Direction finding mean value calculation method based on angle expansion

Abstract

This invention discloses a method for calculating the mean value of direction finding based on angle extension, belonging to the field of radio monitoring technology. Addressing the problem of high computational complexity in current vector averaging methods for calculating the mean value of direction finding, this invention, after the direction finder obtains multiple direction finding results for the same signal source, first determines whether there are discontinuities, i.e., whether there are cross-interval phenomena in the direction finding results. If not, the arithmetic mean of the direction finding results is directly calculated. If there are, the direction finding angles need to be periodically extended so that the direction finding angles on both sides of the discontinuity after periodic extension are based on the same period. Then, the mean value of the direction finding angles is calculated based on the extended and corrected direction finding angles. This invention introduces a simple judgment operation on the basis of direct arithmetic averaging, significantly reducing the computational load compared to the vector averaging method, and improving the monitoring and direction finding capabilities of the direction finder.

Description

Technical Field

[0001] This invention belongs to the field of radio monitoring technology, specifically referring to a method for calculating the mean value of direction finding based on angle extension. Background Technology

[0002] Direction finding is a common technique in radio monitoring systems. It involves analyzing incoming signals to determine the direction of the signal source and using the convergence direction finding capability of multiple direction finding stations to locate the signal source. Direction finding technology has a wide range of applications in both military and civilian fields. After years of development, typical direction finding systems have gradually formed, represented by amplitude comparison direction finding and interferometric direction finding. Among these, the modern direction finding system, represented by spatial spectrum direction finding technology, is a new type of radio signal direction finding system. It not only has high direction finding resolution and sensitivity but also can find the direction of multiple signals on the same frequency, representing the future development direction of radio monitoring systems.

[0003] Although phenomenon-based direction finding systems, such as those based on spatial spectrum, have achieved high accuracy and multi-signal resolution, from a practical application perspective, the instantaneous direction finding value generally cannot remain constant due to sporadic changes in the signal propagation environment, random fluctuations in the signal source's transmission power, and the influence of environmental thermal noise. Instead, it fluctuates continuously within a small range. This fluctuation is detrimental to improving the accuracy of direction finding results and accurately determining the direction of arrival of the target signal source. To obtain more accurate and stable direction finding results, it is generally necessary to perform multiple direction finding operations on the same signal source and average the results, thereby improving the accuracy and stability of the direction finding system.

[0004] To obtain more accurate and stable direction-finding results, multiple direction-finding operations can be performed on the same signal source, and the average of the results can be taken. Assume the direction finder obtains N direction-finding results for the same signal source, denoted as θ1, θ2, ..., θ... N Conceptually, the average direction finding result can be obtained by calculating the arithmetic mean of these N direction finding results.

[0005]

[0006] In most cases, the correct direction-finding average can be obtained by using the direct arithmetic mean method in formula (1), such as... Figure 1 The situation is shown in (a). However, in some special cases, the calculation method in formula (1) cannot obtain the correct direction finding average value, such as... Figure 1 The situation shown in (b) is as follows. Figure 1In (b), the true azimuth of the target signal source is 0 degrees. Since each direction finding result can be considered as a fluctuation generated near the true azimuth, the first direction finding result is θ1 = 1°, and the second direction finding result is θ2 = 359°. If the average value is calculated directly according to the method in formula (1), the average direction finding angle can be obtained as follows: Obviously, the method in formula (1) cannot be used to... Figure 2 In case (b), the correct average direction finding result is given.

[0007] Combination Figure 1 Analyzing the situation in (b), it is not difficult to find that if the first direction finding result is mapped to vector a1 and the second direction finding result is mapped to vector a2, then the direction finding result corresponding to vector a1+a2 will be the correct average direction finding result. It is easy to verify that this method of calculating the direction finding average using vector averaging is also applicable. Figure 1 The situation is shown in (a). In practice, the method for calculating the direction-finding average value based on vector averaging can be expressed as:

[0008] The first step is to obtain N direction-finding results for the same signal source using a direction-finding machine, denoted as θ1, θ2, ..., θ N ;

[0009] The second step is to calculate vector a using the direction finding result of the nth measurement. n ,Right now

[0010]

[0011] The third step is to calculate the vector average, i.e.

