.1 Parallel Baseline Algorithm

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

[0169]

[0170] Substituting equation (11) into equation (13) yields

[0171]

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

[0173] According to equations (12) and (14), under the same signal conditions, the range of ambiguity numbers will increase with the increase of baseline length, and a short baseline ambiguity number can correspond to a long baseline ambiguity number.

[0174] To reduce computational complexity, the parallel baseline algorithm traverses the set of true phase difference ambiguities C. mn All phase difference ambiguity numbers k mn We obtain a series of fuzzy number combinations, denoted as set D, and have:

[0175]

[0176] in, The measured phase difference of the i-th short baseline is 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 Let represent the baseline length, ambiguity 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 referred to as the phase difference of the first short baseline;

[0179] and These represent the baseline length, ambiguity number, and measurement error of the first short baseline, respectively. The measured phase difference of the i-th long baseline is 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 Let represent the baseline length, ambiguity 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 elements 3 and 5 is: Will The phase difference is called the first long baseline, and and These represent the baseline length, ambiguity number, and detection error of the first long baseline, respectively.

[0182] Therefore, D i Represents the i-th fuzzy number combination

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

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

[0185]

[0186] Here, |·| represents taking the absolute value. The combination of fuzzy numbers with the smallest error among each error equation is selected as the result of phase fuzzing resolution, thus obtaining the fuzzy numbers of all adjacent short baselines and their corresponding long baselines. However, in low signal-to-noise ratio (SNR) conditions, the combination of fuzzy numbers with the smallest error is often not the correct combination, resulting in a low success rate for the parallel baseline algorithm in fuzzing resolution under low SNR conditions.

[0187] 2.2 Vector Baseline Fusion Algorithm

[0188] To improve the success rate of defuzzification under low signal-to-noise ratio conditions, this paper proposes a vector baseline fusion algorithm based on the vector relationship between array element baselines, building upon the parallel baseline algorithm. This algorithm considers the relationship between the fuzzy numbers of each baseline and, compared to the parallel baseline algorithm, provides more information for defuzzification. Since the phase difference is obtained by subtracting the phase values ​​measured by each array element in practice, equation (11) can be rewritten as follows:

[0189]

[0190] in, This represents the true phase difference between array element m and array element n;

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

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

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

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

[0195] Because the phase difference between array elements may produce a blurring period, all and The relationship is

[0196]

[0197] With k mn The relationship is

[0198]

[0199] in, This indicates that the phase difference between array elements m and n is measured. k mn This represents the phase difference ambiguity number;

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

[0201] If known and corresponding It can also obtain the correct deblurred phase, so the correct solution is obtained. This also means that the ambiguity has been successfully resolved;

[0202] at this time This is not a fuzzy number in the traditional sense; it is called a pseudo-fuzzy number. If it is known... and corresponding It can also obtain the correct deblurred phase, so the correct solution is obtained. This also means that the ambiguity has been successfully resolved.

[0203] The set of pseudo-fuzzy number combinations Equation (15) can be rewritten as

[0204]

[0205] in,

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

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

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

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

[0210] round(·) rounds to the nearest integer.

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

[0212] The error of the pseudo-fuzzy number combination set is calculated using the following expression:

[0213]

[0214] in, Representing fuzzy number combinations The error;

[0215] Since there is a vector relationship between the phase differences between the array elements, taking baselines 51, 12, 23, 53 as an example, then we have

[0216]

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

[0218]

[0219] By analogy, we can obtain the formula for the existence of an N-element circular matrix.

[0220]

[0221] in This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the clockwise direction;

[0222] This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the counterclockwise direction;

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

[0224] At this point, the problem becomes a combinatorial optimization problem. Equation (23) can be used as a constraint. All pseudo-fuzzy number combinations in equation (20) can be substituted into equation (21) to calculate the error of each baseline fuzzy number combination. All pseudo-fuzzy number combinations of all baselines can be calculated, and the pseudo-fuzzy number combination with the smallest error among all baselines that meets the constraint conditions can be selected. In order to reduce the amount of computation, a step-by-step search method can be adopted. First, candidate solutions for each baseline are initially screened, and then the relationship between pseudo-fuzzy numbers between each baseline is used to perform combination screening to obtain the final solution. Specifically, the error of each baseline within the pseudo-fuzzy number range is first calculated, and several pseudo-fuzzy number combinations with the smallest error are selected.

