A two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints

Abstract

The present invention addresses the problems of low accuracy and high computational complexity of passive angle measurement in the field of electronic countermeasures, and proposes a two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints. This method utilizes the spatial relationship between the antenna distribution position and the electromagnetic wave propagation direction in three-dimensional space, and designs a geometric constraint function for multi-baseline path differences from a geometric analysis perspective. This function can be used to select the optimal path difference combination, thereby obtaining the optimal multi-baseline phase deambiguation parameter. In addition, during the phase deambiguation process, based on the geometric relationship of the multi-baseline projection surface in two-dimensional space, the optimal deambiguation combination of multiple baselines can be obtained by traversing the fuzzy parameters of only two baselines, which is more computationally efficient than traditional methods. Finally, multiple estimated values of the incoming signal direction are obtained by combining multiple groups of dual baselines, and the final estimated value is averaged to obtain the pitch angle and azimuth angle of the incoming signal.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a two-dimensional interference angle measurement method based on spatial geometric relationship constraints. Background Art

[0002] Phase interferometry angle measurement uses the phase difference between the echo signals received by the antennas to measure angles. However, because the phase detector can only measure phase values within a range of 2π, the actual phase difference can differ from the measured phase difference by an integer multiple of 2π. This discrepancy leads to ambiguity and inaccurate angle measurement. A common approach is to use long and short baselines to obtain different phase differences. Then, a phase deambiguation method is performed within a given range of phase ambiguity multiples. The combination that minimizes the error in the long and short baselines predicting the signal source is selected as the deambiguation result. Traditionally, to achieve three-dimensional spatial angle measurement, two sets of perpendicular antennas are used to measure the elevation and azimuth angles separately based on the above angle measurement principle. The MUSIC algorithm is currently the most popular angle measurement algorithm. This method uses signal analysis to separate the source signal from the noise signal through eigendecomposition of the signal autocorrelation matrix. The steering vector is then calculated for each angle within the possible angle range. This is then applied to the core MUSIC formula to produce a continuous curve, with the angle corresponding to the peak being the incoming wave angle.

[0003] The core of phase interferometry angle measurement lies in deambiguating the measured phase difference. Current methods traverse the ambiguity factor and then calculate the angle. The theoretical path difference is then calculated based on the calculated angle, and the calculated angle with the smallest error from the actual path difference is selected as the final measurement result. This method is computationally expensive, involving two back-calculations, and in practical applications consumes a significant amount of processor resources. Furthermore, the MUSIC algorithm uses both phase and amplitude information of the incoming signal. While signal decomposition can mitigate some of the effects of noise, interference still exists. Summary of the Invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints, which can only use the phase information of the incoming signal and does not rely on the amplitude information, thereby avoiding the influence of amplitude noise. The present invention can quickly obtain accurate pitch angles and azimuth angles of the incoming signal under multi-baseline conditions.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints includes the following steps:

[0007] Step 1: Collect multiple phase differences through an antenna array;

[0008] Step 2: Phase deambiguation is performed based on the spatial geometric constraint function to obtain the optimal path difference combination of multiple baselines;

[0009] Step 3: Use the pairwise baseline combination to simulate the incoming wave plane, estimate the incoming wave direction, average the operation to obtain the final incoming wave direction, and calculate the pitch angle and azimuth angle.

[0010] Compared with the existing technology, the beneficial effects of the present invention are: the method proposed in the present invention only requires one angle measurement antenna array to realize the simultaneous measurement of the two-dimensional angle of three-dimensional space signals, without increasing the cost of equipment and calculation. Secondly, only phase information is used in the measurement process, avoiding the influence of signal amplitude noise on angle calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a structural schematic diagram of the present invention.

[0012] Figure 2 Schematic diagram of the spatial projection relationship of three antennas in an embodiment of the present invention. DETAILED DESCRIPTION

[0013] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0014] As mentioned above, there are two existing methods for three-dimensional angle measurement. One, based on the traditional angle measurement principle, uses two perpendicular antenna arrays to measure azimuth and elevation angles, respectively. This requires a more complex equipment structure and a larger amount of back-end computation, which reduces real-time performance. The other method, the MUSIC method, uses judgment criteria derived from eigenvalue decomposition to select the optimal angle. This method requires both phase and amplitude information of the signal and is therefore susceptible to interference from both sources.

