Arrival angle optimization method and device for short-wave single-station positioning based on statistical characteristics

Abstract

The invention relates to an arrival angle optimization method and device for short-wave single-station positioning based on statistical characteristics, and the method comprises the steps: obtaining an original estimation result data set corresponding to a target incoming wave signal arrival angle, and carrying out the two-dimensional probability density distribution statistics of the original estimation result data set, so as to obtain a probability density distribution result; determining a probability density peak value position in the probability density distribution result, extracting a main peak region corresponding to the probability density peak value position 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; and framing a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, and extracting at least one arrival angle estimation result in the confidence ellipse in the original estimation result data set to construct an arrival angle optimal data set, and performing short-wave single-station positioning operation by using the arrival angle optimal data set. Therefore, the problem that positioning points are dispersed easily due to large distribution of the estimation results of the angle of arrival in short-wave single-station positioning is solved.

Description

Technical Field

[0001] The present application relates to the technical field of shortwave detection, and in particular to a method and device for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics. Background Art

[0002] The ionosphere is a layer of the Earth's atmosphere that is partially ionized and has an electron density sufficient to reflect shortwave radio signals and achieve beyond-horizon transmission. Therefore, shortwave signals often use the ionosphere to achieve beyond-horizon communication and detection. The reverse process is to rely on the antenna array of a single receiving station to estimate the arrival angle of the shortwave signal and locate the radiation source in combination with the ionospheric state information. This method is called single-station positioning technology, which has important practical value in radiation source detection, electronic countermeasures, rescue, military and other fields.

[0003] At present, there are many calculation methods for arrival angle estimation in shortwave single-station positioning technology and their effectiveness has been verified in practice. However, due to the influence of short-term radio frequency interference and random disturbance and noise of the ionospheric channel, the angle measurement results are greatly scattered due to the effects of colored noise and white noise, which will lead to a serious decrease in positioning accuracy.

[0004] To solve the above problems, currently common methods include clustering, median, and mean filtering to optimize the angle. However, the clustering method removes the gross errors that are far from the true value due to severe interference, and cannot effectively converge the distribution of the angle measurement results. The median and mean filtering methods have a good effect on white noise interference with Gaussian distribution, but cannot eliminate the overall deviation of the angle measurement results caused by colored noise.

[0005] In summary, the existing technology is difficult to overcome the problem of large dispersion of arrival angle estimation results in shortwave single-station positioning, which leads to dispersion of positioning points, and it is urgent to solve this problem. Summary of the invention

[0006] The present application provides a method and device for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics, so as to solve the problem that the angle of arrival estimation results in shortwave single-station positioning are widely scattered, which easily leads to the dispersion of positioning points.

[0007] The first aspect of the present application provides an arrival angle optimization method for shortwave single-station positioning based on statistical characteristics, comprising the following steps: based on a preset two-dimensional antenna array, obtaining an original estimation result data set corresponding to the arrival angle 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 position in the probability density distribution result, and extracting a main peak area corresponding to the probability density peak position in the probability density distribution result 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; defining a confidence ellipse according to the two-dimensional Gaussian fitting result and a preset confidence level, extracting at least one arrival angle estimation result in the original estimation result data set that is within the confidence ellipse, and constructing 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 a shortwave single-station positioning operation.

[0008] Optionally, in one embodiment of the present application, based on a preset two-dimensional antenna array, an original estimation result data set corresponding to the target incoming signal arrival angle 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, including: based on the two-dimensional antenna array and a preset two-dimensional arrival angle estimation strategy, the azimuth and elevation angle in the arrival angle of the target incoming signal are estimated to obtain an azimuth-elevation pair; the original estimation result data set is constructed according to the azimuth-elevation pair, and discretization statistics are performed on the original estimation result data set to generate the probability density distribution result.

[0009] Optionally, in one embodiment of the present application, a confidence ellipse is framed 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 data set is extracted, and an arrival angle preferred data set is constructed based on the at least one arrival angle estimation result, including: calculating a covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculating a distribution inclination corresponding to the two-dimensional Gaussian fitting result based on the covariance matrix; performing eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculating the azimuth axis and 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 judgment criterion, at least one arrival angle estimation result located within the confidence ellipse in the original estimation result data set is obtained, so as to construct the arrival angle preferred data set based on the at least one arrival angle estimation result.