[0225] Based on pseudo-fuzzy number combination set The three pseudo-fuzzy number combinations with smaller errors are selected, and these selected pseudo-fuzzy number combinations are set as a set. have

[0226]

[0227] in, Let represent the pseudo-fuzzy number combination with the smallest error among the i-th baselines calculated by equation (21);

[0228] This represents the combination of pseudo-fuzzy numbers with the second smallest error in the i-th baseline calculated by equation (21);

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

[0230] Let represent the pseudo-fuzzy number with the smallest error in the i-th long baseline; Let represent the pseudo-fuzzy number with the smallest error in the i-th short baseline;

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

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

[0233] An N-element matrix can yield N sets, which can be obtained by equation (26). By combining sets, a total of N can be obtained. 3 Combinations of pseudo-fuzzy numbers;

[0234]

[0235] Here, combvec(·) is a combination function that represents obtaining all possible combinations of the set;

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

[0237]

[0238] in,

[0239] Let represent the pseudo-fuzziness numbers of the first short baseline and the first long baseline of the nth combination, respectively;

[0240] Let represent the pseudo-fuzziness numbers of the second short baseline and the second long baseline in the nth combination, respectively;

[0241] Let represent the pseudo-fuzziness numbers of the Nth short baseline and the long baseline of the nth combination, respectively.

[0242] At this point, a series of different pseudo-fuzzy number combinations with different baselines are obtained. The optimal pseudo-fuzzy number combination needs to be selected from these combinations. To further improve the defuzzification success rate, the time delay difference information of the signal arriving at different array elements can be utilized. Because... and If the integer is used, a true pseudo-fuzzy number can be obtained. The delay difference sign is the same as or equal to that of the baseline. Based on the pseudo-fuzzy number combination x of each baseline of the N-element matrix n Establish a conditional loss function;

[0243]

[0244] Where h(x) n () represents the loss function for judging N conditions with the same priority;

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

[0246]

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

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

[0249]

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

[0251] Based on the conditional loss function h(x) n ) and pseudo-fuzzy number combination x n Error E(x) n The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function G(x). n As shown in equation (31)

[0252]

[0253] Wherein G(x) n 0 represents the overall loss function; This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the clockwise direction; This represents the pseudo-fuzziness number of the i-th short baseline adjacent to the i-th short baseline in the counterclockwise direction; Let represent the pseudo-fuzzy number of the i-th long baseline; Let represent the pseudo-fuzzy number of the i-th short baseline; Let represent the pseudo-fuzziness numbers of the i-th short baseline and long baseline in the n-th combination, respectively; η is the weight used to adjust the importance of the loss function.

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

[0255] Finally, the corresponding pseudo-fuzzy number is substituted into equation (17). The phase difference after deblurring of the corresponding baseline can then be obtained.

[0256] 2.3 Algorithm Error Tolerance

[0257] After initial screening of equation (25), if the correct pseudo-fuzzy numbers are ensured, the maximum measurement error is considered as the error tolerance. This 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 prior information, it is necessary to iterate through all pseudo-fuzzy number combinations. All the iterated pseudo-fuzzy number combinations are set as set S. Since it is within a certain range, and d... short / d long When the number is irrational, different combinations of pseudo-fuzzy numbers correspond to a phase value, therefore a pseudo-fuzzy phase function y is established. m ,have

[0259]

[0260] in, and Let M represent the m-th pseudo-fuzzy combination of short and long baselines, where M is the cardinality of set S.

[0261] Calculating the error tolerance between pseudo-fuzzy number combinations requires first determining y m Sort all results, and we have Y = [y1, y2, ..., y]. M ],Y sort =sort(Y), where sort(·) sorts the input array in ascending order. Let Y be... sort [j], 0≤j≤M represents the phase value of the j-th pseudo-fuzzy number combination sorted from smallest to largest. The error tolerance Δy(j) of each pseudo-fuzzy number combination is expressed as...

[0262]

[0263] Where min(·) represents the minimum value, and Δy(j) represents the error tolerance of the combination of three fuzzy numbers with the minimum error in the initial screening.

[0264] Let δ max To represent the maximum measurement error, we have in equation (21) And it can be concluded that

[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 a single-element detector, which means that within this phase error range, it can ensure x-axis accuracy in all azimuth directions. n There are correct pseudo-fuzzy number combinations in all of them, while from x n The correct pseudo-fuzzy number combination needs to be calculated using equation (31).

