Angle of arrival preferred method and apparatus for statistical feature based short baseline monostatic positioning

Abstract

The application relates to an angle of arrival optimization method and device for short baseline single station positioning based on statistical characteristics, wherein the method comprises the following steps: obtaining an original estimation result data set corresponding to an angle of arrival of a target incoming wave signal, and performing two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result; determining a probability density peak value position in the probability density distribution result, extracting a main peak area corresponding to the probability density peak value position according to a preset neighborhood interval, and performing two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; according to the two-dimensional Gaussian fitting result and a preset confidence level, a confidence ellipse is framed, at least one angle of arrival estimation result in an original estimation result data set located in the confidence ellipse is extracted to construct an angle of arrival optimization data set, and the angle of arrival optimization data set is used for short baseline single station positioning operation. Thus, the problem that the angle of arrival estimation result is scattered and is prone to causing a dispersed positioning point in short baseline single station positioning is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of short wave reconnaissance, and particularly relates to an angle of arrival optimization method and device for short wave single station positioning based on statistical characteristics. BACKGROUND

[0002] The ionosphere is part of the atmosphere that is partially ionized, and the electron density thereof is sufficient to form reflection on a short wave radio signal to achieve the purpose of over-the-horizon transmission. Therefore, short wave signals often rely on the ionosphere to achieve over-the-horizon communication and detection. The reverse process is to estimate the angle of arrival of a short wave signal by means of an antenna array of a single reconnaissance station, and to combine ionosphere state information to perform radiation source positioning. This method is called single station positioning technology, and has important practical value in the fields of radiation source reconnaissance, electronic countermeasures, rescue and military.

[0003] At present, there are many calculation methods for the angle of arrival estimation in the short wave single station positioning technology, and the effectiveness of the methods has been verified in practice. However, due to the influence of short-time radio frequency interference, ionosphere channel random disturbance and noise, the angle measurement result is scattered due to the effects of colored noise and white noise, thereby causing a serious decrease in positioning accuracy.

[0004] To solve the above problems, the commonly used methods for angle optimization include clustering method, median filtering and mean filtering. However, the clustering method can remove the coarse error deviating from the true value caused by serious interference, but cannot effectively converge the scattering of the angle measurement result. The median filtering and mean filtering methods have good effects on white noise interference in Gaussian distribution, but cannot offset the overall angle measurement result caused by colored noise.

[0005] In summary, the existing technology cannot overcome the problem that the angle of arrival estimation result is scattered in the short wave single station positioning, and the positioning point is dispersed, which needs to be solved urgently. SUMMARY

[0006] The present application provides an angle of arrival optimization method and device for short wave single station positioning based on statistical characteristics, to solve the problem that the angle of arrival estimation result is scattered in the short wave single station positioning, and the positioning point is dispersed.

[0007] The first aspect embodiment of the present application provides a statistical characteristic-based short baseline single station positioning angle of arrival optimization method, comprising the following steps: based on a preset two-dimensional antenna array, obtaining an original estimation result data set corresponding to an angle of arrival of a target incoming wave signal, and performing two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result; determining a probability density peak value position in the probability density distribution result, and extracting a main peak region corresponding to the probability density peak value position in the probability density distribution result according to a preset neighborhood interval, and performing two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region; according to the two-dimensional Gaussian fitting result and a preset confidence level, a confidence ellipse is framed, and at least one angle of arrival estimation result in the original estimation result data set located in the confidence ellipse is extracted, and based on the at least one angle of arrival estimation result, an angle of arrival optimization data set is constructed, so that the angle of arrival optimization data set is used for short baseline single station positioning operation.

[0008] Optionally, in an embodiment of the present application, based on a preset two-dimensional antenna array, obtaining an original estimation result data set corresponding to an angle of arrival of a target incoming wave signal, and performing two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result, comprises: based on the two-dimensional antenna array and a preset two-dimensional angle of arrival estimation strategy, estimating the azimuth and elevation in the angle of arrival of the target incoming wave signal to obtain an azimuth-elevation pair; constructing the original estimation result data set according to the azimuth-elevation pair, and performing discrete statistics on the original estimation result data set to generate the probability density distribution result.

[0009] Optionally, in an embodiment of the present application, according to the two-dimensional Gaussian fitting result and a preset confidence level, a confidence ellipse is framed, and at least one angle of arrival estimation result in the original estimation result data set located in the confidence ellipse is extracted, and based on the at least one angle of arrival estimation result, an angle of arrival optimization data set is constructed, comprising: calculating a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculating a distribution inclination angle corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix; performing eigenvalue decomposition on the covariance matrix to obtain two eigenvalues of the covariance matrix, and calculating an azimuth axis and an elevation axis of the confidence ellipse based on the confidence level and the two eigenvalues to frame the confidence ellipse according to the azimuth axis and the elevation axis; based on a preset decision criterion, obtaining the at least one angle of arrival estimation result in the original estimation result data set located in the confidence ellipse to construct the angle of arrival optimization data set according to the at least one angle of arrival estimation result.

[0010] Optionally, in an embodiment of the present application, the mathematical expression of the decision criterion is:

[0011]

[0012] wherein (β0, θ0) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation pair corresponding to the target incoming wave signal angle of arrival; ψ represents the distribution inclination; and a represents the azimuth axis.

