A joint direction finding and amplitude-phase error estimation method based on airborne circular array rotation measurement fusion
By using an airborne circular array rotation measurement fusion method, and deriving a closed-form analytical solution through multiple rotation observations and the Lagrange multiplier method, the problem of self-correction of amplitude and phase errors on a uniform circular array was solved, achieving high-precision direction-of-arrival estimation and array self-correction.
Patent Information
- Application Number
- CN202610686682.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-19
- Publication Date
- 2026-08-25
AI Technical Summary
Existing technologies struggle to achieve closed-loop self-correction without auxiliary array elements on uniform circular arrays, and iterative algorithms are prone to divergence under large phase errors, failing to effectively estimate the direction of arrival and amplitude-phase error.
By constructing an airborne circular array rotation measurement model, utilizing the covariance matrix decomposition and noise subspace of multiple rotation observation data, a joint orthogonal projection matrix is built. The Lagrange multiplier method is introduced to derive a closed-form analytical solution, thereby achieving self-correction of amplitude and phase errors.
Without the need for auxiliary array elements, complete self-correction of amplitude and phase errors was successfully achieved on a uniform circular array, improving direction finding accuracy and computational stability, and overcoming the challenges of direction finding under strong error environments.
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Figure CN122632178A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing and wireless direction finding technology, specifically relating to a joint direction finding and amplitude and phase error estimation method based on airborne circular array rotation measurement fusion. Background Technology
[0002] Array signal processing, as a key technology for acquiring and analyzing spatiotemporal signals, plays a fundamental role in many fields such as modern radar reconnaissance, sonar detection, electronic warfare, wireless communication, and UAV navigation. Among them, direction of arrival (DOA) estimation technology is a research hotspot in both academia and industry.
[0003] Classical subspace-based super-resolution direction-of-arrival (DOA) algorithms, such as Multiple Signal Classification (MUSIC) and Rotationally Invariant Subspace (ESPRIT), can achieve extremely high DOA accuracy under conditions of low signal-to-noise ratio and few snapshots. However, the performance of these high-resolution algorithms is highly dependent on the precise knowledge of the array manifold. In practical engineering and applications, due to factors such as antenna manufacturing tolerances, device aging, temperature drift, differences in feed line length, and imperfections in manufacturing processes, the array inevitably suffers from amplitude and phase errors. Amplitude and phase errors directly disrupt the spatial phase consistency of the array, leading to array manifold mismatch, which in turn causes a sharp drop in DOA accuracy or even complete algorithm failure. Therefore, robust correction for unknown amplitude and phase errors and high-precision DOA estimation have become critical problems that urgently need to be solved.
[0004] Existing array error correction techniques are mainly divided into offline correction, active correction, and self-correction techniques. Offline physical measurement and lookup table methods can only compensate for the initial static amplitude and phase errors of the array, and cannot achieve online correction of dynamic amplitude and phase mismatches caused by temperature drift or device aging. Active correction techniques use auxiliary signal sources with known positions or waveforms for parameter estimation. Although the accuracy is extremely high, the engineering cost is high. It not only requires the deployment of additional auxiliary transmitters or precision measurement equipment, but also usually requires interruption of normal system operation, making it extremely unsuitable for non-cooperative or highly dynamic electronic reconnaissance scenarios.
[0005] To overcome the aforementioned limitations, self-calibration techniques that utilize only chance signals in the environment for joint parameter estimation have become mainstream, mainly categorized into iterative and closed-form solutions. Iterative methods, such as the WF algorithm and the Newton-Maximum Likelihood (N-ML) algorithm, typically employ an alternating projection strategy, modeling DOA estimation and error correction as a multidimensional nonlinear optimization problem. These algorithms generally face the dual challenges of local convergence and high computational complexity: due to the non-convex objective function, the algorithm is highly sensitive to initial values when facing large phase errors, easily getting trapped in local minima and leading to divergence; simultaneously, operations such as inverting high-dimensional matrices introduce significant computational overhead.
