A high-precision spatial spectrum direction finding method based on a specific non-equidistant array structure

Abstract

The present invention discloses a high-precision spatial spectrum direction finding method based on a specific non-equidistant array structure. The method first establishes a non-equidistant array direction finding model according to the antenna given by a general aircraft; then proposes two direction finding schemes for different search and rescue signal frequencies in the search and rescue system, including a multi-antenna non-equidistant linear array direction finding scheme and a dual-antenna coprime array direction finding scheme, and completes the determination of antenna array elements in the direction finding scheme; finally, direction finding error correction is performed, the channel amplitude and phase errors in the direction finding process are analyzed, and a single auxiliary signal source correction algorithm is used to correct the errors, thereby improving the direction finding accuracy in the search and rescue process. The present invention uses a high-precision spatial spectrum direction finding algorithm to quickly rescue and support people in distress, and provides a technical basis for emergency rescue schemes for multi-aircraft collaborative direction finding and search and rescue.

Description

Technical Field

[0001] The invention belongs to the field of radio technology, and in particular relates to a spatial spectrum direction finding method. Background Art

[0002] The method of using radio direction finding for aviation rescue has been widely used in search and rescue of people in disaster scenarios such as maritime distress and earthquakes, and can quickly determine the location of people in distress and provide rescue support. The traditional radio direction finding method uses an array antenna to receive radio signals, and uses a specific direction finding algorithm to calculate the direction of the target based on the electrical parameters received by different antenna elements, such as amplitude, frequency or phase.

[0003] In applications such as aviation life-saving, the traditional single-machine search and rescue system is currently used. The single-machine search and rescue system can independently detect the direction and other information of the rescue target, and then determine the exact position of the rescue target in combination with geometric constraints. The single-machine search and rescue system has a simple structure and is flexible and maneuverable, but it has many disadvantages, such as large measurement errors, incomplete observation information, and susceptibility to communication interference, resulting in poor search and rescue effects. During the search and rescue process, the multi-machine collaborative search and rescue system conducts collaborative detection of the rescue target from different angles and fuses the information, which can not only improve the survivability of the system, but also ensure that the system can achieve the best direction-finding search and rescue effect with the support of as comprehensive, accurate and timely information as possible. In this case, it is of great significance and application value to study the realization of a high-precision multi-machine collaborative search and rescue system based on a specific non-equidistant array structure. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a high-precision spatial spectrum direction finding method based on a specific non-equidistant array structure. The method first establishes a non-equidistant array direction finding model according to the antenna given by a general aircraft; then proposes two direction finding schemes for different search and rescue signal frequencies in the search and rescue system, including a multi-antenna non-equidistant linear array direction finding scheme and a dual-antenna coprime array direction finding scheme, and completes the determination of antenna elements in the direction finding scheme; finally, direction finding error correction is performed, the channel amplitude and phase errors in the direction finding process are analyzed, and a single auxiliary signal source correction algorithm is used to correct the errors, thereby improving the direction finding accuracy in the search and rescue process. The present invention uses a high-precision spatial spectrum direction finding algorithm to quickly rescue and support people in distress, and provides a technical basis for emergency rescue schemes for multi-aircraft collaborative direction finding and search and rescue.

[0005] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0006] Step 1: According to the aircraft antenna array structure, the antenna element spacing is calculated from the given multi-element specific non-equidistant antenna array;

[0007] Step 2: construct a multi-antenna non-equidistant linear array direction finding solution and a dual-antenna coprime array direction finding solution according to the antenna array element spacing obtained in step 1;

[0008] The multi-antenna non-equidistant linear array direction finding solution is to select at least 5 array elements from the antenna array elements to form a non-equidistant array, and use a high-resolution MUSIC algorithm to perform multi-antenna direction finding;

[0009] The dual-antenna mutually prime array direction finding scheme is to select four array elements to form two two-antenna arrays, and perform dual-antenna direction finding according to the mutually prime array direction finding principle;

[0010] Step 3: Analyze the channel amplitude and phase error characteristics during the direction finding process, use the single auxiliary signal source correction algorithm to correct the error, determine the direction of the rescue target, and improve the direction finding accuracy during the search and rescue process.