[0013] The second aspect embodiment of the present application provides a statistical feature-based short baseline monostatic positioning angle of arrival optimization device, comprising: a statistical module configured to obtain a raw estimation result dataset corresponding to the target incoming wave signal angle of arrival based on a preset two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the raw estimation result dataset to obtain a probability density distribution result; a fitting module configured to determine the peak position of the probability density distribution result, and extract a main peak region corresponding to the peak position of the probability density distribution result according to a preset neighborhood interval, and perform two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region; and an optimization module configured to frame a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, extract at least one angle of arrival estimation result in the raw estimation result dataset located in the confidence ellipse, and construct an angle of arrival optimization dataset based on the at least one angle of arrival estimation result, so as to perform a short baseline monostatic positioning operation by using the angle of arrival optimization dataset.

[0014] Optionally, in an embodiment of the present application, the statistical module comprises: an estimation unit configured to estimate the azimuth and the elevation in the target incoming wave signal angle of arrival based on the two-dimensional antenna array and a preset two-dimensional angle of arrival estimation strategy to obtain an azimuth-elevation pair; and a construction unit configured to construct the raw estimation result dataset according to the azimuth-elevation pair, and perform discrete statistics on the raw estimation result dataset to generate the probability density distribution result.

[0015] Optionally, in an embodiment of the present application, the optimization module comprises: a calculation unit configured to calculate a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate a distribution inclination corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix; an eigenvalue decomposition unit configured to perform eigenvalue decomposition on the covariance matrix to obtain two eigenvalues of the covariance matrix, and calculate an azimuth axis and an elevation axis of the confidence ellipse based on the confidence level and the two eigenvalues, so as to frame the confidence ellipse according to the azimuth axis and the elevation axis; and an acquisition unit configured to acquire the at least one angle of arrival estimation result in the raw estimation result dataset located in the confidence ellipse based on a preset judgment standard, so as to construct the angle of arrival optimization dataset according to the at least one angle of arrival estimation result.

[0016] Optionally, in an embodiment of the present application, the mathematical expression of the decision criterion is:

[0017]

[0018] wherein (β0, θ0) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation pair corresponding to the target incoming wave signal DOA; ψ represents the distribution dip angle; and a represents the azimuth axis.

[0019] A third aspect of the embodiments of the present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the statistical feature based DOA preferred method for short baseline monostatic positioning as described in the above embodiments.

[0020] A fourth aspect of the embodiments of the present application provides a computer readable storage medium, which stores a computer program executable by a processor to implement the statistical feature based DOA preferred method for short baseline monostatic positioning as described above.

[0021] A fifth aspect of the embodiments of the present application provides a computer program product comprising a computer program executable to implement the statistical feature based DOA preferred method for short baseline monostatic positioning as described above.

[0022] Therefore, the embodiments of the present application have the following beneficial effects:

[0023] The embodiments of the present application can obtain a raw estimation result dataset corresponding to the target incoming wave signal DOA based on a preset two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the raw estimation result dataset to obtain a probability density distribution result; determine the peak position of the probability density distribution result, and extract a main peak region corresponding to the peak position of the probability density distribution result according to a preset neighborhood interval, and perform two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region; frame a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, and extract at least one DOA estimation result in the raw estimation result dataset located within the confidence ellipse, and construct a DOA preferred dataset based on the at least one DOA estimation result, and use the DOA preferred dataset to perform a short baseline monostatic positioning operation. The embodiments of the present application filter out the angle measurement results affected by the colored noise interference and the measurement noise points greatly affected by the white noise by extracting the main peak region of the measurement angle probability density distribution and the range framing of the two-dimensional Gaussian fitting and the confidence ellipse, and obtain the preferred azimuth-elevation pair, thereby greatly reducing the dispersion range and improving the positioning accuracy. Thus, the embodiments of the present application solve the problems of large dispersion of the DOA estimation result and easy dispersion of the positioning point in the short baseline monostatic positioning.

[0024] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0025] The foregoing and / or additional aspects and advantages of the application are achieved by providing an embodiment of the application which comprises the features of the independent claims. The dependent claims define embodiments of the application which are considered to be within the scope of the application.

[0026] Figure 1 A schematic diagram of a basic verification scenario provided for an embodiment of the application;

[0027] Figure 2 A geometric relationship diagram of a basic verification scenario provided for an embodiment of the application;

[0028] Figure 3 A schematic diagram of a basic principle of DOA estimation of a incoming wave signal provided for an embodiment of the application;

[0029] Figure 4 A flow chart of a DOA preferred method of a statistical feature based short baseline single station positioning provided according to an embodiment of the application;

[0030] Figure 5 A schematic diagram of execution logic of a DOA preferred method of a statistical feature based short baseline single station positioning provided for an embodiment of the application;

[0031] Fig. 6(a) is a distribution diagram of a 10.4MHz original DOA estimation result provided for an embodiment of the application;

[0032] Fig. 6(b) is a distribution diagram of a 12.1MHz original DOA estimation result provided for an embodiment of the application;

[0033] Fig. 6(c) is a distribution diagram of a 10.2MHz original DOA estimation result provided for an embodiment of the application;

[0034] Fig. 7(a) is a schematic diagram of a probability density distribution of a 10.4MHz original DOA estimation result provided for an embodiment of the application;

[0035] Fig. 7(b) is a schematic diagram of a probability density distribution of a 12.1MHz original DOA estimation result provided for an embodiment of the application;

[0036] Fig. 7(c) is a schematic diagram of a probability density distribution of a 10.2MHz original DOA estimation result provided for an embodiment of the application;