[0015] This invention is a two-dimensional interferometric angle measurement method based on spatial geometric constraints. It uses a spatial geometric constraint function construction method based on multi-baseline path differences to obtain a constraint function, which serves as the optimal metric for path difference combinations during phase deambiguation. This method results in more accurate phase deambiguation results. Furthermore, by using a dual-baseline approximation to calculate the direction of the incoming signal, both the elevation angle and the azimuth angle of the incoming signal can be obtained.

[0016] In the solution of the present invention, Figure 1 As shown,

[0017] First, the antenna array is used to measure the phase and wavelength information of the incoming signal received by a single antenna, and the phase difference of each baseline is calculated;

[0018] Secondly, a reference antenna is selected and a constraint function on the multi-baseline path difference is constructed according to the spatial position of the antenna array.

[0019] Thirdly, the reference antenna is combined with the remaining antennas to obtain multiple baselines. The phase difference corresponding to each baseline is calculated. The spatial geometric constraint function is used to defuzzify the baseline phase difference. The fuzzy number set corresponding to the minimum spatial geometric constraint function value is selected as the output. The optimal fuzzy number set is then used to calculate the actual path difference of each baseline.

[0020] Finally, the pairwise baseline combination determines the incoming wave plane passing through the reference antenna coordinates based on their wave path difference, calculates the plane unit normal vector, i.e., the signal direction, and averages the multiple sets of direction estimates, i.e., takes the average of the multiple sets of estimated values, to obtain the final direction estimate, i.e., the incoming wave direction vector. The signal elevation angle and direction angle are then inverted by the direction estimate.

[0021] The specific implementation steps of the present invention are as follows:

[0022] Step 1: Collect multiple phase differences using an antenna array. In this invention, the antenna array can be arranged in any conventional manner, such as a circular array or a rectangular array. Assume there are s (s ≥ 4) antennas in the antenna array. Select any one of these antennas as the reference antenna. The remaining s-1 antennas and the reference antenna together form s-1 measurement baselines. Obviously, these baselines are not all of equal length.

[0023] Step 2: Perform phase deambiguation based on the spatial geometric constraint function to obtain the optimal path difference combination of multiple baselines. The specific description is as follows:

[0024] Step 2.1: Construct a spatial geometric constraint function based on the antenna array distribution.

[0025] Step 2.1.1, give the coordinate position (x i ,y i ,0), 1≤i≤s, the direction of the signal source is (a,b,c).

[0026] In step 2.1.2, assume that the path differences corresponding to the obtained s-1 baselines are Δ1, Δ2, ..., Δ j ,....,Δ s-1 ;

[0027] Step 2.1.3: Use the reference antenna position coordinates to establish a two-dimensional plane perpendicular to the incoming wave direction (a, b, c), and project the position coordinates of the other s-1 antennas vertically onto the plane to obtain the projection point position coordinates of the s-1 antennas on the plane.

[0028] Step 2.1.4, calculate the s-1 distance vectors between the coordinates of the projection points of the s-1 antennas other than the reference antenna and the coordinates of the reference antenna. When the phase difference is correctly resolved, the above s-1 distance vectors should meet the coplanar requirement, that is, the determinant value of the polynomial composed of the s-1 distance vectors is a minimum value close to 0. After calculation and reasoning, it is verified that the determinant value is not affected by the direction of the incoming wave and is only related to the path difference of the s-1 antennas. Therefore, the present invention uses the determinant value as a spatial geometric constraint function for interferometric angle measurement, expressed as f(Δ1, Δ2, ...., Δ j ,....,Δ s-1 ), by minimizing the value of this function, we can get the optimal path difference combination, where Δ j It represents the path difference of the jth baseline. The jth baseline refers to the baseline formed by the jth antenna and the reference antenna among the s-1 antennas excluding the reference antenna.

