Short baseline synthetic aperture passive positioning method and system based on Root-MUSIC spectrum estimation

Abstract

The invention discloses a synthetic aperture passive positioning method based on a short baseline, and mainly solves the problems of large positioning error caused by residual frequency deviation and large estimation error caused by adopting spectrum estimation frequency in the prior art. According to the implementation scheme, the method comprises the steps that a geometric scene comprising a reconnaissance plane, two short baseline antennas and an unknown radiation source is built; obtaining unknown radiation source signals received by two short baseline antennas on the reconnaissance plane according to the geometric scene; performing correlation method processing on the two received signals to obtain a single-frequency signal; root-MUSIC spectrum estimation is carried out on the single-frequency signal, that is, a frequency estimation value is obtained by using orthogonality of a signal subspace and a noise subspace and a polynomial rooting method; and coordinates of an unknown radiation source are solved according to the frequency estimation value. According to the method, the residual frequency deviation caused by inaccurate carrier frequency estimation of the radiation source emission signal is reduced, the spectrum estimation error is reduced, the positioning accuracy and reliability are greatly improved, and the method can be used for unknown signal sources of short base lines and non-continuous short signal sequences without periodicity.

Description

Technical Field

[0001] The present invention belongs to the field of radar positioning, and further relates to a synthetic aperture passive positioning method and system, which can be used for unknown signal sources with short baselines and non-periodic discontinuous short signal sequences. Background Art

[0002] In the field of synthetic aperture passive location technology, traditional implementations typically use a single-antenna radar system mounted on a reconnaissance platform. This system passively receives electromagnetic signals emitted by an unknown emitter, extracts signal segments equal to the pulse width at specific pulse repetition intervals, and constructs the characteristic parameters of the unknown emitter using the frequency domain, range dimension, and azimuth angle. This system then demodulates the baseband signal to obtain a pure single-frequency signal. However, due to the lack of a collaborative working mechanism between the transmitter and receiver, accurate carrier frequency parameters are difficult to obtain in practical applications. This inherent non-cooperative nature of the system can lead to uncorrected frequency deviations, which in turn affects the accuracy of synthetic aperture imaging.

[0003] Patent document CN202410631740.9 discloses a "method, system, medium, and device for locating near-field radiators of real signals based on a reduced-rank Capon algorithm." The method uses an array antenna with a uniform linear array structure to receive signals and calculate the signal's covariance matrix. The matrix is then subjected to eigenvalue decomposition to achieve rank reduction. The reduced-rank covariance matrix is used to construct the search function of the near-field Capon algorithm. Based on the rank reduction principle, the two-dimensional near-field radiator location problem is transformed into a one-dimensional search for two parameters, angle and distance. Using the root-finding principle, the denominator of the spectrum peak search is converted into a one-dimensional polynomial. The polynomial is then rooted. Using the roots of the polynomial, a rough estimate of the angle and distance is obtained using an approximate signal model. These rough estimates are substituted into the constructed correction matrix to obtain an accurate estimate of the angle and distance of the real signal. This method is susceptible to the inaccurate estimate of the number of signal sources, resulting in reduced positioning accuracy. Furthermore, the algorithm requires the inverse of the reduced-rank covariance matrix, which increases algorithm complexity.

[0004] Dr. Wang Yuqi's paper, "Research on Imaging and Positioning Methods for Radiating Sources Based on Synthetic Aperture Systems," proposed a satellite-based, long-duration synthetic aperture positioning method. This method first establishes a high-order slant range model from the receiving platform to the radiating source. By deconvoluting the line frequency modulation, an azimuth-matched filter is constructed. The high-order frequency modulation of the received signal is estimated using azimuth focusing plus minimum entropy. Next, a cost function is constructed to locate the radiating source by dividing the grid into geographic coordinates. Finally, a positioning performance analysis method based on the orthogonality of the high-order terms is proposed to clarify the algorithm's ability to locate signal sources at different locations, thereby reducing the impact of carrier frequency estimation errors on positioning accuracy. However, this method requires a large amount of computation, which affects the real-time performance of radiating source positioning. Furthermore, the processing of range and residual frequency offsets is complex. Summary of the Invention

[0005] The purpose of the present invention is to address the shortcomings of the above-mentioned existing technologies and propose a short-baseline synthetic aperture passive positioning method and system based on Root-MUSIC spectrum estimation, so as to avoid phase ambiguity and signal coherence dependence while reducing the complexity of positioning and the impact of residual frequency offset on passive positioning, thereby improving positioning accuracy.