[0037] FIG. 8(a) is a schematic diagram of a main peak area of a probability density of a 10.4 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0038] FIG. 8(b) is a schematic diagram of a main peak area of a probability density of a 12.1 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0039] FIG. 8(c) is a schematic diagram of a main peak area of a probability density of a 10.2 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0040] FIG. 9(a) is a schematic diagram of a two-dimensional Gaussian fitting result corresponding to a 10.4 MHz original angle of arrival estimation result, a confidence ellipse and an accepted angle selection result according to an embodiment of the present application;

[0041] FIG. 9(b) is a schematic diagram of a two-dimensional Gaussian fitting result corresponding to a 12.1 MHz original angle of arrival estimation result, a confidence ellipse and an accepted angle selection result according to an embodiment of the present application;

[0042] FIG. 9(c) is a schematic diagram of a two-dimensional Gaussian fitting result corresponding to a 10.2 MHz original angle of arrival estimation result, a confidence ellipse and an accepted angle selection result according to an embodiment of the present application;

[0043] FIG. 10(a) is a positioning scatter plot based on a 10.4 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0044] FIG. 10(b) is a positioning scatter plot based on a 10.4 MHz preferred angle of arrival estimation result according to an embodiment of the present application;

[0045] FIG. 10(c) is a positioning scatter plot based on a 12.1 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0046] FIG. 10(d) is a positioning scatter plot based on a 12.1 MHz preferred angle of arrival estimation result according to an embodiment of the present application;

[0047] FIG. 10(e) is a positioning scatter plot based on a 10.2 MHz original angle of arrival estimation result according to an embodiment of the present application;

[0048] FIG. 10(f) is a positioning scatter plot based on a 10.2 MHz preferred angle of arrival estimation result according to an embodiment of the present application;

[0049] Figure 11 FIG. 11 is a schematic diagram of an angle of arrival preferred device based on statistical characteristics of a short-range single station positioning according to an embodiment of the present application;

[0050] Figure 12 The structural schematic diagram of the electronic device provided by the embodiment of the application is provided.

[0051] Among them, 10 is an angle of arrival preferred device based on statistical characteristics of short single station positioning; 100 is a statistical module, 200 is a fitting module, and 300 is a preferred module; 1201 is a memory, 1202 is a processor, and 1203 is a communication interface. DETAILED DESCRIPTION

[0052] The embodiments of the application are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference signs represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the application, and cannot be understood as a limitation of the application.

[0053] The angle of arrival preferred method and device of short single station positioning based on statistical characteristics of the embodiments of the application are described below with reference to the accompanying drawings. In view of the problems mentioned in the above background art, the application provides an angle of arrival preferred method of short single station positioning based on statistical characteristics, in which, by means of a preset two-dimensional antenna array, a raw estimation result data set corresponding to the angle of arrival of the target incoming wave signal is obtained, and a two-dimensional probability density distribution of the raw estimation result data set is statistically analyzed to obtain a probability density distribution result. The position of the probability density peak value in the probability density distribution result is determined, and a main peak region corresponding to the position of the probability density peak value in the probability density distribution result is extracted according to a preset neighborhood interval, and a two-dimensional Gaussian fitting of the main peak region is performed to generate a two-dimensional Gaussian fitting result corresponding to the main peak region. According to the two-dimensional Gaussian fitting result and a preset confidence level, a confidence ellipse is framed, and at least one angle of arrival estimation result in the raw estimation result data set located within the confidence ellipse is extracted, and based on the at least one angle of arrival estimation result, an angle of arrival preferred data set is constructed to perform a short single station positioning operation by using the angle of arrival preferred data set. By extracting the main peak region of the measurement angle probability density distribution and the range framing of the two-dimensional Gaussian fitting and the confidence ellipse, the angle measurement results affected by the colored noise interference and the measurement noise points greatly affected by the white noise are filtered out in turn, and the preferred azimuth-elevation angle pair is obtained, so that the dispersion range is greatly reduced and the positioning accuracy is improved. Thus, the problem of large dispersion of the angle of arrival estimation result in short single station positioning, which easily leads to dispersion of the positioning point, is solved.

[0054] In order to facilitate the understanding of the execution logic of the angle of arrival preferred method of short single station positioning based on statistical characteristics of the application by those skilled in the art, the following describes and introduces the basic verification scene involved in the angle of arrival preferred method of short single station positioning based on statistical characteristics of the application.

[0055] Basic verification scene:

[0056] One basic verification scenario of the present application is shown in Figure 1 , which includes a transmitting station, a receiving station for ionospheric sounding and a receiving station based on array antenna at the same site. Among them, the transmitting station and the receiving station for ionospheric sounding constitute an ionospheric oblique sounding link, so as to obtain the ionospheric state and provide ionospheric environment information support for single station positioning; and the transmitting station and the receiving station based on array antenna constitute a verification link for angle of arrival estimation, so as to provide direction guidance for single station positioning by estimating the angle of arrival of the signal from the transmitting station. In actual execution process, ionospheric sounding and angle of arrival estimation can be performed in time division.