[0006] In closed-array correction methods, schemes relying on auxiliary array elements significantly increase the hardware cost and complexity of the system, making it difficult to meet the requirements of lightweight airborne systems. Conversely, closed-array correction methods without auxiliary array elements mostly rely strictly on specific array geometries, such as utilizing the Toeplitz property of uniform linear arrays, making them difficult to generalize. Uniform circular arrays (UCA) offer 360° omnidirectional coverage, but because their steering vectors lack the van der Mönch or Toeplitz structure, existing closed-array correction methods without auxiliary array elements are difficult to apply directly. Some existing circular array correction schemes can only mathematically eliminate the influence of phase errors to achieve closed-array direction finding, but they cannot separate and explicitly estimate the specific amplitude and phase error parameters, failing to achieve true complete array correction.
[0007] In summary, existing methods have significant limitations in achieving complete self-calibration for uniform circular arrays: iterative algorithms are prone to divergence due to sensitivity to initial conditions under large phase errors, while existing closed-form algorithms struggle to achieve complete calibration on uniform circular arrays without relying on auxiliary array elements. Currently, there is no non-iterative self-calibration method suitable for uniform circular arrays, requiring no auxiliary array elements, capable of parameter dimensionality reduction through closed-form algebraic derivation, and simultaneously achieving complete joint estimation of DOA and amplitude / phase errors. Effectively decoupling parameters, avoiding divergence risks, and ultimately determining the target direction with high accuracy have become pressing technical challenges. Summary of the Invention
[0008] The technical problem to be solved by the present invention is to provide a joint direction finding and amplitude and phase error estimation method based on the fusion of airborne circular array rotation measurement, which addresses the shortcomings of the prior art.
[0009] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:
[0010] A joint direction finding and amplitude / phase error estimation method based on airborne circular array rotation measurement fusion includes:
[0011] Step 1) Construct an array receiving data model of an airborne circular array under amplitude and phase error environment, control the airborne uniform circular array to perform mechanical step rotation, obtain array receiving data under multiple rotation observations, calculate the covariance matrix of array receiving data under each rotation observation and perform eigenvalue decomposition, and extract the noise subspace corresponding to each rotation observation.
[0012] Step 2), construct a joint orthogonal projection matrix using the orthogonality of the noise subspace and the steering vector, and construct a quadratic optimization objective function containing the amplitude and phase errors to be estimated based on the joint orthogonal projection matrix;
[0013] Step 3) Introduce constraints to eliminate scale ambiguity, and derive the closed-form analytical solution of the amplitude and phase error using the Lagrange multiplier method;
[0014] Step 4) Substitute the analytical solution back into the quadratic optimization objective function, and obtain the estimated direction of arrival of the radiation source through one-dimensional spectral search;
[0015] Step 5) Calculate the total joint orthogonal projection matrix based on the estimated wave direction of arrival, and solve the closed-form solution for the unknown amplitude and phase errors of all channels.
[0016] To optimize the above technical solution, the specific measures also include:
[0017] Step 1) above, which describes constructing an array receiving data model for an airborne circular array under amplitude and phase error conditions, specifically includes:
[0018] Settings include A uniform circular array of omnidirectional elements is mounted on the UAV, with a radius of [missing information]. ; A far-field narrowband unknown radiation source is incident on a circular array, with a wavelength of [wavelength missing]. ;
[0019] The steering vector under error-free conditions is expressed as: ,in, This represents the azimuth angle of the k-th radiation source. This represents the azimuth angle of the m-th array element relative to the reference array element. ;
[0020] Considering the existence of unknown amplitude and phase errors in the array, the amplitude and phase error matrix of the array elements is defined as follows: ,in This represents the amplitude and phase error of the m-th array element relative to the reference array element. This represents the magnitude error of the m-th array element relative to the reference array element. This represents the phase error of the m-th array element relative to the reference array element;
[0021] Define the direction of arrival vector ;
[0022] The array received data model for the l-th snapshot is: ,in, For the number of snapshots, For array manifold matrix, For signal vectors, It is a complex vector of additive white Gaussian noise.