[0269] It is worth noting that, because the formation is a uniform circular array, it is prone to d short / d long = 1 / (1+2cos(360 / N)), where N is the number of array elements. For example, when N is 4 and 6, d short / d longSince the numbers are rational, there may be some angles where the phase error between the pseudo-fuzzy number combinations is zero, making it impossible to select the pseudo-fuzzy number combination with the smallest error. In this case, it is necessary to substitute all possible pseudo-fuzzy number combinations into equation (31) to calculate the comprehensive loss degree and select the pseudo-fuzzy number combination with the smallest loss degree as the defuzzification result. Therefore, in practice, this algorithm should avoid using uniform four-element circular arrays and uniform six-element circular arrays for defuzzification processing. 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 equation (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 selection of the pseudo-fuzzy number combination with the smallest error should also increase.

[0270] 3. Simulation Analysis

[0271] To verify the algorithm's performance, numerical simulation analysis is required. Unless otherwise specified, the conditions are as follows: circular array radius R = 0.2m, sound speed in water c = 1500m / s, and signal frequency... Narrowband signal detection and estimation: Notch filters are used to estimate the arrival time delay and phase information of the CW signal at the array elements.

[20] The signal incident elevation angle α is set to a random value between 0° and 90°, and the horizontal azimuth angle β is set to a random value between 0° and 360°. Each simulation experiment uses 1000 Monte Carlo trials. Successful deblurring is defined as the phase difference when all baselines are correctly deblurred.

[0272] (1) Simulation analysis of the relationship between signal-to-noise ratio and measurement phase error.

[0273] In practical engineering, it is necessary to detect and estimate signals to obtain their time of arrival and phase values. Therefore, the signal-to-noise ratio (SNR) is generally used to measure signal quality. The relationship between SNR and measurement phase error is as follows: Figure 4 As shown, it can be seen that the measurement phase error increases continuously as the signal-to-noise ratio decreases, which is consistent with the actual situation. Therefore, the signal-to-noise ratio is used to replace the measurement phase error in subsequent simulations.

[0274] (2) Simulation analysis of the impact of different weights η on the success probability of defuzzification under different signal-to-noise ratios.

[0275] The array is a five-element circular array, with each element evenly distributed on the circumference. As shown in equation (12), different weights lead to different degrees of loss, affecting the probability of correct defuzzification. Therefore, four sets of weights are set to 0, 1, 2, and 5. The three combinations with the smallest initial error are selected in equation (25), and the probability of successful defuzzification under different signal-to-noise ratios is observed. The signal-to-noise ratio range is set from -16dB to -4dB. Figure 4It can be seen that when the signal-to-noise ratio (SNR) is less than -6dB, adding a loss function composed of time delay information can effectively increase the success probability of deblurring. The effect of increasing the success probability of deblurring becomes more significant as the SNR decreases, and the larger the weight, the greater the increase in the success probability of deblurring. In this figure, the success probability of deblurring is the same when η equals 2 and 5 because the algorithm does not require high accuracy in time delay estimation; it only needs to ensure that the estimated time delay difference and the actual time delay difference have the same positive or negative relationship.

[0276] (3) Simulation analysis of different algorithms for defuzzification under different signal-to-noise ratios.

[0277] A five-element circular array was chosen as the base, and the signal-to-noise ratio (SNR) was set from -16dB to 0dB. The deblurring performance of the parallel baseline algorithm, directional function clustering algorithm, and vector baseline fusion algorithm under different SNR conditions was compared. The directional function clustering algorithm used all adjacent short baselines as the clustering baselines, i.e., the phase difference combination was... Different directional functions were constructed based on the literature for clustering. In the vector baseline fusion algorithm, the weight η was set to 2, and the three combinations with the smallest initial screening error were selected in equation (25). Figure 6 It can be seen that the traditional parallel baseline algorithm is greatly affected by the signal-to-noise ratio (SNR). At an SNR of -2dB, the success rate of deblurring using the parallel baseline algorithm is already below 100%, and this success rate decreases significantly with decreasing SNR. The directional function clustering algorithm also has a success rate below 100% at an SNR of -6dB. One reason for its failure is that the directional function clustering algorithm only seeks the combination of fuzzy numbers with the smallest directional error. However, the smallest directional error only proves that the calculated azimuth of each baseline phase difference combination is the same, and cannot rule out the possibility that this azimuth is not the true target azimuth. At an SNR of -10dB, the vector baseline fusion algorithm improves the deblurring success rate by 44.7% compared to the parallel baseline algorithm and by 6.3% compared to the directional function clustering algorithm. With decreasing SNR, the success rate of deblurring using the vector baseline fusion algorithm decreases more slowly than the other two algorithms. Furthermore, this algorithm achieves the highest success rate under the simulated SNR conditions, indicating that the algorithm presented in this paper has stability and accuracy in deblurring phase ambiguity.