[0057] For the single station positioning scenario of the present application, the basic geometric relationship can be constructed as shown in Figure 2 , according to the coordinates of the transmitting station , wherein is the latitude of the transmitting station, and T is the longitude, and the corresponding coordinates of the receiving station are , then the great circle distance D of the transmitting station and the receiving station can be obtained as follows:

[0058]

[0059] The theoretical azimuth angle of the transmitting station relative to the receiving station should be:

[0060]

[0061] Further, according to the geometric relationship, the present application can obtain the relationship between the great circle distance and the signal propagation group distance P obtained by ionospheric sounding and the virtual height H of transmission:

[0062] D = P·sin(θ) = 2H / tan(θ) (3)

[0063] For the angle of arrival estimation, the present application needs to rely on the array antenna. A commonly used L-shaped antenna array is shown in Figure 3 , which has two baselines and has N and M array elements respectively. Assuming that there are k narrowband signals s i (t) (i = 1, …, k), the corresponding angles of arrival are (β1, θ1), (β2, θ2), …, (β k , θ k ), the present application can construct the steering vector of the array received signal as follows:

[0064]

[0065] a x (β i , θ i ) = [1, exp(j2πdxcosβ isinθ i / λ),…,exp(j2π(N-1)dxcosβ i sinθ i / λ)] T (5)

[0066] a Y (β i ,θ i )=[1,exp(j2πdysinβ i sinθ i / λ),…,exp(j2π(M-1)dysinβ i sinθ i / λ)] T (6)

[0067] in, represents the Knorr product.

[0068] Therefore, the present application can adopt a two-dimensional subspace decomposition-based arrival angle estimation technology to estimate the arrival angle of the incoming signal. For the L array, the following formula is obtained:

[0069]

[0070] Among them, E N is the signal matrix [s1(t),…,s k (t)] T The noise subspace.

[0071] Specifically, Figure 4 This is a flowchart of a method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics provided in an embodiment of the present application.

[0072] like Figure 4 As shown, the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics includes the following steps:

[0073] In step S401, based on a preset two-dimensional antenna array, an original estimation result data set corresponding to the arrival angle of the target incoming wave signal is obtained, and two-dimensional probability density distribution statistics are performed on the original estimation result data set to obtain a probability density distribution result.

[0074] Based on the above-mentioned typical working scenario, for a certain target incoming wave signal, the embodiment of the present application can first obtain the original estimation result data set of the arrival angle of the target incoming wave signal based on the two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the original estimation result data set of the arrival angle, thereby obtaining the probability density distribution result.

[0075] Optionally, in an embodiment of the present application, based on the preset two-dimensional antenna array, a raw estimation result data set corresponding to the target incoming wave signal angle of arrival is obtained, and two-dimensional probability density distribution statistics are performed on the raw estimation result data set to obtain a probability density distribution result, including: based on the two-dimensional antenna array and the preset two-dimensional angle of arrival estimation strategy, the azimuth and elevation of the target incoming wave signal angle of arrival are estimated to obtain an azimuth-elevation pair; the raw estimation result data set is constructed according to the azimuth-elevation pair, and the raw estimation result data set is discretized and statistically analyzed to generate the probability density distribution result.

[0076] It should be noted that the embodiments of the present application can use a two-dimensional antenna array and simultaneously estimate the azimuth and elevation of the incoming wave signal by using a two-dimensional angle of arrival estimation strategy to obtain an azimuth-elevation pair (β, θ), and construct a raw estimation result data set according to the azimuth-elevation pair. At the same time, the embodiments of the present application need to ensure that there is no long-term persistent colored noise on the measurement frequency point during the measurement period, otherwise the frequency point should be considered to be severely disturbed, and it is difficult to accurately estimate the target incoming wave angle of arrival at this time, so the frequency point should be abandoned.

[0077] After that, the embodiments of the present application also need to discretize and statistically analyze the raw estimation result data set, and its distribution function F(β i ,θ j ) is expressed as follows:

[0078]

[0079] Where P(β i ,θ j ) is the probability of the angle of arrival estimation result (β i ,θ j ), [β min ,β max ] is the azimuth estimation interval, [θ min ,θ max ] is the elevation estimation interval, and Δβ and Δθ are the discretization intervals of the probability density statistics of the azimuth and elevation, respectively, and their values should be greater than the azimuth and elevation resolution of the angle of arrival estimation.

[0080] Therefore, the embodiments of the present application do not need to improve the hardware performance and array antenna aperture of the angle of arrival estimation system, but only rely on the statistical characteristics of the measurement results to optimize the angle of arrival, thereby realizing effective convergence and improvement of positioning accuracy.

[0081] In step S402, the probability density peak position in the probability density distribution result is determined, and the main peak region corresponding to the probability density peak position in the probability density distribution result is extracted according to the preset neighborhood interval, and the main peak region is subjected to two-dimensional Gaussian fitting to generate a two-dimensional Gaussian fitting result corresponding to the main peak region.

[0082] Furthermore, if Figure 5 As shown, for the peak position of the probability density (β0, θ0), the embodiment of the present application also needs to specify the neighborhood size δ β and δ θ Extract the main peak area:

[0083]

[0084] Afterwards, the embodiment of the present application may perform a normalized two-dimensional Gaussian fitting on the probability density distribution of the main peak region according to the following formula:

[0085]

[0086] Among them, (σ β ,σ θ ) is the variance of the azimuth and elevation axes, σ βθ is the covariance.

[0087] Therefore, the embodiment of the present application judges the maximum value of the probability density, extracts its main peak area with a neighborhood interval, and performs two-dimensional Gaussian fitting on the main peak area, so as to simultaneously filter out the measurement error points caused by short-term colored noise and the large deviation points caused by white noise.

[0088] In step S403, a confidence ellipse is framed according to the two-dimensional Gaussian fitting result and the preset confidence level, and at least one arrival angle estimation result located within the confidence ellipse in the original estimation result dataset is extracted. Based on the at least one arrival angle estimation result, an arrival angle preferred dataset is constructed to perform shortwave single-station positioning operations using the arrival angle preferred dataset.

[0089] Furthermore, the embodiments of the present application can set the confidence level and frame a confidence ellipse based on the two-dimensional Gaussian fitting results to extract all arrival angle estimation results distributed within the confidence ellipse and construct the corresponding arrival angle preferred data set (i.e., the final preferred result).