[0006] The technical approach to achieving the objectives of the present invention is to combine a reconnaissance aircraft and two short-baseline antennas into a geometric scenario for receiving electromagnetic wave signals from an unknown radiation source; perform correlation processing on the received signal obtained by the reconnaissance aircraft to obtain a single-frequency signal to be measured; use Root-MUSIC spectrum estimation to measure the frequency of the single-frequency signal; and calculate the coordinates of the unknown radiation source based on the frequency estimation results.

[0007] According to the above ideas, the implementation steps of the present invention include the following:

[0008] 1. A short-baseline synthetic aperture passive positioning processing method based on Root-MUSIC spectrum estimation, characterized by comprising:

[0009] (1) Build a geometric scene consisting of a reconnaissance aircraft, two short baseline antennas, and an unknown radiation source;

[0010] (2) Obtain the unknown radiation source signal received by the two short baseline antennas on the reconnaissance aircraft based on the geometric scene and

[0011] (3) Received signal and Perform correlation processing to obtain a single-frequency signal s c (t m ), t m is the time of the mth pulse received by the two antennas;

[0012] (4) For single-frequency signal sc (t m ) Perform Root-MUSIC spectrum estimation to obtain frequency estimates

[0013] 4a) According to the single frequency signal s c (t m ) Construct the spatial pseudo-spectrum P MUSIC (f);

[0014] 4b) For the spatial pseudo-spectrum P MUSIC (f) Perform phase calculation to obtain the optimal frequency estimate

[0015] (5) Based on frequency estimation Solve the coordinates of unknown radiation sources.

[0016] Further, the single frequency signal s c (t m ) Construct the spatial pseudo-spectrum P MUSIC (f), the implementation of which includes:

[0017] 4a1) Simulate the random noise interference in the actual channel and set s c (t m ) After passing through the Gaussian white noise channel, the signal sequence is obtained

[0018] 4a2) Assume that the sampling sequence signal For x(n), calculate its autocorrelation matrix R;

[0019] 4a3) Calculate the eigenvector u of the autocorrelation matrix R i and eigenvalue λ i eigendecomposition of

[0020] 4a4) Transform the eigenvector u i The corresponding eigenvalue λ i After arranging from large to small, the subspace is divided, where the signal subspace is the eigenvector Us=[u1,…,u M ], the noise subspace is the eigenvector U corresponding to NM small eigenvalues n =[u M+1 ,…,u N ];

[0021] 4a5) Based on the noise subspace, the direction vector of the incoming wave signal is used to locate the signal direction using the orthogonality thereof, and the direction vector a(f) of the incoming wave signal is defined;

[0022] 4a6) According to the direction vector a(f) of the incoming signal and the eigenvector U of the noise subspace n, construct the MUSIC pseudo-spectrum definition P MUSIC (f).

[0023] Furthermore, the spatial pseudo spectrum P in 4b) MUSIC (f) Perform phase calculation to obtain the optimal frequency estimate Its implementation includes:

[0024] 4b1) According to the definition of MUSIC pseudo spectrum in 4a), the noise subspace projection matrix P is obtained n ;

[0025] 4b2) Using the noise subspace projection matrix P n Define the polynomial P(z);

[0026] 4b3) Expand the polynomial defined in 4b2) to obtain P(z);

[0027] 4b4) Based on the polynomial of z, solve the phase of the root to obtain the best frequency estimate of the sampled signal x(n)

[0028] 2. A short-baseline synthetic aperture passive positioning system based on Root-MUSIC spectrum estimation, comprising:

[0029] Short baseline positioning geometric scene module, used to establish a scene for positioning unknown radiation sources;

[0030] The short baseline antenna signal receiving module is used to capture electromagnetic wave signals from unknown radiation sources in complex electromagnetic space environments when locating unknown radiation sources.

[0031] A signal correlation method processing module is used to eliminate the residual frequency offset in the received signal obtained in the short baseline antenna signal receiving module and output a single frequency signal;

[0032] The Root-MUSIC spectrum estimation module is used to measure the spectrum of the single-frequency signal output by the signal correlation processing module to achieve high-precision frequency estimation;

[0033] The unknown radiation source coordinate solution module is used to solve the unknown radiation source coordinates based on the precise frequency obtained by the Root-MUSIC spectrum estimation module.

[0034] 3. A computer-readable storage medium for Root-MUSIC spectrum estimation, characterized in that the computer-readable storage medium for synthetic aperture spectrum estimation stores computer instructions, and the computer instructions are used to enable the computer to execute the short-baseline synthetic aperture passive positioning method based on Root-MUSIC spectrum estimation according to any one of claims 1 to 7.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] First, the present invention uses a reconnaissance aircraft equipped with two short-baseline antennas to locate the unknown radiation source when performing synthetic aperture passive positioning, and performs correlation processing on the two received signals. This not only eliminates the residual frequency offset, but also avoids phase ambiguity and signal coherence dependence, reduces the impact of the residual frequency offset caused by inaccurate carrier frequency estimation of the unknown radiation source's transmitted signal, and reduces the computational complexity.