[0029] For example, in the case of four antennas: s1 = [x1, y1, 0], s2 = [x2, y2, 0], s3 = [x3, y3, 0], s4 = [x4, y4, 0], the incoming wave direction vector is [a, b, 1], and the path differences between s2, s3, s4 and the baseline formed by s1 are Δ1, Δ2, and Δ3 respectively. Following the above steps, the value of the determinant is derived as follows:

[0030]

[0031] Among them: w1=-x3 y1+x4 y1+x1 y3-x4 y3-x1 y4+x3 y4

[0032] w2=-x4 y1-x1 y2+x4 y2+x2(y1-y4)+x1 y4

[0033] w3=-x2 y1+x3 y1+x1 y2-x3 y2-x1 y3+x2 y3

[0034] Since the denominator represents the square of the modulus of the direction vector, assuming the incoming wave direction is fixed, the value of the determinant is only related to the denominator. Therefore, the spatial geometric constraint function is defined as follows:

[0035] f(Δ1,Δ2,Δ3)=(w1Δ1+w2Δ2+w3Δ3) 2

[0036] Step 2.2 uses the spatial geometric constraint function constructed in step 2.1 to perform phase deambiguation of multiple baselines to obtain the optimal path difference combination.

[0037] Step 2.2.1, Calculation where φ j is the phase difference of the jth baseline, k j is φ j is the fuzzy number, and λ is the wavelength of the incoming wave.

[0038] Step 2.2.2, bring the path differences of all baselines into the spatial geometric constraint function f(Δ1, Δ2, ..., Δ s-1 ), a spatial geometric constraint function value under the current fuzzy value combination is obtained.

[0039] Step 2.2.3: exhaust all possible fuzzy value combinations within the range of the first and second baselines, and take the defuzzified value combination corresponding to the minimum function value according to the corresponding spatial geometric constraint function value. The defuzzification output of the s-1 baselines is the optimal path difference combination.

[0040] For example, in the present invention, Δ j The calculation method is as follows:

[0041] Step 2.2.1.1: Use the antenna combination to obtain the phase and wavelength information of the incoming signal on each antenna, where the phase measured by the reference antenna is θ n .

[0042] Step 2.2.1.2, calculate the path difference of the first baseline The path difference from the second baseline Where φ1=|θ1-θ n |, φ1 is the phase difference of the first baseline, k1 is the fuzzy number of φ1, φ1=|θ1-θ n |, φ2 is the phase difference of the second baseline, k2 is the fuzzy number of φ2, φ2=|θ2-θ n |; θ1 is the phase of the incoming signal on the first antenna, and θ2 is the phase of the incoming signal on the second antenna.

[0043] In step 2.2.1.3, a two-dimensional plane perpendicular to the incoming signal direction and passing through the reference antenna position is determined based on Δ1 and Δ2. This two-dimensional plane corresponds to the wave plane of the incoming signal (the local area of the signal is assumed to be a plane wave). The principle is that a plane in space can be defined by three non-collinear points. The path differences Δ1 and Δ2 represent the shortest distances from the first and second antennas to the two-dimensional plane, respectively. The path differences Δ1 and Δ2 are used to project points onto the plane. Combined with the reference antenna, the spatial representation of the two-dimensional plane can be determined.

[0044] Calculate the projection of the third antenna to the s-1th antenna on the two-dimensional plane. Combined with the coordinates of the reference antenna, the projection of the third baseline to the s-1th baseline on the two-dimensional plane can be obtained. According to the projection length p m , baseline length lm and path difference Δ m relationship The path difference from the third baseline to the s-1th baseline is calculated, and the corresponding fuzzy values k3, ..., k are deduced. m ,...,k s-1 , Then calculate the path difference under the current fuzzy value, Where 3≤m≤s-1.

[0045] Step 3: Calculate the incoming wave direction and the corresponding elevation and azimuth angles based on the deambiguation results.