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

[0011]

[0012] Among them, (β 0 ,θ 0 ) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation angle pair corresponding to the arrival angle of the target incoming signal; ψ represents the distribution inclination; a represents the azimuth axis.

[0013] The second aspect of the present application provides an arrival angle optimization device for shortwave single-station positioning based on statistical characteristics, including: a statistical module, which is used to obtain an original estimation result data set corresponding to the arrival angle of a 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, which is used to determine the probability density peak position in the probability density distribution result, and 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 two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; a optimization module, which 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 in the original estimation result data set that is located within the confidence ellipse, and based on the at least one arrival angle estimation result, construct an arrival angle optimization data set to perform a shortwave single-station positioning operation using the arrival angle optimization data set.

[0014] Optionally, in one embodiment of the present application, the statistical module includes: an estimation unit, used to estimate the azimuth and elevation of the target incoming signal arrival angle based on the two-dimensional antenna array and a preset two-dimensional arrival angle estimation strategy to obtain an azimuth-elevation pair; a construction unit, used to construct the original estimation result data set based on the azimuth-elevation pair, and perform discretization statistics on the original estimation result data set to generate the probability density distribution result.

[0015] Optionally, in one embodiment of the present application, the preferred module includes: a calculation unit, used to calculate the covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate the distribution inclination corresponding to the two-dimensional Gaussian fitting result based on the covariance matrix; an eigenvalue decomposition unit, used to perform eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculate the azimuth axis and 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, used to acquire the at least one arrival angle estimation result located within the confidence ellipse in the original estimation result data set based on a preset judgment criterion, so as to construct the arrival angle preferred data set based on the at least one arrival angle estimation result.

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

[0017]

[0018] Among them, (β 0 ,θ 0 ) represents the peak position of the probability density; (β, θ) represents the azimuth-elevation angle pair corresponding to the arrival angle of the target incoming signal; ψ represents the distribution inclination; a represents the azimuth axis.

[0019] The third aspect 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 method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics as described in the above embodiment.

[0020] The fourth aspect of the present application provides a computer-readable storage medium, which stores a computer program. When the program is executed by a processor, it implements the above-mentioned method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics.

[0021] The fifth aspect of the present application provides a computer program product, including a computer program, which is executed to implement the above-mentioned method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics.

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

[0023] The embodiment of the present application can obtain the 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 the probability density distribution result; determine the probability density peak position in the probability density distribution result, and extract the main peak area corresponding to the probability density peak position in the probability density distribution result according to the preset neighborhood interval, and perform two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; frame the confidence ellipse according to the two-dimensional Gaussian fitting result and the preset confidence level, and extract at least one arrival angle estimation result in the original estimation result data set that is located within the confidence ellipse, and based on at least one arrival angle estimation result, construct an arrival angle optimization data set to use the arrival angle optimization data set for shortwave single-station positioning operations. The present application extracts the main peak area of ​​the measurement angle probability density distribution and frames the range of the two-dimensional Gaussian fitting and the confidence ellipse, and successively filters out the angle measurement results affected by the interference of colored noise and the measurement noise points with large deviations due to the action of white noise, and obtains the optimized azimuth-elevation angle pair, thereby greatly reducing the dispersion range and improving the positioning accuracy. This solves the problem that the arrival angle estimation results in shortwave single-station positioning are widely scattered, which easily leads to the dispersion of positioning points.