[0037] Secondly, the present invention uses correlation method to process the two received signals obtained by the two antennas of the reconnaissance aircraft to obtain a single-frequency signal corresponding to the direct distance between the first antenna and the unknown radiation source. This can transform the traditional positioning problem into a frequency estimation problem of the signal to be measured, reducing the complexity of the calculation and the implementation cost.

[0038] Thirdly, the present invention obtains the optimal frequency estimation value of the signal to be measured through the Root-MUSIC spectrum estimation algorithm, thereby achieving high precision, high real-time performance and high robustness in frequency estimation of non-periodic and non-continuous single-frequency short signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of the implementation of the short-baseline synthetic aperture passive positioning method based on Root-MUSIC spectrum estimation of the present invention;

[0040] Figure 2 This is a diagram of the short baseline passive positioning geometric model constructed in the present invention.

[0041] Figure 3 This is a block diagram of the short-baseline synthetic aperture passive positioning system based on Root-MUSIC spectrum estimation of the present invention. DETAILED DESCRIPTION

[0042] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0043] Example 1: Short-baseline synthetic aperture passive positioning method based on Root-MUSIC spectrum estimation

[0044] Reference Figure 1 The implementation steps of this example include the following:

[0045] Step 1: Build a geometric scene for passive positioning.

[0046] Reference Figure 2 The geometric scene constructed in this step includes a reconnaissance aircraft, two short baseline antennas and an unknown source, where:

[0047] The two antennas on the reconnaissance aircraft are RX1 and RX2, with a fixed distance d between them. The reconnaissance aircraft flies at a constant speed v in a straight line parallel to the ground plane, and receives signals from an unknown radiation source P during the flight.

[0048] With the initial position of the first antenna RX1 on the reconnaissance aircraft as the coordinate origin, an XOY coordinate system is established for the positioning scene. The X-axis represents the reconnaissance aircraft's flight direction, i.e., the azimuth, and the Y-axis represents the direction of the unknown radiation source relative to the reconnaissance aircraft's flight path, i.e., the distance.

[0049] The coordinates of the unknown radiation source P are (x0, y0), where x0 is the azimuth coordinate of the unknown radiation source P, and y0 is the distance coordinate of the unknown radiation source P.

[0050] The above description is only for the positioning scenario of a single unknown radiation source in this example. For the positioning of multiple unknown radiation sources, a positioning scenario of multiple unknown radiation sources can be built according to the above solution.

[0051] Step 2: The reconnaissance aircraft obtains the received signal.

[0052] In the process of receiving signals from the reconnaissance aircraft, the two short baseline antennas form a multi-path signal channel through spatial electromagnetic wave induction. When the electromagnetic wave signal emitted by the unknown radiation source reaches the antenna, the antenna converts the electromagnetic wave energy into a time domain electrical signal, and then passes through the preamplifier, bandpass filter and other modules of the reconnaissance aircraft system to reduce noise and retain the effective frequency band. The signal of the unknown radiation source received by the two short baseline antennas RX1 and RX2 on the reconnaissance aircraft in the geometric scenario of step 1 is obtained. and They are respectively represented as follows:

[0053]

[0054] in, and are the amplitudes of the signals received by the first antenna RX1 and the second antenna RX2, respectively. τ1 and τ2 are the time delays of the unknown radiation source’s transmitted signal reaching the first antenna RX1 and the second antenna RX2, respectively. φ(t-τ1) and φ(t-τ2) are the phases of the signals received by the first antenna RX1 and the second antenna RX2, respectively. f c is the carrier frequency, and t is the continuous time.

[0055] Step 3: Eliminate the residual frequency offset and obtain the single-frequency signal s c (t m ).

[0056] After the reconnaissance aircraft receives the received signal, it will convert the high-frequency signal into a baseband signal through down-conversion processing. Due to the error in the carrier frequency estimation of the signal, there will be residual frequency offset after down-conversion, which affects the positioning accuracy and needs to be eliminated.