[0046] In this step, based on the basic idea of determining a plane using three points in three-dimensional space, the wave plane is simulated using a combination of two baselines, the wave direction is estimated, and then the average operation is performed to obtain the final wave direction, and the pitch angle and azimuth angle can be further calculated. Figure 2 The spatial projection relationship for three antennas is given in . The specific process can be described as follows:

[0047] Step 3.1 Combining the phase deambiguation values of multiple baselines Calculate the corresponding path difference Δ1 * , Δ2 * ,....,Δ s-1 * , a signal wave plane can be determined by combining two baselines. Assuming the signal wave plane is ax+by+cz+d=0, the projection points of the two antennas, excluding the reference antenna, on the signal wave plane form two line segments within the signal wave plane with the reference antenna. Using the four conditions that the directions of the two line segments are perpendicular to the normal vector and that the lengths of the two line segments are equal to the path difference, a system of equations about (a, b, c, d) is constructed. Solving this system of equations yields the mathematical representation of the signal wave plane. Furthermore, since the plane passes through the reference antenna, if the reference antenna position is used as the spatial origin, the wave plane can be transformed to ax+by+cz=0. Determining the normal vector determines the signal wave plane, and this normal vector is the incoming wave direction. Using the projection points of the two antennas, excluding the reference antenna, on the signal wave plane, using the two conditions that the direction of the line connecting the projection points is perpendicular to the normal vector and that the lengths of the two line segments are equal to the path difference, a system of equations about (a, b, c) is constructed. Solving this system of equations yields the mathematical representation of the signal wave plane. For s-1 baselines, we can get The incoming wave plane is estimated, where the incoming wave direction vector of the tth estimate is ω t =[a t , b t , c t ],

[0048] Taking a simplified dual-baseline angle measurement system as an example, the specific process of solving the wave plane normal vector is as follows: the reference antenna coordinates are s1 = [0, 0, 0], and the coordinates of the other two antennas are s2 = [x2, y2, 0] and s3 = [x3, y3, 0]. Assume that the wave plane of the incoming wave passing through the reference antenna is: ax+by+cz = 0, and the wave plane normal vector is [a, b, c]. Project s2 and s3 onto this wave plane, and the coordinates of the projection point position (s′2 = [x′2, y′2, z′2], s′3 = [x′3, y′3, z′3])

[0049]

[0050] From this we can get the three-variable equation system about a, b, and c:

[0051]

[0052] Solving this equation gives an estimate of the incoming wave direction under two baselines (ω1 = [a1, b1, c1])

[0053] Step 3.2 The final direction of the incoming wave signal can be obtained by averaging the incoming wave directions. The pitch angle of the incoming signal is The azimuth is

[0054] In order to verify the effectiveness of the theory proposed in this invention, a simulation experiment was carried out on a computer. On a circular antenna array composed of 5 antennas, the pitch angle and azimuth angle of the hypothetical incoming wave can be accurately measured without noise disturbance. When Gaussian noise disturbance is added, there will be a certain deviation.

[0055] In summary, this invention analyzes the spatial geometric relationships of signals received by antenna arrays and proposes a method for constructing a spatial geometric constraint function for multi-antenna path differences. This method is applicable to any antenna array configuration. This constraint function can be used to evaluate the superiority of multiple sets of path differences obtained after deambiguation, select the optimal set, and then determine the optimal predicted angle based on the geometric relationship between path differences and angles. Furthermore, this method utilizes the spatial distribution of antennas during the angle estimation process. Compared to current phase difference deambiguation methods, this method can significantly reduce computational complexity and improve the efficiency of angle measurement algorithms. This method is particularly suitable for measuring the azimuth angle of radiating sources in passive reconnaissance.