[0090] Therefore, the embodiment of the present application uses the probability density distribution statistics method to extract the main peak area of ​​the probability density of the original arrival angle estimation result data set to filter out short-time colored noise interference, and performs angle optimization through two-dimensional Gaussian fitting and confidence ellipse framing based on the confidence level to filter out coarse error scatter points with large white noise interference, thereby obtaining a converged arrival angle optimization data set, and using this angle optimization result to perform shortwave single-station positioning to greatly reduce the dispersion range, thereby improving positioning accuracy.

[0091] Optionally, in an embodiment of the present application, the confidence ellipse is framed according to the two-dimensional Gaussian fitting result and the preset confidence level, and at least one angle of arrival estimation result in the original estimation result data set located in the confidence ellipse is extracted, and based on the at least one angle of arrival estimation result, the angle of arrival preferred data set is constructed, including: calculating the covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculating the distribution dip angle corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix; performing eigenvalue decomposition on the covariance matrix to obtain two eigenvalues of the covariance matrix, and calculating the azimuth axis and the elevation axis of the confidence ellipse based on the confidence level and the two eigenvalues to frame the confidence ellipse according to the azimuth axis and the elevation axis; obtaining at least one angle of arrival estimation result in the original estimation result data set located in the confidence ellipse based on the preset decision criterion, to construct the angle of arrival preferred data set according to the at least one angle of arrival estimation result.

[0092] In the process of specific implementation, the embodiments of the present application can also calculate the covariance matrix of the Gaussian fitting result of the two-dimensional probability density of the angle of arrival estimation result, as shown in the following formula:

[0093]

[0094] Therefore, the distribution dip angle can be calculated:

[0095]

[0096] And the eigenvalue decomposition is performed on the covariance matrix, and then two eigenvalues λ β and λ θ of the covariance matrix can be obtained; and according to the specified confidence level η, the azimuth axis and the elevation axis of the confidence ellipse are respectively:

[0097]

[0098] Therefore, the confidence ellipse can be framed:

[0099]

[0100] After that, the embodiments of the present application can obtain the angle of arrival estimation result in the original estimation result data set located in the confidence ellipse according to the preset decision criterion, to construct the angle of arrival preferred data set.

[0101] Optionally, in an embodiment of the present application, the mathematical expression of the decision criterion is:

[0102]

[0103] Wherein, (β0, θ0) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation pair corresponding to the angle of arrival of the target incoming wave signal; ψ represents the distribution dip angle; and a represents the azimuth axis.

[0104] It should be noted that the decision criterion of the application embodiment for constructing the angle of arrival preferred data set is shown in the following formula:

[0105]

[0106] Wherein, (β0, θ0) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation pair corresponding to the target incoming wave signal angle of arrival; ψ represents the distribution inclination; a represents the azimuth axis.

[0107] In addition, the embodiments of the application can also adjust the confidence level flexibly to determine the strictness of the angle preference, thereby achieving a balance between real-time and the strictness of the dispersion constraint of the estimation result.

[0108] The execution logic and effects of the angle of arrival preference method of the statistical feature-based short single station positioning of the application are described below through a specific embodiment and in conjunction with the accompanying drawings.

[0109] In a specific embodiment of the application, an actual observation instance is: when the transceiver stations are located at (114.37°E, 30.54°N) and (120.95°E, 31.50°N) respectively, N=M=9 is taken, 3200, 2269 and 2869 effective angle of arrival estimation results of 10.4, 12.1 and 10.2 MHz signals respectively obtained in three time periods of August 15, 2022, 08:42-08:54, 08:57-09:06 and 09:27-09:37, with a resolution of 0.1°, their distributions are shown in FIG. 6(a), FIG. 6(b) and FIG. 6(c) respectively, although the angle measurement results of the 12.1 MHz signal have a large dispersion range, they still show a central divergence pattern. The difference is that the 10.4 and 10.2 MHz signals are obviously divided into multiple families; for the 10.4 MHz signal, it can be roughly divided into three clusters, respectively, the azimuth angle is distributed in [262°, 265°], the elevation angle is distributed in [21°, 22°]; the azimuth angle is [263°, 265°], the elevation angle is [22°, 23°], the azimuth angle is [264°, 266.5°], and the elevation angle is [23°, 25°]; similarly, the angle of arrival of the 10.2 MHz signal can also be divided into four groups according to the elevation angle, respectively, [19°, 20°], [20°, 21°], [21°, 22°] and [22°, 23°], when the hardware platform remains the same, this grouping dispersion can be regarded as a kind of colored noise interference.

[0110] After calculating their respective probability density distributions, the results shown in FIG. 7(a), FIG. 7(b) and FIG. 7(c) can be obtained, obviously, they all have a single peak structure, indicating that the colored noise causing interference is short-term.

[0111] Therefore, the main peak region of the peak point neighborhood 2° of the embodiments of the present application is shown in FIG. 8(a), FIG. 8(b) and FIG. 8(c) respectively, and it can be found that they all have similar dispersion characteristics with Gaussian distribution.

[0112] Then, the embodiments of the present application perform two-dimensional Gaussian fitting on the respective main peak regions, and when the confidence level is 0.9, the confidence ellipses and the preferred angles framed thereby are shown in FIG. 9(a), FIG. 9(b) and FIG. 9(c) respectively. For the three frequencies, the number of effective preferred points in the confidence interval is 138, 123 and 238 respectively, accounting for 4.31%, 5.43% and 8.3% of the respective initial estimates.