[0057] Existing methods for resolving residual frequency offset include pilot-based frequency offset estimation, digital signal processing compensation, correlation methods, and feedback tracking loops. This example uses, but is not limited to, correlation methods to eliminate residual frequency offset. Its implementation includes the following:

[0058] 3.1) According to the geometric scene and the cosine theorem, the instantaneous slant distance R1 (t m ) and R2(t m ):

[0059]

[0060] Among them, R 10 is the instantaneous slant distance between the first antenna RX1 and the unknown radiation source P when the reconnaissance aircraft first receives the signal from the unknown radiation source, d is the distance between the first antenna RX1 and the second antenna RX2, and t m is the time when the mth pulse is received by the two antennas RX1 and RX2, v is the speed of the reconnaissance aircraft, and θ is the angle between the straight direction between the reconnaissance aircraft and the unknown radiation source and the flight direction of the reconnaissance aircraft, which is obtained by estimating the angle of arrival (DOA).

[0061] 3.2) Based on the instantaneous slant range, the time delay expression for the unknown radiation source's transmitted signal to reach the first antenna RX1 and the second antenna RX2 is obtained:

[0062] 3.3) Set the delay τ i Substitute the received signal and Then down-convert the signal to get the pulse signal received by the first antenna RX1 and the second antenna RX2 respectively. and

[0063]

[0064] in, and are the amplitudes of the signals received by the first antenna RX1 and the second antenna RX2, respectively. τ1 and τ2 are the time delays of the unknown radiation source’s transmitted signal reaching the first antenna RX1 and the second antenna RX2, respectively. m -τ1) and φ(t m-τ2) are the phases of the signals received by the first antenna RX1 and the second antenna RX2 respectively, f c is the carrier frequency, is the residual frequency offset caused by the frequency measurement error, is the measured carrier frequency, c is the speed of light;

[0065] 3.4) The pulse signals received by the first antenna RX1 and the second antenna RX2 are respectively and Carry out relevant legal processing, that is, The conjugate signal and Multiply them together to get the single frequency signal s c (t m ):

[0066]

[0067] Among them, "*" represents the conjugate operation, The simplified single-frequency signal s c (t m ), is a single frequency signal s c (t m ), is a single frequency signal s c (t m ) phase value.

[0068] Step 4: Use the Root-MUSIC spectrum estimation method to estimate the single-frequency signal s c (t m ) to perform spectrum measurements.

[0069] Based on the functional relationship between the frequency of the single-frequency signal and the initial slant distance required for locating the unknown radiation source, high-precision frequency measurement of the single-frequency signal is completed to achieve accurate positioning of the unknown radiation source.

[0070] Existing frequency measurement methods include: zero-crossing detection method, wavelet transform method, fast Fourier transform method, Root-MUSIC spectrum estimation method, etc. This example selects but is not limited to the Root-MUSIC spectrum estimation method for frequency measurement, and its implementation includes the following:

[0071] 4.1) Simulate the random noise interference in the actual channel and transform the single frequency signal s c (t m ) After passing through the Gaussian white noise channel, the signal sequence is obtained

[0072]

[0073] Where w(n) is a Gaussian white noise signal, is the number of signal accumulations, T is the signal accumulation time, △t m is the sampling interval, △A is the simplified single-frequency signal s c (t m ), f p is a single frequency signal s c (t m ), is a single frequency signal s c (t m )’s phase value;

[0074] 4.2) Assume that the sampling sequence signal For x(n), in order to adapt to the limited snapshot and non-ideal conditions, calculate its autocorrelation matrix R

[0075] R=E[xx H ],

[0076] where E[·] is the mathematical expectation, x=[x(0),x(1),…,x(Q-1)] T is the signal vector, Q is the signal length, x H is the conjugate transpose of x;

[0077] 4.3) In order to strictly separate the signal subspace and the noise subspace from the autocorrelation matrix R and improve computational efficiency by retaining the noise subspace for dimensionality reduction, the following eigendecomposition is performed on the autocorrelation matrix R:

[0078]

[0079] Among them, U is the eigenvector matrix, Λ is the diagonal matrix containing eigenvalues, U H is the transposed matrix of U, λ i is the i-th eigenvalue, u i is the i-th eigenvector, u i H for u i The transposed eigenvector of ;

[0080] 4.4) The eigenvector u i The corresponding eigenvalue λ i After arranging from large to small, the subspace is divided, where the eigenvectors corresponding to the first M large eigenvalues are Us=[u1,…,u M ] is the signal subspace, and the eigenvector U corresponding to the remaining NM small eigenvalues n =[u M+1 ,…,u N ] is the noise subspace, which is orthogonal to the signal subspace, M is the number of signals, and N is the total number of eigenvectors;

[0081] 4.5) Based on the noise subspace, the direction of the incoming signal is determined by using its orthogonality. The direction vector a(f) of the incoming signal is defined as:

[0082] a(f)=[1,e j2πf ,e j2π2f ,…,e j2π(K-1)f ] T ,

[0083] Where a(f) is a vector composed of the signals received by K array elements, and an array element is a sensor that independently collects incoming wave signals;

[0084] 4.6) According to the obtained direction vector of the incoming signal a(f) and the eigenvector U of the noise subspace n , construct the MUSIC pseudo spectrum as:

[0085]

[0086] Among them U n H For U n The conjugate transpose vector of .