Claims

1. A two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints, characterized in that: The steps include: Step 1: Collect multiple phase differences through an antenna array; Step 2: Phase deambiguation is performed based on the spatial geometric constraint function to obtain the optimal path difference combination of multiple baselines; The spatial geometric constraint function is constructed by the following steps: Step 2.1.1, give the coordinate position (x i ,y i ,0), 1≤i≤s, s is the number of antennas; the direction of the signal source is (a,b,c); Step 2.1.2, select any antenna as the reference antenna, and the other s-1 antennas and the reference antenna form s-1 baselines of different lengths. Assume that the corresponding path differences are Δ1, Δ2, ...., Δ j ,....,Δ s-1 ; Step 2.1.3: Use the reference antenna position coordinates to create a two-dimensional plane perpendicular to the incoming wave direction (a, b, c). Project the position coordinates of the other s-1 antennas perpendicularly onto this plane to obtain the position coordinates of the projection points of the s-1 antennas on this plane. Step 2.1.4, calculate the s-1 distance vectors between the coordinates of the projection points of the s-1 antennas excluding the reference antenna and the coordinates of the reference antenna, and use the determinant of the polynomial composed of the s-1 distance vectors as the spatial geometric constraint function for interferometric angle measurement, expressed as f(Δ1,Δ2,....,Δ j ,....,Δ s-1 ), the optimal path difference combination is obtained by minimizing the value of this function, where Δ j is the path difference of the jth baseline, where the jth baseline is the baseline formed by the jth antenna and the reference antenna among the s-1 antennas excluding the reference antenna; The method for obtaining the optimal path difference combination based on spatial geometric constraint function defuzzification is as follows: Step 2.2.1, Calculation where φ j is the phase difference of the jth baseline, k j is φ j The fuzzy number, λ is the wavelength of the incoming wave; calculate Δ j The method is as follows: Step 2.2.1.1: Use the antenna combination to obtain the phase and wavelength information of the incoming signal on each antenna, where the phase measured by the reference antenna is θ n ; Step 2.2.1.2, calculate the path difference of the first baseline The path difference from the second baseline Where φ1=|θ1-θ n |, φ1 is the phase difference of the first baseline, k1 is the fuzzy number of φ1, φ2=|θ2-θ n |, φ2 is the phase difference of the second baseline, k2 is the ambiguity number of φ2, θ1 is the phase of the incoming signal on the first antenna, and θ2 is the phase of the incoming signal on the second antenna; Step 2.2.1.3, determine the vertical wave direction based on Δ1 and Δ2 and pass through the two-dimensional plane of the reference antenna position, calculate the projection of the third antenna to the s-1th antenna on the two-dimensional plane, and combine the coordinates of the reference antenna to obtain the projection of the third baseline to the s-1th baseline on the two-dimensional plane. According to the projection length p m , baseline length l m and path difference Δ m relationship Calculate the path difference from the third baseline to the s-1th baseline, and inversely deduce the corresponding fuzzy values k3,...,k m ,...,k s-1 , and then calculate the path difference under the current fuzzy value, Where 3≤m≤s-1; Step 2.2.2, bringing the path differences of all baselines into the spatial geometric constraint function to obtain a spatial geometric constraint function value under the current fuzzy value combination; Step 2.2.3: exhaust all possible fuzzy value combinations within the range of the first and second baselines, and take the defuzzified value combination corresponding to the minimum function value according to the corresponding spatial geometric constraint function value. The defuzzification output of the s-1 baselines is the optimal path difference combination; In step 2.2.1 and step 3, the wave plane is simulated by using a combination of two baselines, the wave direction is estimated, the final wave direction is obtained by averaging operation, and the pitch angle and azimuth angle are calculated.

2. The two-dimensional interferometric angle measurement method based on spatial geometric relationship constraints according to claim 1, characterized in that: In step 3, the method for calculating the incoming wave direction and the corresponding elevation angle and azimuth angle is as follows: Step 3.1, based on the obtained defuzzified value combination Calculate the corresponding path difference Δ1 * ,Δ2 * ,....,Δ j * ,....,Δ s-1 * , the two baselines determine a signal wave plane, expressed as ax+by+cz+d=0; the projection points of the two antennas other than the reference antenna in the two baselines on the signal wave plane form two line segments in the signal wave plane with the reference antenna. Using the four conditions that the directions of the two line segments are perpendicular to the normal vector and the lengths of the two line segments are equal to the path difference, a system of equations about (a, b, c, d) is constructed. Solving the system of equations gives the mathematical representation of the signal wave plane; for s-1 baselines, we get The incoming wave plane is estimated, where the incoming wave direction vector of the tth estimate is ω t =[a t ,b t ,c t ], Step 3.2, The direction of the incoming wave is averaged to obtain the final direction of the incoming wave signal The pitch angle of the incoming signal is The azimuth is

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