[0113] In order to obtain the ionospheric characteristics in the measurement period, the embodiments of the present application perform two ionospheric oblique measurements at 08:36 and 09:16 respectively, and the oblique ionospheric maps are shown in FIG. 10(a), FIG. 10(b), FIG. 10(c), FIG. 10(d), FIG. 10(e) and FIG. 10(f) respectively. It can be seen that the three frequencies are all reflected and propagated through the Es layer at this time, and the reflected virtual height of the 10.2, 10.4 MHz signal is 119.61 km, and the reflected virtual height of the 12.1 MHz signal is 114.04 km. The corresponding theoretical elevation angles are 20.61° and 19.72° respectively. In combination with the theoretical azimuth angle of the transmitting station relative to the receiving station being 262° (with the north direction as the initial and the clockwise direction as the positive direction), the root mean square error (RMSE) comparison results of the preferred pre- and post-arrival angle estimation results are shown in Table 1:

[0114] Table 1

[0115]

[0116] From Table 1, it can be seen that β or and θ or represent the azimuth and elevation angles before optimization, and β opt and θ opt represent the azimuth and elevation angles after optimization. In comparison, the RMSE of the azimuth angle is improved by 0.81°, 0.25° and 1.28° before and after optimization, and the RMSE of the elevation angle is improved by 0.79°, 1.03° and 0.90°.

[0117] Finally, based on the arrival angle measurement and the optimization results thereof, in combination with the ionospheric state observation information, the positioning results before and after optimization can be obtained, and the positioning result statistics table is shown in Table 2:

[0118] Table 2

[0119]

[0120] As shown in Table 2, the statistical positioning error is ΔD, the relative error is defined as δ, δ or ,δ opt are the relative errors before and after optimization respectively, and the standard deviations of the positioning errors are denoted as STD(ΔD or ) and STD(ΔD opt ) respectively; it can be seen from Table 2 that after the angle of arrival is optimized, the positioning point dispersion is effectively converged, and the positioning accuracy is obviously improved, the error standard deviations of the three frequencies are improved by 22.94 km, 14.53 km and 91.87 km respectively, and the relative positioning error is also obviously improved, as shown in the following formula, and the accuracy is improved by about 3%.

[0121]

[0122] Therefore, for the problem of large dispersion of the angle of arrival estimation result in short-range single station positioning, which leads to the dispersion of the positioning point, the embodiments of the present application filter out the angle measurement results affected by the colored noise interference and the measurement noise points with large deviation affected by the white noise in sequence by extracting the main peak area of the measured angle probability density distribution and the range framing of the two-dimensional Gaussian fitting and the confidence ellipse, to obtain the optimized azimuth-elevation pair, and it is confirmed by the experimental scene and the experimental measurement data that the dispersion of the angle of arrival estimation result is significantly inhibited, and correspondingly, the positioning accuracy is also significantly improved by about 3%, thereby it is proved that the embodiments of the present application have important significance and application prospect for improving the positioning accuracy of fixed targets or slow-moving targets.

[0123] The angle of arrival optimization method for short-range single station positioning based on statistical characteristics according to the embodiments of the present application obtains the original estimation result data set corresponding to the angle of arrival of the target incoming wave signal based on the preset two-dimensional antenna array, and performs two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result; the probability density peak position in the probability density distribution result is determined, and the main peak area corresponding to the probability density peak position in the probability density distribution result is extracted according to the preset neighborhood interval, and the main peak area is subjected to two-dimensional Gaussian fitting to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; a confidence ellipse is framed according to the two-dimensional Gaussian fitting result and the preset confidence level, and at least one angle of arrival estimation result located within the confidence ellipse in the original estimation result data set is extracted, and an angle of arrival optimization data set is constructed based on the at least one angle of arrival estimation result, so as to perform a short-range single station positioning operation by using the angle of arrival optimization data set. By extracting the main peak area of the measured angle probability density distribution and the range framing of the two-dimensional Gaussian fitting and the confidence ellipse, the embodiments of the present application filter out the angle measurement results affected by the colored noise interference and the measurement noise points with large deviation affected by the white noise in sequence, to obtain the optimized azimuth-elevation pair, thereby greatly reducing the dispersion range and improving the positioning accuracy.

[0124] Secondly, the preferred device of the angle of arrival of the statistical feature-based short baseline single station positioning according to the embodiments of the present application is described with reference to the drawings.

[0125] Figure 11 is the block schematic diagram of the preferred device of the angle of arrival of the statistical feature-based short baseline single station positioning according to the embodiments of the present application.

[0126] As shown in the figure, the preferred device of the angle of arrival of the statistical feature-based short baseline single station positioning 10 comprises a statistical module 100, a fitting module 200 and a preferred module 300. Figure 11

[0127] The statistical module 100 is configured to obtain a raw estimation result dataset corresponding to the angle of arrival of the target incoming wave signal based on a preset two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the raw estimation result dataset to obtain a probability density distribution result.

[0128] The fitting module 200 is configured to determine the position of the probability density peak in the probability density distribution result, extract a main peak region corresponding to the position of the probability density peak in the probability density distribution result according to a preset neighborhood interval, and perform two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region.

[0129] The preferred module 300 is configured to frame a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, extract at least one angle of arrival estimation result in the raw estimation result dataset located within the confidence ellipse, and construct an angle of arrival preferred dataset based on the at least one angle of arrival estimation result, so as to perform a short baseline single station positioning operation by using the angle of arrival preferred dataset.