[0087] 4.7) According to the definition of MUSIC pseudo-spectrum in step 4.6), the noise subspace projection matrix P is obtained n for:

[0088] P n =U n U n H ,

[0089] Among them, U n is the eigenvector of the noise subspace, U n H For U n The conjugate transposed eigenvector of , this projection matrix projects the direction vector a(f) into the noise subspace, which can effectively suppress noise interference and improve estimation accuracy;

[0090] 4.8) In order to avoid the traditional MUSIC spectrum peak search and reduce the complexity of calculation, the noise subspace projection matrix P is used n Define the polynomial P(z):

[0091] P(z)=a T (z -1 )P n a(z),

[0092] Where a(z)=[1,z,z 2 ,…,z K-1 ] Tis the direction vector, z=e j2πf is the signal received by the array element, a T (z -1 ) is the conjugate transposed direction vector of a(z);

[0093] 4.9) Expand the polynomial defined in step 4.8) to obtain the expanded polynomial P(z):

[0094]

[0095] Among them, z -m is the phase delay of the mth array element relative to the reference array element, The noise subspace matrix P n The coefficients calculated from the elements, u k,i Indicates U n The k-th row and i-th column element, u k+m,i Indicates U n The element in the k+|m|th row and i-th column of for u k+m,i The conjugate transpose of ; this polynomial is valid only when z corresponds to the true signal direction;

[0096] 4.10) Based on the relationship between the phase of the polynomial root and the frequency of the signal, the phase of the polynomial root P(z) of z is solved to obtain the estimated frequency

[0097]

[0098] in, F s is the sampling rate, z k is the root of P(z).

[0099] Step 5, by estimating the frequency Calculate the two-dimensional coordinates of the unknown radiation source.

[0100] 5.1) Based on the functional relationship between the frequency value of the single frequency signal and the initial slant range required to locate the unknown radiation source, the best frequency estimate is used. Inversely solve the initial slope distance R 10 :

[0101]

[0102] Where d is the distance between the first antenna RX1 and the second antenna RX2, v is the speed of the reconnaissance aircraft, θ is the angle between the straight direction of the reconnaissance aircraft and the unknown radiation source and the flight direction of the reconnaissance aircraft, and f c is the carrier frequency, c is the speed of light;

[0103] 5.2) Using the initial slope distance R10 and the angle θ, perform two-dimensional coordinate transformation of the radiation source to complete the final positioning of the unknown radiation source:

[0104]

[0105] Among them, x0 is the azimuth coordinate of the unknown radiation source P, and y0 is the distance coordinate of the unknown radiation source P.

[0106] Example 2: Short baseline synthetic aperture passive positioning system based on Root-MUSIC spectrum estimation,

[0107] Reference Figure 3 This example includes: a short baseline positioning geometry scene module 1, a short baseline antenna signal receiving module 2, a signal correlation method processing module 3, a Root-MUSIC spectrum estimation module 4, and an unknown radiation source coordinate solution module 5. Among them, the signal correlation method processing module 3 includes a pulse dimension signal solution submodule 31 and a single frequency signal extraction submodule 32, and the Root-MUSIC spectrum estimation module 4 includes an autocorrelation matrix calculation submodule 41, a MUSIC pseudo-spectrum definition submodule 42, a Root-MUSIC model solution submodule 43, and a polynomial root finding submodule 44. The working principle of the entire system is as follows:

[0108] The short baseline positioning geometric scene module 1 is used to establish a scene for positioning an unknown radiation source;

[0109] The short baseline antenna signal receiving module 2 is used to capture the electromagnetic wave signal of the unknown radiation source in a complex electromagnetic space environment in the scenario of locating the unknown radiation source, and transmit it to the correlation method processing module 3;

[0110] The signal correlation method processing module 3 is used to eliminate the residual frequency offset in the received signal obtained in the short baseline antenna signal receiving module, wherein the pulse dimension signal solver module 31 solves the electromagnetic wave signal into a pulse dimension signal, and the single frequency signal extraction submodule 32 performs conjugate processing on the solved pulse dimension signal to extract the single frequency signal and transmit it to the Root-MUSIC spectrum module 4;

[0111] The Root-MUSIC spectrum estimation module 4 is used to perform spectrum measurement on the single-frequency signal output by the signal correlation method processing module 3 to achieve high-precision frequency estimation. The autocorrelation matrix calculation submodule 41 is used to calculate the autocorrelation matrix of the single-frequency signal. The pseudo-spectrum definition submodule 42 defines the MUSIC pseudo-spectrum by using the orthogonality between the noise subspace and the direction vector obtained after eigendecomposition of the autocorrelation matrix. The Root-MUSIC model solution submodule 43 constructs a polynomial whose roots correspond to the signal frequency through the MUSIC pseudo-spectrum definition. The polynomial root finding submodule 44 is used to obtain the optimal frequency estimate using the roots within the unit circle of the polynomial and transmit it to the unknown radiation source coordinate solution module 5.