[0011] Furthermore, the dual-antenna mutual prime array direction finding scheme is specifically as follows:

[0012] In the process of direction finding, the element spacing of each two-antenna array is d=mλ / 2, and the element spacing m of the two two-antenna arrays is mutually prime. The direction vector of the array is expressed as:

[0013]

[0014] Among them, m1~m n denote the values ​​of m of the 1st to nth antenna arrays respectively, and a(θ) is the direction vector of the actual incident angle θ of the signal;

[0015] When there is angular ambiguity between two antenna arrays:

[0016]

[0017] Where θ represents the true incident angle, and θ′ represents the blur angle;

[0018] In formula (2), k n The value of m is an integer. n The value of is a positive integer, the array angle measurement range is (-90°, 90°), and the range of sinθ is (-1, 1); so The value range is (-2,2), Yes |k n | <m n value, when m n When they are mutually prime, Therefore, when the array element spacings of different arrays are mutually prime, sinθ-sinθ'=0, the direction finding results of the two arrays both show spectral peaks, and there is no angle ambiguity, thus achieving accurate direction finding under mutually prime arrays.

[0019] Furthermore, the step 3 is specifically as follows:

[0020] Taking into account the channel amplitude and phase error G, the steering vector of the antenna array changes to A is the ideal steering vector of the antenna array; the output data covariance matrix of the array is:

[0021]

[0022] Among them, X(t) is an M×1 dimensional matrix, representing the snapshot data vector output by the array; N(t) is an M×1 dimensional matrix, representing the noise data vector of the array; S(t) is an N×1 dimensional matrix, representing the spatial incoming wave signal vector; A is an M×N dimensional matrix, representing the flow matrix of the spatial array, and E[.] represents the mathematical expectation;

[0023] Assume that there is only amplitude error in the channel array, the number of channels is M, and the amplitude errors are The array error matrix is ​​expressed as The output data covariance matrix of the array becomes:

[0024]

[0025] Among them, R s =E[S(t)S(t) H ], represents the covariance matrix of the array signal, σ n 2 represents the noise power;

[0026] Perform M eigenvalue decompositions, arrange the obtained M eigenvalues ​​in non-decreasing order and record them as λ1,λ2,…,λ M , normalize it to get the normalized eigenvalues ​​η1,η2,…,η M :

[0027]

[0028] in represents the estimated value of a;

[0029] When the array error matrix G is unknown and the channel amplitude error exists, the spatial spectrum function is transformed into:

[0030]

[0031] Among them, U N represents the noise subspace;

[0032] When only the channel amplitude error exists, the position of the maximum point of the spatial spectrum function of the antenna array remains unchanged, but the amplitude decreases. Therefore, the amplitude error will not affect the angle of direction finding, but only the height of the spatial spectrum peak.

[0033] Assume that there is only phase error in the channel array, the number of channels is M, and the phase errors are [β1β2…β M ], the error matrix is ​​expressed as The output data covariance matrix is:

[0034]

[0035] Perform M eigenvalue decompositions to obtain the signal subspace and noise subspace of the array. Finally, when the channel phase error exists, the spatial spectrum function is transformed into:

[0036]

[0037] When only the channel phase error exists, the position of the maximum point of the spatial spectrum function of the antenna array is affected by the phase error term. The spatial spectrum function reaches the maximum point when and only when the phase error is 0, that is, sinθ1=sinθ;

[0038] The single auxiliary source correction algorithm uses a single auxiliary source with known directional information to estimate the channel error. Assuming that amplitude and phase errors exist simultaneously in the array channel, the auxiliary source correction algorithm needs to set a calibration source with known position parameters in space. Assuming that the azimuth angle of the calibration source is θ c , the source signal is S(t), and the signal power is The noise power is When there is an amplitude and phase error G in the channel, the received distress target signal is:

[0039]

[0040] The covariance matrix of the received signal is:

[0041]