[0278] (4) Simulation analysis of the defuzzification performance of algorithms with different array element numbers.

[0279] Comparing the defuzzification performance of uniform five-element, seven-element, and nine-element circular array algorithms, 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 Equation (25) to select the five pseudo-fuzzy number combinations with the smallest error.

[0280] from Figure 7 It can be seen that the algorithm used has a high success rate of defuzzification in different array configurations. When the signal-to-noise ratio is -10dB, the success rate of defuzzification in all three array configurations can reach 100%. When the signal-to-noise ratio is below -10dB, the more array elements there are, the higher the success rate of defuzzification. This indicates that the more array elements there are, the more constraint information can be utilized, and the easier it is to successfully defuzzify.

[0281] 4. Experimental Analysis

[0282] The performance of the algorithm presented in this paper was verified using an ultra-short baseline positioning experiment conducted in Songhua Lake, Jilin Province, in November 2023. The average water depth during the experiment was 62m. The experimental equipment was an ultra-short baseline system developed by Harbin Engineering University, with a uniform five-element planar array and a circular array radius of 0.1625m. The transmitted signal was a 25kHz CW signal. The positioning result output coordinates were set with the dock as the origin, north as the y-axis, and east as the x-axis. The target was placed on the lake bottom, and... Figure 8 As shown, the lake bottom depth is approximately 62m. The target's coordinates were obtained using a long baseline intersection algorithm and considered as the true target location. The effectiveness of the algorithm's de-ambiguity resolution was assessed by analyzing the target location information calculated by the algorithm presented in this paper. During the experiment, the transmission and reception distance was approximately between 200m and 400m. Figure 9 This experiment measured the relationship between the phase difference and the true phase difference. 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. However, a relatively accurate phase difference value can be obtained by inferring from the actual 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 array element at the time of arrival 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 as follows: Figure 10 As shown, the final target localization results exhibit clustering. This is because the Songhua Lake experiment involved strong multipath effects and a low signal-to-noise ratio, leading to large phase estimation errors and causing the deblurring algorithm to malfunction. The resulting number of incorrectly defined ambiguities ultimately results in incorrect localization. Since deblurring errors significantly deviate from the target's true location, the performance of the deblurring algorithm can be verified by checking if the final localization result is near the target's true location. It can be seen that the parallel baseline algorithm produces the most clusters, while the vector baseline fusion algorithm produces the fewest. Localization results within a 20m radius circle near the real target are considered successful deblurring. The probabilities of successful deblurring for different algorithms are statistically analyzed, and the results are shown in Table 1. Table 1 shows that the vector baseline fusion algorithm has the highest deblurring success rate, consistent with the simulation results, proving the algorithm's effectiveness.

[0283] Table 1. Statistical results of the success rate of different algorithms in defuzzification at a test distance of approximately 300m.

[0284]

[0285] To test in more complex underwater environments, the vessel was moved to a position approximately 700 meters from the target to observe the positioning performance. The measured phase difference between array elements was compared to the actual phase difference as follows: Figure 11 As shown, it can be seen that the measurement phase difference error increases with increasing distance, which is consistent with the actual underwater environment. Figure 12 As shown in Table 2, the defuzzification success rates of the three algorithms all decreased at this point, but the algorithm in this paper showed the least performance decline, still achieving a defuzzification success rate of 92.6%, indicating that the algorithm can also exhibit excellent performance in real and complex underwater environments.

[0286] Table 2. Statistical results of the success rate of different algorithms in defuzzification at a test distance of approximately 700m.