[0012]

[0013] The fourth step is to calculate the average vector. The phase angle is calculated and used as the average value for direction finding.

[0014] Combining the above four steps, the direction-finding average value based on vector averaging can be obtained as follows:

[0015]

[0016] Using the vector averaging method in formula (2), the expected direction finding average value can be correctly calculated in various situations. However, compared with the method based on direct arithmetic averaging, i.e., formula (1), vector averaging introduces a large number of trigonometric and inverse trigonometric function operations, resulting in a significant increase in computational complexity compared to formula (1). In application scenarios with large direction finding calculations, such as when detecting and finding multiple frequency points simultaneously, the computational complexity introduced by formula (2) places higher demands on the overall computational capability of the direction finding machine. Under the premise that the overall computational capability of the direction finding machine is certain, using the vector averaging method in formula (2) will reduce the monitoring and direction finding capabilities of the direction finding machine. Summary of the Invention

[0017] Using the vector averaging method in formula (2), the desired direction finding average can be correctly calculated under various conditions. However, compared with the direct arithmetic averaging method in formula (1), vector averaging introduces a large number of trigonometric and inverse trigonometric function operations, resulting in a significant increase in computational complexity. In application scenarios with large direction finding calculations, such as simultaneous detection and direction finding of multiple frequency points, the computational complexity introduced by the vector averaging method places higher demands on the overall computational capability of the direction finding machine. Under the premise that the overall computational capability of the direction finding machine is fixed, using the vector averaging method in formula (2) will reduce the monitoring and direction finding capabilities of the direction finding machine. To solve the problem of excessive computation in vector averaging, this invention proposes a direction finding average calculation method based on angle extension.

[0018] The direction finding average calculation method based on angle extension provided by this invention includes a corresponding direction finding average calculation module, which obtains N direction finding results θ1, θ2, ..., θ from the direction finding machine for the same signal source. N Then, the direction finding mean calculation module performs direction finding mean calculation based on angle extension, and outputs the final direction finding mean. The direction finding mean calculation includes the following steps:

[0019] Step 1: Determine whether the N direction finding results contain discontinuities; if no discontinuities are found, directly calculate the arithmetic mean of the N direction finding results and output it; if discontinuities are found, continue to step 2.

[0020] The method for determining whether a discontinuity exists is as follows: a threshold T is set in advance. If there is an angle interval between two directions in the N directions that is greater than T, then the N directions are considered to contain a discontinuity; otherwise, the N directions are considered not to contain a discontinuity. π≤T<2π.

[0021] Step 2: Iterate through the N direction finding results in sequence, determine the location of the discontinuity, and periodically expand the direction finding angle;

[0022] Among them, the direction finding angles on both sides of the discontinuity are located in two adjacent cycles, and the direction finding angles between two adjacent discontinuities are located in the same cycle; for the direction finding angles in two adjacent cycles, the direction finding angles in one of the cycles are periodically extended, and after periodic extension, the interval between the direction finding angles on both sides of the discontinuity is no greater than T.

[0023] Step 3: Divide the N direction finding angles into two groups: the group without periodic extension and the group with periodic extension. Calculate the mean of the direction finding angles in each group, and then calculate the average of the mean values ​​of the two groups. Return the average value to the interval [0, 2π) to obtain the final average value of the direction finding.

[0024] In step 2, if the interval between two adjacent direction-finding angles is greater than T, it indicates that there is a discontinuity between the two adjacent direction-finding angles.

[0025] In step 2, the direction finding angles on both sides of the discontinuity are compared, and the direction finding angle on the side with the smaller value within the same period is extended by adding 2π.

[0026] In step 3, the average of the mean of the un-periodic expansion group and the mean of the periodically expanded group is calculated to obtain... Will Taking the modulus of 2π, we obtain the final average value of the direction finding.

[0027] The advantages and positive effects of this invention are as follows: The direction finding mean calculation method based on angle extension of this invention only requires introducing a simple judgment operation on the basis of formula (1) which is based on direct arithmetic mean, to solve the problem. Figure 1 (b) In the case of calculating the mean value of the direction finding, compared with the vector averaging method in formula (2), the judgment operation introduced does not introduce a large amount of computation. Its main computational amount is still determined by formula (1). Therefore, the computational amount of the method of the present invention is significantly reduced compared with the vector averaging method in formula (2), that is, it achieves the technical effect of obtaining the direction finding result of the signal source with a lower computational amount, and improves the monitoring and direction finding capabilities of the direction finding machine. Attached Figure Description

[0028] Figure 1 These are schematic diagrams illustrating the different scenarios that occur when calculating the mean value of the direction finding.