[0042] Where, Γ represents the gamma function;

[0043] Perform eigenvalue decomposition on the covariance matrix of the signal:

[0044]

[0045] in, is a diagonal matrix of eigenvalues, Arrange in non-monotonic increasing order, in is the signal subspace of the antenna array, is the noise subspace of the antenna array. When there is no amplitude or phase error in the channel, and a(θ c ) The column space spanned by is equivalent and parallel. When there is an amplitude and phase error G in the channel, With Ga(θ c ) are equivalently parallel, so:

[0046]

[0047] Where k is an unknown complex constant, formula (12) is converted to:

[0048]

[0049] According to formula (14), the channel amplitude and phase error is:

[0050]

[0051] During the direction finding process, corrections are made based on the obtained amplitude and phase errors, thereby improving the direction finding accuracy of multi-aircraft collaborative search and rescue.

[0052] The beneficial effects of the present invention are as follows:

[0053] The present invention improves the detection performance and spatial resolution capability of a single-machine direction-finding system, reduces the ambiguity of target information, improves the reliability of system detection, and significantly improves target direction-finding accuracy, target identification capability, and other aspects. The high-precision multi-machine collaborative search and rescue system based on a specific non-equidistant array structure of the present invention combines the advantages of high resolution and low latency of the spatial spectrum direction-finding algorithm. The present invention establishes a direction-finding error correction module to improve the direction-finding accuracy of the existing direction-finding method during the search and rescue process. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of the method of the present invention.

[0055] Figure 2 Schematic diagram of a direction finding model for multi-aircraft collaborative search and rescue according to an embodiment of the present invention, wherein (a) is a schematic diagram of multi-aircraft collaborative direction finding search and rescue, and (b) is a general aircraft antenna array structure.

[0056] Figure 3 The diagrams are result diagrams of direction finding of a multi-antenna non-equidistant linear array and a dual-antenna coprime array according to an embodiment of the present invention, wherein (a) is a result diagram of direction finding of a multi-antenna non-equidistant linear array, and (b) is a result diagram of direction finding of a dual-antenna coprime array.

[0057] Figure 4 It is a diagram of direction finding results after a single auxiliary signal source correction algorithm is adopted in an embodiment of the present invention, wherein (a) is a GUI interface display of a signal wave direction of 0°, and (b) is a GUI interface display of a signal wave direction of 10°. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] The present invention firstly establishes a direction finding model for multi-aircraft collaborative search and rescue for a general aircraft specific array structure, and proposes two non-equidistant direction finding schemes for a non-equidistant antenna array structure. Then, the channel amplitude and phase error characteristics in the direction finding process are analyzed, and a single auxiliary signal source correction algorithm is used to correct the error, thereby improving the direction finding accuracy in the search and rescue process. Figure 1 As shown, the specific steps are as follows:

[0060] 1. Optimizing the design of the structure of the non-equidistant array can reduce the number of continuous elements in the antenna array and increase the array aperture, thereby improving the direction finding performance. The antenna array structure of a general aircraft is analyzed, and the antenna element spacing is calculated based on the given 7-element non-equidistant array, and a direction finding model for multi-aircraft collaborative search and rescue is established, as follows:

[0061] The general aircraft is given a specific non-equidistant array of 7 elements. The frequency range of the signal to be measured is: 240MHz-250MHz. The array element distribution is as follows Figure 2 (b) The requirement of the direction finding system is to use any given antenna array element to achieve direction finding of the incoming signal. According to the formula λ = c / f, c is the propagation speed of the electromagnetic wave, which is 3×10 8 m / s. Assuming the signal frequency is 250MHz, the signal wavelength is 120cm. The antenna element spacing is calculated as:

[0062] The array element spacing between array element 1 and array element 2 is: 3600mm÷1200mm=3λ;

[0063] The array element spacing between array element 2 and array element 3 is: 750mm÷1200mm=0.625λ;

[0064] The array element spacing between array element 3 and array element 4 is: 1050mm÷1200mm=0.875λ;

[0065] The array element spacing between array element 4 and array element 7 is: (3610mm+1500mm)÷1200mm=4.258λ;

[0066] The array element spacing between array element 5 and array element 6 is: (600 mm+300 mm)÷1200 mm=0.75λ.