[0024] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

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

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

[0028] Figure 3 A schematic diagram of the basic principle of an incoming signal arrival angle estimation provided for an embodiment of the present application;

[0029] Figure 4 A flowchart of a method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics provided according to an embodiment of the present application;

[0030] Figure 5 A schematic diagram of the execution logic of a method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics provided in one embodiment of the present application;

[0031] FIG6( a ) is a distribution diagram of 10.4 MHz original arrival angle estimation results provided by an embodiment of the present application;

[0032] FIG6( b ) is a distribution diagram of 12.1 MHz original arrival angle estimation results provided by an embodiment of the present application;

[0033] FIG6( c ) is a distribution diagram of 10.2 MHz original arrival angle estimation results provided by an embodiment of the present application;

[0034] FIG. 7( a ) is a schematic diagram of a probability density distribution of a 10.4 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0035] FIG7( b ) is a schematic diagram of probability density distribution of a 12.1 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0036] FIG7( c ) is a schematic diagram of probability density distribution of a 10.2 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0037] FIG8( a ) is a schematic diagram of a main peak region of a probability density of a 10.4 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0038] FIG8( b ) is a schematic diagram of a main peak region of a probability density of a 12.1 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0039] FIG8( c ) is a schematic diagram of a main peak region of a probability density of a 10.2 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0040] FIG9( a ) is a schematic diagram of a two-dimensional Gaussian fitting result and a confidence ellipse and an acceptance angle selection result corresponding to a 10.4 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0041] FIG9( b ) is a schematic diagram of a two-dimensional Gaussian fitting result and a confidence ellipse and an acceptance angle selection result corresponding to a 12.1 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0042] FIG9( c ) is a schematic diagram of a two-dimensional Gaussian fitting result and a confidence ellipse and an acceptance angle selection result corresponding to a 10.2 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0043] FIG10( a ) is a positioning scatter plot based on 10.4 MHz original arrival angle estimation results provided by an embodiment of the present application;

[0044] FIG10( b ) is a positioning scatter plot based on a 10.4 MHz preferred angle of arrival estimation result provided by an embodiment of the present application;

[0045] FIG10( c ) is a positioning scatter plot based on 12.1 MHz original arrival angle estimation results provided by an embodiment of the present application;

[0046] FIG10( d ) is a positioning scatter plot based on a 12.1 MHz preferred angle of arrival estimation result provided by an embodiment of the present application;

[0047] FIG10( e ) is a positioning scatter plot based on the 10.2 MHz original arrival angle estimation result provided by an embodiment of the present application;

[0048] FIG10( f ) is a positioning scatter plot based on a 10.2 MHz preferred arrival angle estimation result provided by an embodiment of the present application;

[0049] Fig.11 This is an exemplary diagram of an arrival angle optimization device for shortwave single-station positioning based on statistical characteristics according to an embodiment of the present application;

[0050] Fig.12 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

[0051] Among them, 10-arrival angle optimization device for shortwave single-station positioning based on statistical characteristics; 100-statistical module, 200-fitting module, 300-optimization module; 1201-memory, 1202-processor, 1203-communication interface. DETAILED DESCRIPTION

[0052] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0053] The following describes the angle of arrival optimization method and device for shortwave single-station positioning based on statistical features of the embodiment of the present application with reference to the accompanying drawings. In response to the problems mentioned in the above background technology, the present application provides an angle of arrival optimization method for shortwave single-station positioning based on statistical features, in which the original estimation result data set corresponding to the angle of arrival of the target incoming wave signal is obtained based on a preset two-dimensional antenna array, and the original estimation result data set is subjected to two-dimensional probability density distribution statistics 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 a preset neighborhood interval, and a two-dimensional Gaussian fitting is performed on the main peak area 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 a preset confidence level, and at least one angle of arrival estimation result in the original estimation result data set that is within the confidence ellipse is extracted, and based on at least one angle of arrival estimation result, an angle of arrival optimization data set is constructed to perform a shortwave single-station positioning operation using the angle of arrival optimization data set. This application extracts the main peak area of ​​the probability density distribution of the measurement angle, and the range of the two-dimensional Gaussian fitting and the confidence ellipse, and successively filters out the angle measurement results affected by the interference of colored noise and the measurement noise points with large deviations due to the action of white noise, and obtains the optimized azimuth-elevation angle pair, thereby greatly reducing the dispersion range and improving the positioning accuracy. In this way, the problem of large dispersion of the arrival angle estimation results in shortwave single-station positioning is solved, which easily leads to the dispersion of positioning points.