[0029] Figure 2 This is a schematic diagram illustrating the range of angle values ​​considering the periodicity of the angle variable in the method of this invention.

[0030] Figure 3 This is a flowchart of an implementation of the method of the present invention. Detailed Implementation

[0031] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0032] The method for calculating the mean value of direction finding based on angle extension implemented in this invention, such as... Figure 2 As shown, theoretically, the range of values ​​for the angle variable is [0, 2π), which is also called the principal value interval. Considering the periodicity of the angle variable, a more generalized range of values ​​for the angle variable can be expressed as [0, 2π) + 2kπ. For a given value of k, it can be called the k-th periodic interval. It is not difficult to find that the periodic interval when k = 0 is precisely the principal value interval.

[0033] observe Figure 1 (a) and Figure 1 In the two cases in (b), it can be found that when all the direction-finding angles θ1, θ2, ..., θ N When all values ​​are within the principal value range, the direct averaging method in formula (1) can yield the correct average direction finding result; however, when all direction finding angles θ1, θ2, ..., θ N When cross-interval phenomena occur, the direct averaging method using formula (1) will not yield accurate average direction finding results. Figure 1 The reason for the situation in (b) is that the angle variable is not continuous when changing across intervals; there are obvious discontinuities between 2π in the previous interval and 0 in the current interval. By definition, the mean obtained by the arithmetic mean is the point with the smallest distance to each sample point in a continuous space. Therefore, in a discontinuous space, the arithmetic mean cannot yield correct results.

[0034] To address this problem with lower complexity, this invention proposes a method for calculating the average value of direction finding based on angle extension, such as... Figure 3 As shown, it includes the following steps:

[0035] The first step is to obtain N direction-finding results for the same signal source using a direction-finding machine, denoted as θ1, θ2, ..., θ N ;

[0036] The second step is to calculate the minimum and maximum values ​​among the N direction finding results, i.e.

[0037] θ min =min{θ1, θ2, ..., θ N}

[0038] θ max =max{θ1, θ2, ..., θ N}

[0039] The third step is to determine whether the N direction finding results contain discontinuities.

[0040] This invention pre-sets a threshold T, when θ minand θ max When the angular interval between points is greater than a threshold, the direction finding result is considered to contain discontinuities. The threshold T is set in the range [π, 2π). In this embodiment of the invention, the threshold T is set to π. If θ min and θ max The angular interval between them |θ min -θ max If the threshold value is greater than π, then the N direction finding results are considered to contain discontinuities; otherwise, the N direction finding results are considered not to contain discontinuities. In practical applications, the threshold value T can be set relatively large, for example, T can be set to 1.5π.

[0041] Fourth step: If the N direction finding results do not contain discontinuities, the arithmetic mean of the N direction finding results can be calculated directly using formula (1) and output; if the N direction finding results contain discontinuities, the angle of the next cycle interval (to the right of the discontinuity) needs to be extended.

[0042] The N direction finding results are arranged according to the measurement time. When there are discontinuities in the N direction finding results, the N direction finding results will be traversed in order to determine whether the angle interval between two adjacent direction finding values ​​A and B is greater than the threshold T. If it is greater, it means that the direction finding values ​​A and B are in different periods, and the direction finding angle on the side with the smaller angle needs to be periodically extended.

[0043] Without loss of generality, suppose there exists a discontinuity in the N direction finding results, located at θ. N-M and θ N-M+1 Between, and θ N-M+1 Less than θ N-M The last M angles θ N-M+1 θ N-M+2 , …, θ N Located in the next period interval, these angles are periodically extended to improve the direction finding results θ. m After periodic expansion, the following was obtained θ m ∈[θ N-M+1 θ N-M+2 , …, θ N ].