[0067] The direction finding system requires that for a given non-equidistant array, it can distinguish multiple incoming wave signals at the same time, and establish a multi-machine collaborative search and rescue direction finding model based on the above array element spacing.

[0068] 2. Select a direction finding scheme for direction finding. The direction finding system requires that for a given non-equidistant array, it can distinguish multiple incoming signals at the same time. Multi-antenna direction finding scheme: select array element 1, array element 2, array element 3, array element 4 and array element 7 to form a 5-element non-equidistant linear array for multi-antenna direction finding; dual-antenna direction finding scheme: select array element 3 and array element 4 to form a two-antenna array element group, array element 5 and array element 6 to form a two-antenna array element group, and perform dual-antenna direction finding based on the principle of coprime array direction finding, as follows:

[0069] (1) Direction finding using multi-antenna unequally spaced linear arrays

[0070] When the MUSIC algorithm can effectively perform direction finding, the number of noise feature vectors that need to be used is at least 1. For the non-equidistant linear array composed of 5 elements, the dimension of the subspace is 5. From the perspective of array signal theory, it can achieve simultaneous direction finding for at most 5 incoming signals. When the number of incoming signals is greater than 5 at a certain moment, the MUSIC algorithm will fail. In the actual direction finding application scenario, in order to maintain the accuracy of direction finding and reduce the processing requirements of the amplitude hardware, generally at most three directions of incoming signals are processed. The element position of the non-equidistant array composed of the selected 5 elements is: dd = [0, 3λ, 0.625λ, 0.875λ, 4.258λ].

[0071] (2) Dual-antenna mutual prime array direction finding

[0072] According to the requirements of high direction finding accuracy and low hardware cost in actual application scenarios, two array elements are generally used for direction finding in the actual process. Here, the dual-antenna mutually prime array direction finding method is adopted. The mutually prime array direction finding method requires that the array element spacing d = mλ / 2 of the direction finding array is required in the direction finding process, where the value of m is mutually prime. The specific description is as follows. The direction vector of the array can be expressed as:

[0073]

[0074] So when there is angle blur:

[0075]

[0076] In the above formula, k n The value of m is an integer. n The value of is a positive integer. The array angle measurement range is (-90°, 90°), so the range of sinθ is (-1, 1), so The value range of is (-2,2), and |k n | <m n value, when m n When they are mutually prime, Therefore, when the array element spacings of different arrays are prime numbers to each other, sinθ-sinθ'=0, which means that there is no angle ambiguity.

[0077] According to the principle of coprime array direction finding, array elements 3 and 4 are selected to form two antenna array element groups, and the array element spacing is d=7 / 8λ. Array elements 5 and 6 are selected to form two antenna array element groups, and the array element spacing is d=3 / 4λ. Theoretically, when the direction is measured separately, the above two array element groups will have direction finding ambiguity. However, at the target angle, the direction finding results of the two arrays both have spectral peaks. By taking the intersection, the ambiguity can be resolved, thereby realizing accurate direction finding under the coprime array.

[0078] 3. Analyze the channel amplitude and phase error characteristics during the direction finding process, use the single auxiliary signal source correction algorithm to correct the error, accurately determine the direction of the rescue target, and improve the direction finding accuracy during the search and rescue process. The details are as follows:

[0079] The channel amplitude and phase error has nothing to do with the direction of the signal. It is a complex gain error that includes amplitude error and phase error. Considering the channel amplitude and phase error G, the steering vector of the antenna array changes to The output data covariance matrix of the array becomes:

[0080]

[0081] In the process of spatial spectrum direction finding and rescue, the amplitude and phase errors of the array are unknown, so the true array steering vector is also unknown. It is easy to blindly use the ideal steering vector A of the antenna array instead of Estimating spatial spectrum DOA will lead to direction finding errors. Assuming that there is only amplitude error in the channel array, the number of channels is M, and the amplitude errors are The array error matrix can be expressed as The output data covariance matrix of the array becomes:

[0082]

[0083] Perform M eigenvalue decompositions, arrange the obtained M eigenvalues ​​in non-decreasing order and record them as λ1,λ2,…,λ M , normalize it to get the normalized eigenvalues ​​η1,η2,…,η M .