[0054] In order to facilitate those skilled in the art to understand the execution logic of the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics of the present application, the basic verification scenarios involved in the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics of the present application are explained and introduced as follows.

[0055] Basic verification scenario:

[0056] A basic verification scenario for this application is as follows Figure 1 As shown in the figure, it includes a transmitting station, a receiving station for ionospheric detection and a receiving station based on an array antenna at the same location. Among them, the transmitting station and the ionospheric detection receiving station form an ionospheric oblique detection link to obtain the ionospheric state and provide ionospheric environmental information support for single-station positioning; and the transmitting station and the receiving station based on the array antenna form an arrival angle estimation verification link, which estimates the arrival angle of the incoming wave of the transmitting station's signal and provides direction guidance for single-station positioning. In the actual implementation process, ionospheric detection and arrival angle estimation can be performed in time.

[0057] For the single-station positioning scenario of this application, basic geometric relationships can be constructed such as Figure 2 As shown, according to the coordinates of the transmitting station in, is the latitude of the transmitting station, α T is the longitude, and the corresponding receiving station coordinates are Then the great circle distance D of the transceiver station can be obtained as:

[0058]

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

[0060]

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

[0062] D=P·sin(θ)=2H / tan(θ) (3)

[0063] For the arrival angle estimation of the incoming wave, this application needs to rely on array antennas. A commonly used L-shaped antenna array is Figure 3 As shown, the two baselines have N and M array elements respectively. Assuming there are k narrowband signals s i (t)(i=1,…,k), the corresponding arrival angles of the incoming waves are (β 1 ,θ 1 ),(β 2 ,θ 2 ),…,(β k ,θ k ), then the present application can construct the steering vector of the array receiving signal as shown in the following formula:

[0064]

[0065] a x (β i ,θ i )=[1,exp(j2πdxcosβ i sinθ 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 wave arrival angle estimation technology based on subspace decomposition to estimate the arrival angle of the wave signal. For the L array, the following formula is obtained:

[0069]

[0070] Among them, E N is the signal matrix [s 1 (t),…,s k (t)] T The noise subspace.

[0071] Specifically, Figure 4 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, an embodiment of the present application can first obtain an original estimation result data set of the arrival angle of the target incoming wave signal based on a 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 a probability density distribution result.

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

[0076] It should be noted that the embodiments of the present application may adopt a two-dimensional antenna array, and use a two-dimensional arrival angle estimation strategy to simultaneously estimate the azimuth and elevation of the incoming signal, obtain an azimuth-elevation pair (β, θ), and construct an original estimation result data set based on the azimuth-elevation pair; at the same time, the embodiments of the present application need to ensure that there is no long-term continuous colored noise on the measurement frequency during the measurement period, otherwise it should be regarded as that this frequency is severely interfered, and it is difficult to accurately estimate the arrival angle of the target incoming wave, and the frequency should be abandoned.

[0077] Afterwards, the embodiment of the present application further needs to perform discretization statistics on the original estimation result data set, and its distribution function F(β i ,θ j ) is expressed as follows:

[0078]

[0079] Among them, P(β i ,θ j ) The arrival angle estimation result is (β i ,θ j ), [β min ,β max ] is the azimuth estimation interval, [θ min ,θ max ] is the elevation angle estimation interval, Δβ and Δθ are the discretization intervals of the probability density statistics of the azimuth and elevation angles, respectively, and their values ​​should be larger than the elevation and azimuth resolutions of the arrival angle estimation.

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

[0081] In step S402, 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 a two-dimensional Gaussian fitting is performed on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area.

[0082] Furthermore, if Figure 5 As shown in Figure 2, the peak position of the probability density (β 0 ,θ 0 ), the embodiment of the present application also needs to specify the neighborhood size δ β With 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 data set is extracted, and based on at least one arrival angle estimation result, an arrival angle preferred data set is constructed to use the arrival angle preferred data set to perform shortwave single-station positioning operations.