[0130] Optionally, in an embodiment of the present application, the statistical module 100 comprises an estimation unit and a construction unit.

[0131] The estimation unit is configured to estimate the azimuth and elevation in the angle of arrival of the target incoming wave signal based on the two-dimensional antenna array and a preset two-dimensional angle of arrival estimation strategy to obtain an azimuth-elevation pair.

[0132] The construction unit is configured to construct the raw estimation result dataset according to the azimuth-elevation pair, and perform discretization statistics on the raw estimation result dataset to generate the probability density distribution result.

[0133] Optionally, in an embodiment of the present application, the preferred module 300 comprises a calculation unit, an eigenvalue decomposition unit and an acquisition unit.

[0134] The calculation unit is configured to calculate a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate a distribution dip angle corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix. ​

[0135] an eigenvalue decomposition unit configured to perform eigenvalue decomposition on the covariance matrix to obtain two eigenvalues of the covariance matrix, and calculate an azimuth axis and an elevation axis of a confidence ellipse based on the confidence level and the two eigenvalues to frame the confidence ellipse according to the azimuth axis and the elevation axis.

[0136] an acquisition unit configured to acquire at least one angle of arrival estimation result in the original estimation result dataset within the confidence ellipse based on a preset decision criterion, and construct an angle of arrival preferred dataset according to the at least one angle of arrival estimation result.

[0137] Optionally, in an embodiment of the present application, the mathematical expression of the decision criterion is:

[0138]

[0139] wherein (β0, θ0) represents the probability density peak position; (β, θ) represents the azimuth-elevation pair corresponding to the angle of arrival of the target incoming wave signal; ψ represents the distribution inclination angle; and a represents the azimuth axis.

[0140] It should be noted that the aforementioned explanation and description of the embodiment of the angle of arrival preferred method for statistical feature-based short baseline single station positioning also applies to the embodiment of the angle of arrival preferred device for statistical feature-based short baseline single station positioning, which will not be described here again.

[0141] The angle of arrival preferred device for statistical feature-based short baseline single station positioning according to the embodiment of the present application comprises a statistical module 100 configured to acquire an original estimation result dataset corresponding to the angle of arrival of the target incoming wave signal based on a preset two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the original estimation result dataset to obtain a probability density distribution result; a fitting module 200 configured to determine the probability density peak position in the probability density distribution result, extract a main peak region corresponding to the probability density peak position in the probability density distribution result according to a preset neighborhood interval, and perform two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region; and a preferred module 300 configured to frame a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, extract at least one angle of arrival estimation result in the original estimation result dataset within the confidence ellipse, and construct an angle of arrival preferred dataset based on the at least one angle of arrival estimation result to perform a short baseline single station positioning operation by using the angle of arrival preferred dataset. The main peak region of the measurement angle probability density distribution and the range framing of the two-dimensional Gaussian fitting and the confidence ellipse are extracted in the present application, and the angle measurement results affected by the colored noise interference and the measurement noise points greatly affected by the white noise are filtered out in sequence, so that the preferred azimuth-elevation pair is obtained, thereby greatly reducing the dispersion range and improving the positioning accuracy.

[0142] Figure 12A structural schematic diagram of an electronic device is provided for an embodiment of the present application. The electronic device can include

[0143] The memory 1201, the processor 1202 and the computer program stored in the memory 1201 and executable on the processor 1202.

[0144] The processor 1202 implements the angle of arrival preferred method of the statistical characteristic-based short-range single station positioning provided in the above embodiments when executing the program.

[0145] Further, the electronic device further includes

[0146] The communication interface 1203 is used for communication between the memory 1201 and the processor 1202.

[0147] The memory 1201 is used for storing the computer program executable on the processor 1202.

[0148] The memory 1201 can include a high-speed RAM memory, and can also include a non-volatile memory, for example, at least one disk memory.

[0149] If the memory 1201, the processor 1202 and the communication interface 1203 are independently implemented, the communication interface 1203, the memory 1201 and the processor 1202 can be connected to each other through a bus and complete communication between each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 12 Only one thick line is used in the middle, but it does not mean that there is only one bus or one type of bus.

[0150] Optionally, in a specific implementation, if the memory 1201, the processor 1202 and the communication interface 1203 are integrated on a chip, the memory 1201, the processor 1202 and the communication interface 1203 can complete communication between each other through an internal interface.

[0151] The processor 1202 can be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or a plurality of integrated circuits configured to implement one or more embodiments of the present application.

[0152] The embodiments of the present application further provide a computer readable storage medium, which has stored a computer program, and the computer program is executed by a processor to implement the above-mentioned statistical feature based short baseline monostatic positioning angle of arrival optimization method.

[0153] The embodiments of the present application further provide a computer program product, which comprises a computer program, and the computer program is executed to implement the above-mentioned statistical feature based short baseline monostatic positioning angle of arrival optimization method.

[0154] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in one or N embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present application and the features of the different embodiments or examples without contradiction.

[0155] In addition, the terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "N" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0156] Any process or method descriptions in flow charts or described elsewhere herein can be understood as representing one or N executable instructions, code segments, or portions of computer readable code that include the steps for implementing the custom logic function or process, and the scope of the preferred embodiments of the present application includes additional implementation involving other processes or methods that can be performed according to the claimed application, either manually, as a separate process, or in combination with any other process or method steps, in an order different than that shown or discussed, including substantially concurrently or in reverse order, as appropriate, which will be understood by those skilled in the art.