[0084]

[0085] When the array error matrix G is unknown and the channel amplitude error exists, the spatial spectrum function can be transformed into:

[0086]

[0087] When only the channel amplitude error exists, the position of the maximum point of the spatial spectrum function of the antenna array remains unchanged, but the amplitude decreases. Therefore, the amplitude error will not affect the angle of direction finding, but only the height of the spatial spectrum peak. Assume that there is only a phase error in the channel array, the number of channels is M, and the phase errors are [β1β2…β M ], the error matrix can be expressed as The output data covariance matrix is:

[0088]

[0089] Perform M eigenvalue decompositions to obtain the signal subspace and noise subspace of the array. Finally, when the channel phase error exists, the spatial spectrum function is transformed into:

[0090]

[0091] When only the channel phase error exists, the position of the maximum point of the spatial spectrum function of the antenna array is affected by the phase error term. The spatial spectrum function reaches its maximum point when and only when the phase error is 0, that is, when sinθ1=sinθ. Therefore, when the channel phase error exists, it affects the peak position of the spatial spectrum, and the amplitude of the spectrum peak will also be affected.

[0092] The single auxiliary source correction algorithm uses a single auxiliary source with precisely known directional information to estimate the channel error. Assuming that amplitude and phase errors exist simultaneously in the array channel, the auxiliary source correction algorithm needs to set a calibration source with known position parameters in space. Assuming that the azimuth angle of the calibration source is θ c , the source signal is S(t), and the signal power is The noise power is When there is an amplitude and phase error G in the channel, the received distress target signal is:

[0093]

[0094] The covariance matrix of the received signal is:

[0095]

[0096] Perform eigenvalue decomposition on the covariance matrix of the signal:

[0097]

[0098] in, is a diagonal matrix of eigenvalues, Arrange in non-monotonic increasing order, in is the signal subspace of the antenna array, is the noise subspace of the antenna array. When there is no amplitude or phase error in the channel, and a(θ c ) The column space spanned by is equivalent and parallel. When there is an amplitude and phase error G in the channel, With Ga(θ c ) are equivalently parallel, so:

[0099]

[0100] Where k is an unknown complex constant, formula (12) is converted to:

[0101]

[0102] According to formula (14), the channel amplitude and phase error is:

[0103]

[0104] During the direction finding process, correction can be made based on the obtained amplitude and phase errors, thereby improving the direction finding accuracy of multi-aircraft collaborative search and rescue.

[0105] Figure 1 The present invention is a flow chart of the method, which mainly includes analyzing the antenna array structure of a general aircraft, establishing a direction finding model for multi-aircraft collaborative search and rescue, then determining the antenna array in two direction finding schemes of the multi-aircraft collaborative search and rescue system, and finally analyzing the channel amplitude and phase error characteristics in the direction finding process, using a single auxiliary signal source correction algorithm to correct the error, and improving the direction finding accuracy in the search and rescue process.

[0106] Figure 2 Schematic diagram of the direction finding model of multi-aircraft collaborative search and rescue, (a) Schematic diagram of multi-aircraft collaborative direction finding search and rescue, (b) is the general aircraft antenna array structure. A single carrier aircraft uses the onboard antenna array to independently detect the distress target and obtain the target's angle information. When the electromagnetic interference around the carrier aircraft is large or the antenna array itself fails, it will cause large measurement errors and incomplete observation information. After a single aircraft completes the angle information detection of the distress target, it transmits the information to a unified information processing center for fusion processing of the direction finding information.