[0287]

[0288] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for ultra-short baseline localization based on vector baseline fusion algorithm to resolve phase ambiguity, characterized in that: The specific process of the method is as follows: Step 1, in In the circular matrix, the set of pseudo-fuzzy number combinations in each baseline combination is calculated by using the phase of the received signal, and the set of pseudo-fuzzy number combinations in each baseline combination is set as follows: ; ; Step 2: Based on the error of the pseudo-fuzzy number combination set, select the pseudo-fuzzy number set that satisfies the constraints, and obtain... Pseudo-fuzzy number combination of each baseline of the element array ; Step 3, based on Pseudo-fuzzy number combination of each baseline of the element array Establish a conditional loss function ; Calculate pseudo-fuzzy number combinations error ; Step 4: Based on the conditional decision loss function Combination with pseudo-fuzzy numbers error The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function. ; Find using enumeration The pseudo-fuzzy number combination corresponding to the minimum value , The value in the table is the pseudo-fuzzy number corresponding to the baseline. Substituting the pseudo-fuzzy number into the table... Obtain the phase difference after deblurring of the corresponding baseline; in, Indicates array element Harmony Formation The true phase difference; and Representing array elements respectively Harmony Formation Detected phase value; The pseudo-fuzzy number representing the detected phase difference; Indicates array element The detection error, Indicates array element The detection error; Step 5: Calculate the azimuth function based on the deblurred phase difference of the corresponding baseline. Based on azimuth function Determine the location of the target; In step 1, in In the circular matrix, the set of pseudo-fuzzy number combinations in each baseline combination is calculated by using the phase of the received signal, and the set of pseudo-fuzzy number combinations in each baseline combination is set as follows: ; The specific process is as follows: Step 11 The array elements are uniformly distributed in a spatial rectangular coordinate system. A radius on the plane The distribution of array element numbers on a circle centered at the origin is denoted as... ; Order No. The coordinates of each element are ; in, Indicates the first Individual elements and The included angle of the axis; exist In a uniform array of 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. ; 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: Any two adjacent array elements , The relationship between the true phase difference and the phase measurement value is shown in the following formula: in, Indicates array element Harmony Formation The true phase difference; and Representing array elements respectively Harmony Formation Detected phase value, Indicates array element The detection error, Indicates array element The detection error; The pseudo-fuzzy number representing the detected phase difference; make The result is , Indicates array element and The detection phase difference; Detecting pseudo-fuzzy numbers of phase difference Blur number of phase difference from the actual phase The relationship between them is: in, This represents the ambiguity number of the true phase difference; Step 13, the A combination of pseudo-fuzzy numbers The set of pseudo-fuzzy number combinations for: in, Indicates the first The pseudo-fuzzy number of long baselines; Indicates the first The pseudo-fuzzy number of short baselines; Indicates the first Detection phase difference of short baselines, Indicates the first Detection phase difference of long baselines; Indicates the first Measurement error of a long baseline; Indicates the first Measurement error of a short baseline; Indicates the first The baseline length of a long baseline; Indicates the first The baseline length of a long baseline; To round to the nearest integer; Step 14: Calculate the error of the pseudo-fuzzy number combination set, expressed as: in, Representing fuzzy number combinations The error; In step 2, based on the error of the pseudo-fuzzy number combination set, a pseudo-fuzzy number set that satisfies the constraints is selected, thus obtaining... Pseudo-fuzzy number combination of each baseline of the element array The specific process is as follows: Step 21: Based on the error of the pseudo-fuzzy number combination set, select three pseudo-fuzzy number combinations with smaller errors, and set the selected pseudo-fuzzy number combinations as a set. ,have , in, This represents the error expression calculated from the set of pseudo-fuzzy numbers. The pseudo-fuzzy number combination with the smallest error in the baseline; This represents the error expression calculated from the set of pseudo-fuzzy number combinations. The combination of pseudo-fuzzy numbers with the second smallest error in the baseline; This represents the error expression calculated from the set of pseudo-fuzzy number combinations. The combination of pseudo-fuzzy numbers with the third smallest baseline error; Indicates the first The pseudo-fuzzy number with the smallest error in a long baseline; Indicates the first The pseudo-fuzzy number with the smallest error among short baselines; Indicates the first The pseudo-fuzzy number with the second smallest error in a long baseline; Indicates the first The pseudo-fuzzy number with the second smallest error in the short baseline; Indicates the first The pseudo-fuzzy number with the third smallest mean error for long baselines; Indicates the first The pseudo-fuzzy number with the third smallest mean error among short baselines; Step 22 The Yuan Array can obtain A set, containing all Combining sets yields A total of Combinations of pseudo-fuzzy numbers; in, This is a combination function, representing the collection of all possible combinations of a set; Step 23, set For set The elements in, then This represents a pseudo-fuzzy number combination. The form is in, They represent the first The pseudo-fuzzy numbers of the first short baseline and long baseline of the combination; They represent the first The pseudo-fuzzy numbers of the second short baseline and long baseline in the combination; They represent the first The first combination The pseudo-fuzzy numbers of short and long baselines; Step 3 is based on Pseudo-fuzzy number combination of each baseline of the element array Establish a conditional loss function ; Calculate pseudo-fuzzy number combinations error The specific process is as follows: Step 31, based on Pseudo-fuzzy number combination of each baseline of the element array Establish a conditional loss function; expressed as: , in, This represents the conditional loss function; Indicates an indicator function, which is expressed as: , in, Indicates the first The time delay difference between the short baselines; Step 32: Calculate the pseudo-fuzzy number combination error ; indicates as: in, Represents pseudo-fuzzy number combinations The error, Indicates error; Step 4 is based on the conditional decision loss function. Combination with pseudo-fuzzy numbers error The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function. ; Find using enumeration The pseudo-fuzzy number combination corresponding to the minimum value , The value in the table is the pseudo-fuzzy number corresponding to the baseline. Substituting the pseudo-fuzzy number into the table... Obtain the phase difference after deblurring of the corresponding baseline; The specific process is as follows: Step 41: Based on the conditional decision loss function Combination with pseudo-fuzzy numbers error The combined optimization model is obtained, and the combined optimization model is defined as the comprehensive loss function. ; indicates as: in, Represents the overall loss function; Indicates the first The pseudo-fuzziness number of adjacent baselines along the clockwise direction of a short baseline; Indicates the first The pseudo-fuzziness number of adjacent baselines along the counterclockwise direction of a short baseline; Indicates the first The pseudo-fuzzy number of long baselines; Indicates the first The pseudo-fuzzy number of short baselines; Let represent the pseudo-fuzziness numbers of the i-th short baseline and long baseline in the n-th combination, respectively; For weights; Find using enumeration The pseudo-fuzzy number combination corresponding to the minimum value , The value in the value is the pseudo-fuzzy number of the corresponding baseline; Substitute the corresponding pseudofuzzy numbers The phase difference after deblurring of the corresponding baseline is obtained.