[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 a corresponding arrival angle optimization data set (ie, the final optimization 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-term colored noise interference, and performs angle optimization through two-dimensional Gaussian fitting and confidence ellipse frame 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 one embodiment of the present application, a confidence ellipse is framed according to the two-dimensional Gaussian fitting result and a preset confidence level, and at least one arrival angle estimation result in the original estimation result data set that is within the confidence ellipse is extracted, and based on the at least one arrival angle estimation result, an arrival angle preferred data set is constructed, including: calculating the covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculating the distribution inclination corresponding to the two-dimensional Gaussian fitting result based on the covariance matrix; performing eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculating the azimuth axis and 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, obtaining at least one arrival angle estimation result in the original estimation result data set that is within the confidence ellipse, so as to construct an arrival angle preferred data set based on the at least one arrival angle estimation result.

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

[0093]

[0094] The distribution inclination can be calculated:

[0095]

[0096] And perform eigenvalue decomposition on its covariance matrix, then we can get its two eigenvalues ​​λ β and λ θ ; According to the specified confidence level η, the azimuth axis and elevation axis of the confidence ellipse are:

[0097]

[0098] This allows us to define a confidence ellipse:

[0099]

[0100] Afterwards, the embodiment of the present application may obtain the arrival angle estimation results located within the confidence ellipse in the original estimation result data set based on a preset decision criterion to construct an arrival angle preferred data set.

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

[0102]

[0103] Among them, (β 0 ,θ 0) 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; a represents the azimuth axis.

[0104] It should be noted that the decision criterion for constructing the arrival angle optimization data set in the embodiment of the present application is as follows:

[0105]

[0106] Among them, (β 0 ,θ 0 ) 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; a represents the azimuth axis.

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

[0108] The following is an explanation of the execution logic and effect of the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics of the present application through a specific embodiment and in combination with the accompanying drawings.

[0109] In a specific embodiment of the present application, an actual observation example 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, and 3200, 2269 and 2869 effective arrival angle estimation results are obtained for 10.4, 12.1 and 10.2 MHz signals in the three time periods of 08:42-08:54, 08:57-09:06, and 09:27-09:37 on August 15, 2022, respectively, with a resolution of 0.1°. Their distributions are shown in Figures 6(a), 6(b) and 6(c), respectively. Although the angle measurement results of the 12.1 MHz signal have a larger dispersion range, they still present a central divergence shape. The difference is that the 10.4 and 10.2MHz signals are clearly divided into multiple families. For the 10.4MHz signal, it can be roughly divided into three clusters, namely, the azimuth distribution is [262°, 265°], the elevation distribution is [21°, 22°]; azimuth [263°, 265°], elevation [22°, 23°], azimuth [264°, 266.5°], and elevation [23°, 25°]. Similarly, the arrival angle of the 10.2MHz signal can also be divided into four groups according to the elevation angle, namely [19°, 20°], [20°, 21°], [21°, 22°] and [22°, 23°]. When the hardware platform remains consistent, this grouping dispersion can be regarded as a kind of colored noise interference.

[0110] After calculating their respective probability density distributions, we can obtain the results shown in Figure 7(a), Figure 7(b) and Figure 7(c) respectively. Obviously, they all have a single-peak structure, indicating that the colored noises that cause interference are all short-term.

[0111] Therefore, the specific embodiment of the present application can extract the main peak area of ​​2° in the neighborhood of the peak point as shown in Figure 8(a), Figure 8(b) and Figure 8(c) respectively. It can be found that they all have similar dispersion characteristics to the Gaussian distribution.

[0112] Afterwards, the specific embodiments of the present application perform two-dimensional Gaussian fitting on their respective main peak regions. When the confidence level is 0.9, the confidence ellipse and the preferred angle framed by it are shown in Figures 9(a), 9(b) and 9(c), respectively. For the three frequencies, the number of valid preferred points in their confidence intervals are 138, 123 and 238, respectively, accounting for 4.31%, 5.43% and 8.3% of their respective initial estimation results.