[0107] Figure 3The following are the direction finding results of multi-antenna non-equidistant linear array and dual-antenna coprime array. In the simulation, it is assumed that the incident signal source is a Gaussian stationary random process and the direction of the incoming signal is 20°. In the simulation, an omnidirectional non-equidistant linear array consisting of 5 selected array elements is used. The positions of the array elements are: dd = [0, 3λ, 0.625λ, 0.875λ, 4.258λ], the number of sampling snapshots is set to 100, and the signal-to-noise ratio is set to 5dB. The corresponding direction finding results of the multi-antenna non-equidistant linear array are shown in Figure (a). Under the same conditions, the positions of the coprime arrays are: dd1 = [0, 7 / 8λ] and dd2 = [0, 3 / 4λ], the number of sampling snapshots is set to 500, and the signal-to-noise ratio is set to -5dB. The corresponding direction finding results of the dual-antenna coprime array are shown in Figure (b). From Figure 3 It can be seen that the two direction-finding schemes, multi-antenna and dual-antenna, adopted according to the given non-equidistant array structure can both achieve accurate direction-finding of the distress target in the idealized simulation process.

[0108] Figure 4 This is the direction finding result diagram after using the single auxiliary signal source correction algorithm. The errors of multiple receiving channels in the direction finding system during the sampling, capture and tracking process and the use of internal active devices will affect the amplitude and phase characteristics of the receiving channel. During the experiment, the transmission signal frequency was set to 243MHz, the signal wave direction was 0°, the dual antenna baseline length was set to 0.566 meters, the receiver data acquisition was short type, the system master clock was set to 57.344MHz during the data acquisition process, the I / Q correlation accumulation period was 4.8KHz, and the sampling effective data was 590. The CCS data was converted and the effectively converted data was selected for multi-machine collaborative search and rescue direction finding result calculation. (a) is the GUI interface display of the signal wave direction 0°, and (b) is the GUI interface display of the signal wave direction 10°. It can be seen from the figure that in the actual direction finding data processing process, due to the amplitude and phase errors in the channel, the phase difference at the output of the dual-channel receiver in the direction finding system is not equal to the phase difference at the input, but a certain phase offset is superimposed. In addition, in the signal processing process, such as mixing accuracy and A / D sampling accuracy, signal capture and tracking, etc., will affect the results of signal processing, resulting in deviations in the final direction finding results. By using the 0° source receiving signal as an auxiliary source to correct the channel error, the direction finding result also has a certain degree of deviation when the incoming signal is 10°. However, after error correction by a single auxiliary source, local correction of the error can be achieved, and the direction finding accuracy can be maintained within 5°, which greatly improves the accuracy of direction finding and can be applied to multi-machine collaborative search and rescue.

[0109] The high-precision spatial spectrum direction finding method of the present invention is based on a specific non-equidistant array structure, which improves the detection performance and spatial resolution capability of a single-machine direction finding system, reduces the ambiguity of target information, improves the reliability of system detection, and significantly improves target direction finding accuracy, target recognition capability, etc.