[0023] The signal vectors of the aforementioned K far-field narrowband unknown radiation sources are independent and identically distributed, and are incoherent generalized statistical processes with a mean of zero; the additive white Gaussian noise complex vector is white in space, has a mean of 0, and is statistically independent of the radiation source signals.
[0024] In step 1) above, while keeping the incident angle of the radiation source constant, rotate the airborne uniform circular array. From several angles, including the initial physical state, a total of [number] processes are carried out. The observation, i.e., the total number of observation groups is W, is used to obtain array received data under multiple rotation observations;
[0025] For each rotation observation, calculate the covariance matrix of the array received data and perform eigenvalue decomposition:
[0026] ,in, This represents a diagonal matrix consisting of K large eigenvalues, whose corresponding eigenvectors constitute the signal subspace. ; Indicates by The diagonal matrix formed by the smaller eigenvalues, and the corresponding eigenvectors constitute the noise subspace. ; The sign for conjugate transpose;
[0027] Extracting the noise subspace corresponding to the w-th rotation observation ,in .
[0028] The total number of observation groups W of the aforementioned airborne uniform circular array satisfies: .
[0029] Step 2) above utilizes the orthogonality between the noise subspace of each observation and the steering vector affected by amplitude and phase errors to search for an arbitrary spatial angle. Construct a joint observation matrix by combining the conditions of W observations:
[0030]
[0031] in, The search angle corresponding to the w-th observation Error-free guiding vector;
[0032] Based on the joint observation matrix, the joint orthogonal projection matrix is constructed as follows: ;
[0033] Constructing a framework for the search angle based on the joint orthogonal projection matrix. and the amplitude and phase error vector to be estimated The second-order optimization objective function .
[0034] Step 3) above: Set the amplitude error of the reference array element. Phase error This makes the first element of amplitude and phase error To eliminate scale ambiguity, constraints are introduced: ,in, ;
[0035] Construct the Lagrange function using the Lagrange multiplier method. ,in, For the Lagrange operator, derive the fixed search angle. At that time, the optimal amplitude and phase error closed-form analytical solution that minimizes the quadratic optimization objective function is found. .
[0036] Step 4) above substitutes the closed-form analytical solution of the amplitude and phase error back into the quadratic optimization objective function to obtain the angle... The problem of finding the minimum value, i.e., finding Make Minimize; Defined as a one-dimensional spatial spectral function; for scalar search angles A one-dimensional search is performed to find K angles that maximize the one-dimensional spatial spectral function, thereby obtaining estimates of the directions of arrival (DOAs) of the K radiation sources. .
[0037] Step 5 above: Calculate the joint orthogonal projection matrix corresponding to each of the K directions of arrival estimates. And add them together to obtain the total joint orthogonal projection matrix. The total joint orthogonal projection matrix Substituting into the constrained minimization problem solution model, the closed-form solution of the unknown amplitude and phase errors of all channels is calculated. .
[0038] The present invention has the following beneficial effects:
[0039] This invention addresses the limitations of existing self-calibrating iterative algorithms, which are prone to getting trapped in local extrema, and the fact that closed-form solutions often rely on special array structures such as auxiliary array elements or uniform linear arrays. It successfully achieves self-calibration on a uniform circular array without the need for auxiliary array elements, effectively overcoming the underdetermined problem of static observation and significantly improving the direction finding accuracy and computational stability under strong error environments.