[0113] In order to obtain the ionospheric characteristics of the measurement period, the specific embodiment of the present application carried out two ionospheric oblique measurements at 08:36 and 09:16, respectively. The oblique ionograms are shown in Figures 10(a), 10(b), 10(c), 10(d), 10(e) and 10(f), respectively. It can be seen that at this time, the three frequencies are reflected and propagated through the Es layer. After measurement, it can be obtained that the reflection virtual height of the 10.2 and 10.4 MHz signals is 119.61 km, and the reflection virtual height of the 12.1 MHz signal is 114.04 km. The corresponding theoretical elevation angles are 20.61° and 19.72°, respectively. Combined with the theoretical azimuth angle of the transmitting station relative to the receiving station is 262° (with the north direction as the initial direction and the clockwise direction as the positive direction), the root mean square error (RMSE) comparison results of the arrival angle estimation results before and after the optimization are shown in Table 1:

[0114] Table 1

[0115]

[0116] From Table 1, we can see that β or and θ or represents the azimuth and elevation before optimization, β opt and θ opt In contrast, the RMSE of the azimuth angles before and after optimization improved by 0.81°, 0.25°, and 1.28°, and that of the elevation angles improved by 0.79°, 1.03°, and 0.90°.

[0117] Finally, based on the arrival angle measurement and its optimization results, combined with the ionospheric state observation information, the positioning results before and after positioning optimization can be obtained. The positioning result statistics are shown in Table 2:

[0118] Table 2

[0119]

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

[0121]

[0122] Therefore, for the problem that the arrival angle estimation results in shortwave single-station positioning are widely scattered, resulting in the dispersion of positioning points, the embodiments of the present application extract the main peak area of ​​the measurement angle probability density distribution and the range frame of the two-dimensional Gaussian fitting and the confidence ellipse, and filter out the angle measurement results affected by colored noise interference and the measurement noise points with large deviations due to the effect of white noise in turn, and obtain the optimized azimuth-elevation angle pairs. In combination with the experimental scenario and confirmed by the experimental measurement data, the dispersion of the arrival angle estimation results is significantly suppressed, and accordingly, the positioning accuracy is also significantly improved by about 3%, which strongly demonstrates that the embodiments of the present application have important significance and application prospects for improving the positioning accuracy of fixed targets or slow-moving targets.

[0123] According to the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics proposed in an embodiment of the present application, an original estimation result data set corresponding to the arrival angle of the target incoming wave signal is obtained based on a preset two-dimensional antenna array, and a two-dimensional probability density distribution statistics is performed 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 a preset neighborhood interval, and a two-dimensional Gaussian fitting is performed on the main peak area 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 a preset confidence level, and at least one arrival angle estimation result in the original estimation result data set that is located within the confidence ellipse is extracted, and based on at least one arrival angle estimation result, an arrival angle optimization data set is constructed to perform a shortwave single-station positioning operation using the arrival angle optimization data set. The present application extracts the main peak area of ​​the measurement angle probability density distribution and the range frame of the two-dimensional Gaussian fitting and the confidence ellipse, and successively filters out the angle measurement results affected by colored noise interference and the measurement noise points with large deviations due to the effect of white noise, and obtains the optimized azimuth-elevation angle pair, thereby greatly reducing the dispersion range and improving the positioning accuracy.

[0124] Secondly, the arrival angle optimization device for shortwave single-station positioning based on statistical characteristics proposed in an embodiment of the present application is described with reference to the accompanying drawings.

[0125] Fig.11 It is a block diagram of an arrival angle optimization device for shortwave single-station positioning based on statistical characteristics according to an embodiment of the present application.

[0126] like Fig.11 As shown, the arrival angle optimization device 10 for shortwave single-station positioning based on statistical characteristics includes: a statistical module 100, a fitting module 200 and an optimization module 300.

[0127] Among them, the statistical module 100 is used to obtain the 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.

[0128] The fitting module 200 is used to determine the probability density peak position in the probability density distribution result, and 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 two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area.

[0129] The preferred module 300 is used to frame a confidence ellipse according to the two-dimensional Gaussian fitting results 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 preferred data set based on at least one arrival angle estimation result, so as to use the arrival angle preferred data set to perform shortwave single-station positioning operations.

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

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

[0132] The construction unit is used to construct an 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 a probability density distribution result.