Claims

1. A high-precision spatial spectrum direction finding method based on a specific non-equidistant array structure, characterized in that: The steps include: Step 1: According to the aircraft antenna array structure, the antenna element spacing is calculated from the given multi-element specific non-equidistant antenna array; Step 2: construct a multi-antenna non-equidistant linear array direction finding solution and a dual-antenna coprime array direction finding solution according to the antenna array element spacing obtained in step 1; The multi-antenna non-equidistant linear array direction finding solution is to select at least 5 array elements from the antenna array elements to form a non-equidistant array, and use a high-resolution MUSIC algorithm to perform multi-antenna direction finding; The dual-antenna mutually prime array direction finding scheme is to select four array elements to form two two-antenna arrays, and perform dual-antenna direction finding according to the mutually prime array direction finding principle; The dual-antenna mutual prime array direction finding scheme is specifically as follows: In the process of direction finding, the element spacing of each two-antenna array is d=mλ / 2, and the element spacing m of the two two-antenna arrays is mutually prime. The direction vector of the array is expressed as: Among them, m1~m n denote the values ​​of m of the 1st to nth antenna arrays respectively, and a(θ) is the direction vector of the actual incident angle θ of the signal; When there is angular ambiguity between two antenna arrays: Where θ represents the true incident angle, and θ′ represents the blur angle; In formula (2), k n The value of m is an integer. n The value of is a positive integer, the array angle measurement range is (-90°, 90°), and the range of sinθ is (-1, 1); so The value range is (-2,2), Yes |k n | <m n value, when m n When they are mutually prime, Therefore, when the array element spacings of different arrays are mutually prime, sinθ-sinθ'=0, and the direction finding results of the two arrays both show spectral peaks, and there is no angle ambiguity, thus achieving accurate direction finding under mutually prime arrays. Step 3: Analyze the channel amplitude and phase error characteristics during the direction finding process, use the single auxiliary signal source correction algorithm to correct the error, determine the direction of the rescue target, and improve the direction finding accuracy during the search and rescue process; Taking into account the channel amplitude and phase error G, the steering vector of the antenna array changes to A is the ideal steering vector of the antenna array; the output data covariance matrix of the array is: Among them, X(t) is an M×1 dimensional matrix, representing the snapshot data vector output by the array; N(t) is an M×1 dimensional matrix, representing the noise data vector of the array; S(t) is an N×1 dimensional matrix, representing the spatial incoming wave signal vector; A is an M×N dimensional matrix, representing the flow matrix of the spatial array, and E[.] represents the mathematical expectation; Assume that there is only amplitude error in the channel array, the number of channels is M, and the amplitude errors are The array error matrix is ​​expressed as The output data covariance matrix of the array becomes: Among them, R s =E[S(t)S(t) H ], represents the covariance matrix of the array signal, σ n 2 represents the noise power; Perform M eigenvalue decompositions, arrange the M eigenvalues ​​obtained in non-decreasing order and record them as λ1,λ2,…,λ M , normalize it to get the normalized eigenvalues ​​η1,η2,…,η M : in represents the estimated value of a; When the array error matrix G is unknown and the channel amplitude error exists, the spatial spectrum function is transformed into: Among them, U N represents the noise subspace; When only the channel amplitude error exists, the position of the maximum point of the spatial spectrum function of the antenna array remains unchanged, but the amplitude decreases. Therefore, the amplitude error will not affect the angle of direction finding, but only the height of the spatial spectrum peak. Assume that there is only phase error in the channel array, the number of channels is M, and the phase errors are [β1β2…β M ], the error matrix is ​​expressed as The output data covariance matrix is: Perform M eigenvalue decompositions to obtain the signal subspace and noise subspace of the array. Finally, when the channel phase error exists, the spatial spectrum function is transformed into: When only the channel phase error exists, the position of the maximum point of the spatial spectrum function of the antenna array is affected by the phase error term. The spatial spectrum function reaches the maximum point when and only when the phase error is 0, that is, sinθ1=sinθ; The single auxiliary source correction algorithm uses a single auxiliary source with known directional information to estimate the channel error. Assuming that amplitude and phase errors exist simultaneously in the array channel, the auxiliary source correction algorithm needs to set a calibration source with known position parameters in space. Assuming that the azimuth angle of the calibration source is θ c , the source signal is S(t), and the signal power is The noise power is When there is an amplitude and phase error G in the channel, the received distress target signal is: The covariance matrix of the received signal is: Where, Γ represents the gamma function; Perform eigenvalue decomposition on the covariance matrix of the signal: in, is a diagonal matrix of eigenvalues, Arrange in non-monotonic increasing order, in is the signal subspace of the antenna array, is the noise subspace of the antenna array. When there is no amplitude or phase error in the channel, and a(θ c ) The column space spanned by is equivalent and parallel. When there is an amplitude and phase error G in the channel, With Ga(θ c ) are equivalently parallel, so: Where k is an unknown complex constant, formula (12) is converted to: According to formula (14), the channel amplitude and phase error is: During the direction finding process, corrections are made based on the obtained amplitude and phase errors, thereby improving the direction finding accuracy of multi-aircraft collaborative search and rescue.

Images