[0112] The unknown radiation source coordinate solution module 5 is used to solve the unknown radiation source coordinates according to the optimal frequency estimation value obtained by the Root-MUSIC spectrum estimation module 4.

[0113] It should be noted that the above-mentioned functional modules can be implemented in whole or in part through software, hardware, firmware, or any combination thereof. When implemented using software, these functional modules can be implemented in whole or in part in the form of a program instruction product. The program instruction product includes one or a group of program instructions, which, when loaded and executed on a computer, can fully or partially generate the aforementioned process or function. The computer here can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or can be transferred from a computer-readable storage medium to a computer-readable and writable storage medium of another computer.

[0114] In this embodiment, the direct coupling or communication connection between the various functional modules displayed or discussed can be achieved through the indirect coupling or communication connection of some interfaces, devices or modules. For example, the short baseline positioning geometry scene module is responsible for establishing the positioning scene, the short baseline antenna signal receiving module captures the electromagnetic wave signal, the signal correlation method processing module eliminates the frequency offset and extracts the single-frequency signal, the Root-MUSIC spectrum estimation module performs spectrum measurement, and the unknown radiation source coordinate solution module finally solves the radiation source coordinates. These modules and their submodules can run dynamically in a processing component, or they can exist independently physically, or two or more modules can work together in the same processing component. This flexible configuration method makes the system highly adaptable and scalable.

[0115] The aforementioned dynamic components can be implemented as software modules and sold or used as standalone products. These modules can be stored on computer-readable media, such as memory, disks, or optical disks. When needed, they can be quickly deployed and run simply by loading the corresponding module into a computer, greatly improving the flexibility and convenience of the system.

[0116] Example 3, Root-MUSIC spectrum calculation computer readable storage medium,

[0117] This embodiment provides a Root-MUSIC spectrum calculation computer-readable storage medium, which stores multiple instructions that can be loaded by a processor to execute the steps of any of the short-baseline synthetic aperture passive positioning methods based on Root-MUSIC spectrum estimation provided by the embodiments of the present invention. The synthetic aperture spectrum calculation computer-readable storage medium includes removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Computer storage media include, but are not limited to, dynamic random access memory (DRAM), read-only memory (ROM), compact disc read-only memory (CD-ROM) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices, or any other non-transmission media for storing information that can be accessed by a computing device.

[0118] The above descriptions are merely three specific examples of the present invention and do not constitute any limitation to the present invention. Obviously, after understanding the content and principles of the present invention, professionals in this field may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0119] It should be noted that the step numbers in the specification and claims of the present invention are only for a clear description of the embodiments of the present invention and for ease of understanding, and the order of the step numbers is not limited.

Claims

1. A short-baseline synthetic aperture passive positioning processing method and system based on Root-MUSIC spectrum estimation, characterized in that: These include: (1) Build a geometric scene consisting of a reconnaissance aircraft, two short baseline antennas, and an unknown radiation source; (2) Obtain the unknown radiation source signal received by the two short baseline antennas on the reconnaissance aircraft based on the geometric scene and (3) Received signal and Perform correlation processing to obtain a single-frequency signal s c (t m ), where t m is the time of the mth pulse received by the two antennas; (4) For single-frequency signal s c (t m ) Perform Root-MUSIC spectrum estimation to obtain frequency estimates 4a) According to the single frequency signal s c (t m ) Construct the spatial pseudo-spectrum P MUSIC (f); 4b) For the spatial pseudo-spectrum P MUSIC (f) Perform phase calculation to obtain the optimal frequency estimate (5) Based on frequency estimation Solve the coordinates of unknown radiation sources.