[0040] This invention constructs a joint observation model by introducing a multi-moment rotation mechanism of an airborne circular array, effectively overcoming the underdetermined problem caused by array manifold mismatch under static observation. It rigorously derives and separates the closed-form analytical solution for amplitude and phase errors using the Lagrange multiplier method, completely eliminating complex nonlinear iterative searches and effectively avoiding the risk of the algorithm getting trapped in local extrema and diverging under strong error environments. Without introducing auxiliary array elements, it breaks through the strict dependence of existing closed-form solutions on specific array structures such as uniform linear arrays, successfully achieving complete decoupling of error parameters and direction-of-arrival (DOA) information on a uniform circular array with omnidirectional coverage advantages. Then, high-precision DOA estimation is achieved through one-dimensional dimensionality reduction search, and the total orthogonal projection matrix is reconstructed based on this angle estimate, directly obtaining the final closed-form solution for the amplitude and phase errors of the entire array channels. This completes the array's self-calibration, significantly improving the direction-finding accuracy and computational robustness of the system in practical engineering applications under extremely low signal-to-noise ratio and strong phase perturbation environments. Attached Figure Description
[0041] Figure 1 A flowchart of a joint direction finding and amplitude and phase error estimation method based on airborne circular array rotation measurement fusion provided by the present invention;
[0042] Figure 2 This is a schematic diagram of the airborne uniform circular array direction finding scenario described in this invention;
[0043] Figure 3 This is a comparison of the spatial spectra of the method described in this invention and the traditional algorithm under unknown amplitude and phase errors;
[0044] Figure 4 This is a comparison chart of the true and estimated values of the array amplitude and phase error obtained by the method described in this invention;
[0045] Figure 5 This is a graph showing the root mean square error performance of the direction of arrival estimation method described in this invention as a function of signal-to-noise ratio.
[0046] Figure 6 This is a comparison chart of the root mean square error of the direction finding method described in this invention under different error conditions in a real-world scenario. Detailed Implementation
[0047] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
[0048] This invention discloses a joint direction finding and amplitude / phase error estimation method based on airborne circular array rotation measurement fusion. First, a multi-time rotation observation model of an airborne uniform circular array under amplitude / phase error conditions is constructed. The covariance matrix of each observation (multiple sets of array received data) is calculated and eigenvalue decomposition is performed to extract the corresponding noise subspace. Second, utilizing the orthogonality between the noise subspace of each observation and its corresponding steering vector disturbed by amplitude / phase error, a system quadratic optimization objective function and a joint orthogonal projection matrix are constructed. Next, reference array element constraints are introduced to eliminate scale ambiguity. The optimization problem is solved using the Lagrange multiplier method, deriving and separating the closed-form analytical expression of the amplitude / phase error at a fixed angle, thus decoupling the error parameter from the angle information. Then, the analytical solution of the amplitude / phase error is substituted back into the quadratic optimization objective function, and a high-precision direction-of-arrival estimation of the radiation source is achieved through one-dimensional dimensionality reduction search. Finally, the overall joint orthogonal projection matrix is calculated based on the obtained direction-of-arrival estimation value, substituted back into the constrained minimization problem solution model, and the closed-form solution of the unknown amplitude / phase error of the entire array channel is obtained. Figure 1 As shown, the method specifically includes the following steps:
[0049] Step 1) Construct an array receiving data model of an airborne circular array under amplitude and phase error environment, control the airborne uniform circular array to perform mechanical step rotation, obtain array receiving data under multiple rotation observations, calculate the covariance matrix of array receiving data under each rotation observation and perform eigenvalue decomposition, and extract the noise subspace corresponding to each rotation observation.
[0050] Step 2), construct a joint orthogonal projection matrix using the orthogonality of the noise subspace and the steering vector, and construct a quadratic optimization objective function containing the amplitude and phase errors to be estimated based on the joint orthogonal projection matrix;
[0051] Step 3) Introduce constraints to eliminate scale ambiguity, and derive the closed-form analytical solution of the amplitude and phase error using the Lagrange multiplier method;
[0052] Step 4) Substitute the analytical solution back into the quadratic optimization objective function, and obtain the estimated direction of arrival of the radiation source through one-dimensional spectral search;
[0053] Step 5) Calculate the total joint orthogonal projection matrix based on the estimated wave direction of arrival, and solve the closed-form solution for the unknown amplitude and phase errors of all channels.