[0157] The logic and / or steps represented in the flowcharts and / or described herein, for example, can be considered as a sequence of instructions to implement logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device, such as a computer-based system, processor- based system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For purposes of this specification, a "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be a computer- readable storage medium or a computer-readable signal medium. The computer- readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include the following: an electrical connection having one or more wires (electrical connections), a portable computer diskette (a magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via, for example, optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.

[0158] It should be understood that aspects of the application can be implemented in hardware, software, firmware or combinations thereof. In the above embodiments, the N steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented in hardware and in another embodiment, any of the following technologies, known in the art, or their combinations can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), etc.

[0159] Those skilled in the art can understand that all or part of the steps carried out by the above-mentioned embodiment methods can be completed by programs instructing related hardware, and the programs can be stored in a computer-readable storage medium. When the programs are executed, one or a combination of the steps of the method embodiments is included.

[0160] In addition, each of the functional units in the various embodiments of the present application can be integrated in one processing module, or each of the units can be physically present separately, or two or more units can be integrated in one module. The integrated module can be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer readable storage medium.

[0161] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

Claims

1. A method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics, characterized in that: The following steps are involved: Based on a preset two-dimensional antenna array, an original estimation result data set corresponding to the arrival angle of the target incoming wave signal is obtained, and two-dimensional probability density distribution statistics are performed on the original estimation result data set to obtain a probability density distribution result; Determine the probability density peak position in the probability density distribution result, extract the main peak area corresponding to the probability density peak position in the probability density distribution result according to a preset neighborhood interval, and perform a two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; A confidence ellipse is defined according to the two-dimensional Gaussian fitting result and a preset confidence level, and at least one arrival angle estimation result located within the confidence ellipse in the original estimation result dataset is extracted. Based on the at least one arrival angle estimation result, an arrival angle preferred dataset is constructed to perform shortwave single-station positioning operations using the arrival angle preferred dataset.

2. The method according to claim 1, characterized in that The method of obtaining an original estimation result data set corresponding to the arrival angle of the target incoming wave signal based on a preset two-dimensional antenna array, and performing two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result includes: Based on the two-dimensional antenna array and a preset two-dimensional arrival angle estimation strategy, estimating the azimuth and elevation angles of the arrival angle of the target incoming signal to obtain an azimuth-elevation angle pair; The original estimation result data set is constructed according to the azimuth-elevation angle pairs, and discretization statistics are performed on the original estimation result data set to generate the probability density distribution result.

3. The method according to claim 2, characterized in that The step of defining a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, extracting at least one angle of arrival estimation result located within the confidence ellipse from the original estimation result dataset, and constructing an angle of arrival optimization dataset based on the at least one angle of arrival estimation result, includes: Calculating a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculating a distribution inclination angle corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix; Performing eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculating an azimuth axis and an elevation axis of the confidence ellipse based on the confidence level and the two eigenvalues, so as to frame the confidence ellipse according to the azimuth axis and the elevation axis; Based on a preset decision criterion, the at least one arrival angle estimation result located within the confidence ellipse in the original estimation result dataset is obtained, so as to construct the arrival angle preferred dataset according to the at least one arrival angle estimation result.

4. The method according to claim 3, characterized in that The mathematical expression of the judgment criterion is: Wherein, (β0,θ0) represents the probability density peak position; (β,θ) represents the azimuth-elevation angle pair corresponding to the arrival angle of the target incoming signal; ψ represents the distribution inclination; and a represents the azimuth axis.

5. An arrival angle optimization device for shortwave single-station positioning based on statistical characteristics, characterized in that: include: A statistics module is used to obtain an original estimation result data set corresponding to the arrival angle of the target incoming wave signal based on a preset two-dimensional antenna array, and perform two-dimensional probability density distribution statistics on the original estimation result data set to obtain a probability density distribution result; a fitting module, configured to determine a probability density peak position in the probability density distribution result, extract a main peak region corresponding to the probability density peak position in the probability density distribution result according to a preset neighborhood interval, and perform a two-dimensional Gaussian fitting on the main peak region to generate a two-dimensional Gaussian fitting result corresponding to the main peak region; The optimization module is used to frame a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, and extract at least one arrival angle estimation result located within the confidence ellipse in the original estimation result data set, and construct an arrival angle optimization data set based on the at least one arrival angle estimation result, so as to use the arrival angle optimization data set to perform shortwave single-station positioning operations.

6. The device according to claim 5, characterized in that The statistics module includes: an estimating unit, configured to estimate the azimuth and elevation angles of the arrival angle of the target incoming signal based on the two-dimensional antenna array and a preset two-dimensional arrival angle estimation strategy to obtain an azimuth-elevation angle pair; A construction unit is used to construct the original estimation result data set according to the azimuth-elevation angle pair, and perform discretization statistics on the original estimation result data set to generate the probability density distribution result.

7. The device according to claim 6, characterized in that The preferred modules include: a calculation unit, configured to calculate a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate a distribution inclination angle corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix; an eigenvalue decomposition unit, configured to perform eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculate an azimuth axis and an elevation axis of the confidence ellipse based on the confidence level and the two eigenvalues, so as to frame the confidence ellipse according to the azimuth axis and the elevation axis; An acquisition unit is configured to acquire, based on a preset decision criterion, the at least one arrival angle estimation result located within the confidence ellipse in the original estimation result dataset, so as to construct the arrival angle preferred dataset according to the at least one arrival angle estimation result.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics as described in any one of claims 1 to 4.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics as described in any one of claims 1 to 4.

10. A computer program product comprising a computer program, characterized in that The computer program is executed to implement the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics as described in any one of claims 1 to 4.

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