2. The method according to claim 1, characterized in that The geometric scene in (1) is constructed, including a reconnaissance aircraft, two short baseline antennas, and an unknown radiation source, and its implementation includes: Two antennas, RX1 and RX2, are installed on a reconnaissance aircraft, with a fixed interval d between them. The reconnaissance aircraft flies at a constant speed v parallel to the ground plane in a straight line, and receives signals emitted by an unknown radiation source P during the flight. With the initial position of the first antenna RX1 on the reconnaissance aircraft as the coordinate origin, an XOY coordinate system is established for the positioning scene. The X-axis represents the reconnaissance aircraft's flight direction, i.e., the azimuth, and the Y-axis represents the direction of the unknown radiation source relative to the reconnaissance aircraft's flight path, i.e., the distance. Assume that the coordinates of the unknown radiation source P are (x0, y0), where x0 is the azimuth coordinate of the unknown radiation source P, and y0 is the distance coordinate of the unknown radiation source P.

3. The method according to claim 1, characterized in that In (2), the signal of the unknown radiation source received by the two short baseline antennas on the reconnaissance aircraft is obtained according to the geometric scene. and They are respectively represented as follows: in, and are the signal amplitudes received by the first antenna RX1 and the second antenna RX2, τ1 and τ2 are the time delays of the unknown radiation source’s transmitted signal reaching the first antenna RX1 and the second antenna RX2, φ(t-τ1) and φ(t-τ2) are the phases of the signals received by the first antenna RX1 and the second antenna RX2, respectively. c is the carrier frequency, and t is the continuous time.

4. The method according to claim 1, wherein The received signal in (3) and Perform correlation processing to obtain a single-frequency signal s c (t m ), whose implementation includes: 3a) According to the geometric scene and the cosine theorem, the instantaneous slant distance R1 (t m ) and R2(t m ): where R 10 is the instantaneous slant distance between the first antenna RX1 and the unknown radiation source P when the reconnaissance aircraft first receives the signal from the unknown radiation source, d is the distance between the first antenna RX1 and the second antenna RX2, and t m is the time when the mth pulse is received by the two antennas RX1 and RX2, v is the speed of the reconnaissance aircraft, and θ is the angle between the straight direction between the reconnaissance aircraft and the unknown radiation source and the flight direction of the reconnaissance aircraft, which is obtained by estimating the angle of arrival (DOA). 3b) The instantaneous slant distance R1 (t m ) and the instantaneous slant distance R2 (t m ) are substituted into the received signal after down conversion and Get the pulse dimension signals received by the first antenna RX1 and the second antenna RX2 respectively and in, and are the amplitudes of the signals received by the first antenna RX1 and the second antenna RX2, respectively. τ1 and τ2 are the time delays of the unknown radiation source’s transmitted signal reaching the first antenna RX1 and the second antenna RX2, respectively. m -τ1) and φ(t m -τ2) are the phases of the signals received by the first antenna RX1 and the second antenna RX2 respectively, f c is the carrier frequency, is the residual frequency offset caused by the frequency measurement error, is the measured carrier frequency, c is the speed of light; 3c) The pulse signals received by the first antenna RX1 and the second antenna RX2 respectively and Perform correlation processing to obtain a single-frequency signal s c (t m ): Among them, "*" represents the conjugate operation, The simplified formula is the single-frequency signal s c (t m ), is a single frequency signal s c (t m ), is a single frequency signal s c (t m ) phase value.

5. The method according to claim 1, wherein In the above 4a), according to the single frequency signal s c (t m ) Construct the spatial pseudo-spectrum P MUSIC (f), the implementation of which includes; 4a1) Simulate the random noise interference in the actual channel and set s c (t m ) After passing through the Gaussian white noise channel, the signal sequence is obtained Where w(n) is a Gaussian white noise signal, is the number of signal accumulations, T is the signal accumulation time, △t m is the sampling interval, △A is the simplified single-frequency signal s c (t m ), f p is a single frequency signal s c (t m ), is a single frequency signal s c (t m )’s phase value; 4a2) Assume that the sampling sequence signal For x(n), calculate its autocorrelation matrix R R=E[xx H ], where E[·] is the mathematical expectation, x=[x(0),x(1),…,x(n-1)] T is the signal vector, n is the signal length, x H is the conjugate transpose of x; 4a3) Perform the following eigendecomposition on the autocorrelation matrix R: Among them, U is the eigenvector matrix, Λ is the diagonal matrix containing eigenvalues, U H is the transposed matrix of U, λ i is the i-th eigenvalue, u i is the i-th eigenvector, u i H for u i The transposed eigenvector of ; 4a4) Transform the eigenvector u i The corresponding eigenvalue λ i After arranging from large to small, the subspace is divided, where the signal subspace is the eigenvector Us=[u1,…,u M ], the noise subspace is the eigenvector U corresponding to NM small eigenvalues n =[u M+1 ,…,u N ], M is the number of signals, N is the total number of eigenvectors; 4a5) Based on the noise subspace, the direction of the incoming signal is located by using its orthogonality. The direction vector a(f) of the incoming signal is defined as: a(f)=[1,e j2πf ,And j2π2f ,…,And j2π(K-1)f ] T , Where a(f) is a vector composed of the signals received by K array elements, and an array element is a sensor that independently collects incoming wave signals; 4a6) According to the obtained incoming signal direction vector a(f) and the eigenvector U of the noise subspace n , construct the MUSIC pseudo spectrum as: Among them U n H For U n The conjugate transpose vector of .