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: The The acquisition process is as follows: Since there is a vector relationship between the phase differences between the array elements, then we have in, Indicates the first The detection phase difference between adjacent short baselines in a clockwise direction; Indicates the first The detection phase difference between adjacent short baselines in the counterclockwise direction; Indicates the first Detection phase difference of long baselines; Indicates the first The detection phase difference of a short baseline; Indicates the first Detection phase difference of short baselines, Indicates the first Detection phase difference of long baselines; Will Substitution The formula for the relationship between the pseudo-fuzzy numbers of long baselines and short baselines is obtained. 。 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 5, the azimuth function is calculated based on the deblurred phase difference of the corresponding baseline. Based on azimuth function Determine the location of the target; The specific process is as follows: Step 51: Calculate the elements of two adjacent arrays and The phase difference is expressed as: make in, For array element , phase difference, For array element , The distance between them For array element , The tilt angle of the formed baseline, The sum of the baseline tilt angles. This is the difference in baseline tilt angle; Step 52, based on , , , Solving for the direction function ; Step 53: Based on the direction function Calculate the pitch angle of the incident signal Horizontal azimuth angle of signal incidence ; Step 54: Elevation angle based on signal incidence Horizontal azimuth angle of signal incidence Calculate the final target position.

4. The ultra-short baseline positioning method based on vector baseline fusion algorithm for phase ambiguity resolution according to claim 3, characterized in that: In step 52, based on , , , Solving for the direction function ; indicates as: in, For direction function, The imaginary unit, .

5. The ultra-short baseline positioning method based on vector baseline fusion algorithm for phase ambiguity resolution according to claim 4, characterized in that: Step 53 is based on the direction function Calculate the pitch angle of the incident signal Horizontal azimuth angle of signal incidence ; indicates as: in, To find the principal value of the argument, In order to achieve the polarity of the sinusoid.

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: In step 54, the elevation angle based on the signal incidence is used. Horizontal azimuth angle of signal incidence Calculate the final target position; expressed as: in, The distance from the target to the center of the array. , , The target position is in a spatial rectangular coordinate system.

Images