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

[0134] The calculation unit is used to calculate the covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate the distribution inclination corresponding to the two-dimensional Gaussian fitting result according to the covariance matrix.

[0135] The eigenvalue decomposition unit is used to perform eigenvalue decomposition on the covariance matrix to obtain two eigenvalues ​​of the covariance matrix, and calculate the azimuth axis and 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.

[0136] The acquisition unit is used to acquire at least one arrival angle estimation result located within the confidence ellipse in the original estimation result data set based on a preset decision criterion, so as to construct an arrival angle preferred data set according to the at least one arrival angle estimation result.

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

[0138]

[0139] Among them, (β 0 ,θ 0 ) 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; a represents the azimuth axis.

[0140] It should be noted that the aforementioned explanation of the implementation example of the method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics is also applicable to the device for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics of this implementation example, and will not be repeated here.

[0141] The arrival angle optimization device for shortwave single-station positioning based on statistical characteristics proposed in an embodiment of the present application includes a statistical module 100, which is used to obtain an original estimation result data set corresponding to the arrival angle of a 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 200, which is used to determine the probability density peak position in the probability density distribution result, and 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 two-dimensional Gaussian fitting on the main peak area to generate a two-dimensional Gaussian fitting result corresponding to the main peak area; a optimization module 300, which 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 in the original estimation result data set that is located within the confidence ellipse, and based on at least one arrival angle estimation result, construct an arrival angle optimization data set, so as to use the arrival angle optimization data set to perform a shortwave single-station positioning operation. The present application extracts the main peak area of ​​the measurement angle probability density distribution and the range frame of the two-dimensional Gaussian fitting and the confidence ellipse, and successively filters out the angle measurement results affected by colored noise interference and the measurement noise points with large deviations due to the effect of white noise, and obtains the optimized azimuth-elevation angle pair, thereby greatly reducing the dispersion range and improving the positioning accuracy.

[0142] Fig.12 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

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

[0144] When the processor 1202 executes the program, the arrival angle optimization method for shortwave single-station positioning based on statistical characteristics provided in the above embodiment is implemented.

[0145] Furthermore, the electronic device further comprises:

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

[0147] The memory 1201 is used to store computer programs that can be executed on the processor 1202 .

[0148] The memory 1201 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0149] If the memory 1201, the processor 1202 and the communication interface 1203 are implemented independently, the communication interface 1203, the memory 1201 and the processor 1202 can be connected to each other through a bus and communicate with 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. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.12 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only 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 communicate with each other through an internal interface.

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

[0152] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics.

[0153] An embodiment of the present application also provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned method for optimizing the angle of arrival of shortwave single-station positioning based on statistical characteristics.

[0154] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0155] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0156] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0157] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or N wirings (electronic devices), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing in other suitable ways as necessary and then storing it in a computer memory.

[0158] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above embodiment, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0159] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0160] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0161] The storage medium mentioned above may 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 can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify 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, and 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 data set is extracted. Based on the at least one arrival angle estimation result, an arrival angle preferred data set is constructed to perform shortwave single-station positioning operations using the arrival angle preferred data set.

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, the azimuth and elevation of the arrival angle of the target incoming signal are estimated to obtain an azimuth-elevation 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 arrival angle estimation result located within the confidence ellipse from the original estimation result data set, and constructing an arrival angle optimization data set based on the at least one arrival angle 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 the azimuth axis and the 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 data set is obtained to construct the arrival angle preferred data set 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: Among them, (β0,θ0) represents the peak position of the probability density; (β,θ) represents the azimuth-elevation angle pair corresponding to the arrival angle of the target incoming signal; ψ represents the distribution inclination; 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 statistical 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, used to determine the probability density peak position in the probability density distribution result, and 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; 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 estimation unit, configured to estimate the azimuth and elevation of the target incoming signal arrival angle based on the two-dimensional antenna array and a preset two-dimensional arrival angle estimation strategy to obtain an azimuth-elevation 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, used to calculate the covariance matrix corresponding to the two-dimensional Gaussian fitting result, and calculate the 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; An acquisition unit is used 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 data set, so as to construct the arrival angle preferred data set 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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