6. The method according to claim 1, characterized in that In the above 4b), the spatial pseudo spectrum P MUSIC (f) Perform phase calculation to obtain the optimal frequency estimate Its implementation includes: 4b1) According to the definition of MUSIC pseudo spectrum in 4a), the noise subspace projection matrix P is obtained n for: P n =U n IN n H , Among them, U n is the eigenvector of the noise subspace, U n H For U n The conjugate transposed eigenvector of ; 4b2) In order to avoid the traditional MUSIC spectrum peak search, the noise subspace projection matrix P is used n Define the polynomial P(z): P(z)=a T (z -1 )P n a(z) Where a(z)=[1,z,z 2 ,…,z K-1 ] T is the direction vector, z=e j2πf is the signal received by the array element, a T (z -1 ) is the conjugate transposed direction vector of a(z); 4b3) Expand the polynomial defined in 4b2) to obtain the expanded polynomial P(z): Among them, z -m is the phase delay of the mth array element relative to the reference array element, and the coefficient By the noise subspace matrix P n The elements of u are calculated. k,i Indicates U n The k-th row and i-th column element, u k+m,i Indicates U n The element in the k+|m|th row and i-th column of for u k+m,i The conjugate transpose of ; this polynomial is valid only when z corresponds to the true signal direction; 4b4) Based on the polynomial P(z) of z, the phase of its root is solved to obtain the estimated frequency in, F s is the sampling rate, z k is the root of P(z).

7. The method according to claim 1, characterized in that According to the best frequency estimation value in (5) Solve the coordinates of unknown radiation sources, which includes: 5a) Based on the obtained frequency estimate Inversely solve the initial slant distance R required for positioning 10 : Where d is the distance between the first antenna RX1 and the second antenna RX2, v is the speed of the reconnaissance aircraft, θ is the angle between the straight direction of the reconnaissance aircraft and the unknown radiation source and the flight direction of the reconnaissance aircraft, and f c is the carrier frequency, c is the speed of light; 5b) From the initial slope distance R 10 The unknown radiation source is located by estimating the DOA with the known angle of arrival:

8. A short-baseline synthetic aperture passive positioning system based on Root-MUSIC spectrum estimation, characterized in that: include: Short baseline positioning geometric scene module, used to establish a scene for positioning unknown radiation sources; The short baseline antenna signal receiving module is used to capture electromagnetic wave signals from unknown radiation sources in complex electromagnetic space environments when locating unknown radiation sources. A signal correlation method processing module is used to eliminate the residual frequency offset in the received signal obtained in the short baseline antenna signal receiving module and output a single frequency signal; The Root-MUSIC spectrum estimation module is used to measure the spectrum of the single-frequency signal output by the signal correlation processing module to achieve high-precision frequency estimation; The unknown radiation source coordinate solution module is used to solve the unknown radiation source coordinates based on the optimal frequency estimation value obtained by the Root-MUSIC spectrum estimation module.

9. The system according to claim 7, characterized in that: The signal correlation method processing module includes: The pulse-dimensional signal solver module is used to solve the pulse-dimensional signals received by the two antennas; The single-frequency signal extraction submodule is used to perform conjugate processing on the pulse-dimensional signals received by the two antennas to extract the single-frequency signal; The Root-MUSIC spectrum estimation module includes: An autocorrelation matrix calculation submodule is used to calculate the autocorrelation matrix of the input signal; The MUSIC pseudo-spectrum definition submodule is used to estimate the signal direction by measuring the orthogonality of the direction vector function and the noise subspace; The Root-MUSIC model solving submodule is used to construct a polynomial whose roots correspond to the signal direction through the MUSIC pseudo-spectrum definition; The polynomial root finding submodule is used to consider the roots of the polynomial near the unit circle, eliminate the pseudo roots caused by noise, convert the root angles into DOA estimates, and avoid the high computational cost of spectral peak search in the traditional MUSIC algorithm.

10. A computer-readable storage medium for Root-MUSIC spectrum calculation, characterized in that: The synthetic aperture spectrum computer readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the short-baseline synthetic aperture passive positioning method based on Root-MUSIC spectrum estimation according to any one of claims 1 to 7.

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