[0044] In N directions, there may be multiple discontinuities. Suppose there are k discontinuities, k>1. The directions of the two sides of the discontinuity are in two adjacent period intervals. At this time, the directions of the two adjacent discontinuities are in the same period interval. Similarly, for each discontinuity, the directions of the side with the smaller angle of the discontinuity are periodically extended. The directions of the same period interval are periodically extended only once.

[0045] After periodically expanding the direction-finding angles based on the discontinuities, a new set of N direction-finding angles is obtained. Subsequently, the average value is calculated using these new N direction-finding angles. The method of this invention divides the N direction-finding angles into two groups: a group without periodic expansion and a group with periodic expansion. The average value of the direction-finding angles in each group is calculated, and then the average value of the two groups is calculated. This embodiment of the invention uses only θ... N-M and θ N-M+1 Taking the case with a discontinuity as an example, the newly obtained N direction-finding angles are: The average value of these direction finding angles is calculated to obtain as follows:

[0046]

[0047] Fifth step, calculate the average value in equation (3). By taking the modulus of 2π to restore it to the principal value interval of [0, 2π), the final direction-finding average value is obtained. as follows:

[0048]

[0049] It is easy to see from the above method that the main computational workload of the method proposed in this invention is reflected in formula (3). However, by comparing the vector average in formula (2), it is not difficult to find that formula (3) only uses simple addition operations to calculate the average value, so its computational complexity is much less than the large number of trigonometric operations in formula (2).

[0050] It should be noted that, in the embodiment of the present invention, a preferred implementation is provided when periodically extending the direction-finding angle. However, periodic extension can also be performed on the side with the larger direction-finding angle, for example, on a certain angle θ. m The extension method is to subtract that angle from 2π, that is... As long as the discontinuity is eliminated after periodic expansion, the interval between the direction-finding angles on both sides of the discontinuity will not be greater than the threshold T.

[0051] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The embodiments described above do not represent all embodiments consistent with this application. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the protection scope of this invention.

Claims

1. A method for calculating the mean value of direction finding based on angle extension, characterized in that, The method obtains N times of direction finding results for the same signal source by a direction finder Then, the following steps are performed by a direction finding mean value calculation module: Step 1: Determine whether the N direction finding results contain discontinuities; if no discontinuities are found, directly calculate the arithmetic mean of the N direction finding results and output it; if discontinuities are found, continue to step 2. The method for determining whether a discontinuity exists is as follows: a threshold T is preset, if... If there is an angle interval greater than T between two direction finding results in N direction finding results, then the N direction finding results are considered to contain discontinuities; otherwise, the N direction finding results are considered not to contain discontinuities. ≤T<2 ; Step 2: Iterate through the N direction finding results in sequence, determine the location of the discontinuity, and periodically expand the direction finding angle; Among them, the direction finding angles on both sides of the discontinuity are located in two adjacent cycles, and the direction finding angles between two adjacent discontinuities are located in the same cycle; for the direction finding angles in two adjacent cycles, the direction finding angles in one of the cycles are periodically extended, and after periodic extension, the interval between the direction finding angles on both sides of the discontinuity is no greater than T. The periodic expansion of the direction finding angles refers to the following: if the interval between two adjacent direction finding angles is greater than T, it indicates that there is a discontinuity between the two adjacent direction finding angles. The direction finding angles on both sides of the discontinuity are compared, and the angle within the same period on the side with the smaller value is increased by 2. To perform periodic extension, or by using the direction-finding angle within the same period on the side with the larger value, Subtract this angle to expand the cycle; Step 3: Divide the N direction finding angles into two groups: the group without periodic extension and the group with periodic extension. Calculate the mean of the direction finding angles in each group, and then average the mean values ​​of the two groups. Restore the average value to the previous value. The interval is used to obtain the final average value of the direction finding.

2. The method according to claim 1, characterized in that, In step 1, obtain The maximum value in the direction finding results and minimum value ,like and angular interval between If it is greater than the threshold T, then it is considered If the Nth direction finding result contains discontinuities, it is considered that the Nth direction finding result does not contain discontinuities.

3. The method according to claim 1, characterized in that, In step 3, the average of the mean of the un-periodic expansion group and the mean of the periodically expanded group is calculated to obtain... ,Will right The modulus value is taken to obtain the final average value of the direction finding. .

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