[0054] In the embodiment, step 1) constructs a DOA estimation model for an airborne uniform circular array under amplitude and phase error conditions to obtain array received data under each rotation observation; such as Figure 2 As shown, the settings include A uniform circular array of omnidirectional elements is mounted on the UAV, with a radius of [missing information]. ; A far-field narrowband unknown radiation source is incident on a circular array, with a wavelength of [wavelength missing]. ;
[0055] Assume the radiation source signal is an incoherent generalized statistical process with zero mean, and the noise is additive white Gaussian noise;
[0056] The steering vector under error-free conditions is expressed as: ,in, This represents the azimuth angle of the k-th radiation source. This represents the azimuth angle of the m-th array element relative to the reference array element. This method takes The array element is used as the reference array element;
[0057] Considering that actual arrays have unknown amplitude and phase errors due to factors such as device aging, the amplitude and phase error matrix of the array elements is defined as follows: ,in This represents the amplitude and phase error of the m-th array element relative to the reference array element. This represents the magnitude error of the m-th array element relative to the reference array element. The phase error of the m-th array element relative to the reference array element is represented; the direction-of-arrival vector is defined. Then the array received data model for the l-th snapshot is corrected as follows: ,in, For the number of snapshots, For array manifold matrix, For signal vectors, It is a complex vector of additive white Gaussian noise;
[0058] Step 1) Control the airborne uniform circular array to perform mechanical step rotation and obtain the noise subspace under multiple observations; while keeping the incident angle of the radiation source constant, rotate the airborne uniform circular array. From several angles, including the initial physical state, a total of [number] processes are carried out. The number of observations, i.e., the total number of observation groups, is W;
[0059] For each observation, calculate the covariance matrix of the array received data and perform eigenvalue decomposition: ,in, This represents a diagonal matrix consisting of K large eigenvalues, whose corresponding eigenvectors constitute the signal subspace. ; Indicates by The diagonal matrix formed by the smaller eigenvalues, and the corresponding eigenvectors constitute the noise subspace. Obtain the noise subspace corresponding to the w-th observation. ,in ;
[0060] The direction-finding environment and signal in step 1) satisfy the following assumptions:
[0061] The signal vectors of the K far-field narrowband unknown radiation sources are independently and identically distributed, and are incoherent generalized statistical processes with a mean of zero; the additive white Gaussian noise complex vector is white in space, has a mean of 0, and is statistically independent of the radiation source signals.
[0062] Step 2) Merge W observation data and introduce a one-dimensional scalar search angle. The system constructs a quadratic optimization objective function and a joint orthogonal projection matrix. Under a single static observation, the number of equations constructed using orthogonality is MK, while the number of unknowns is M+K, forming an underdetermined system of equations that cannot be directly solved. Therefore, this invention increases the number of equations by obtaining multiple sets of observation data through a rotating circular array. Utilizing the orthogonality between the noise subspace of each observation and the steering vector affected by amplitude and phase errors, the system searches for arbitrary spatial angles. Construct a joint observation matrix by combining the conditions of W observations:
[0063]
[0064] in, The search angle corresponding to the w-th observation Error-free guiding vector;
[0065] Define the joint orthogonal projection matrix as , construct about search perspective and the amplitude and phase error vector to be solved The second-order optimization objective function This optimization problem aims to find and This ensures that the noise subspace obtained from W observations is as orthogonal as possible to the corresponding steering vector affected by amplitude and phase error disturbances; by combining W observations, the number of independent orthogonal equations that the system can provide is expanded to W(MK).
[0066] Step 3) Introduce reference array element constraints and derive the closed-form analytical solution of amplitude and phase error using the Lagrange multiplier method;
[0067] Since g in the objective function is equivalent to a constant multiple of cg, meaning the equation still holds if g is scaled, this leads to an infinite number of spurious solutions, a problem known as "scale ambiguity." To eliminate scale ambiguity during the optimization process, this invention sets an amplitude error for the reference array elements. Phase error This makes the first element of amplitude and phase error To eliminate scale ambiguity, linear constraints are introduced: ,in, Construct the Lagrange function using the Lagrange multiplier method. ,in, Let Lagrange be the Lagrange operator, and let the Lagrange function pair... Find the partial derivative and set it to be This leads to the derivation of a fixed search angle. When the objective function is minimized, the optimal closed-form analytical solution for amplitude and phase error is found. ;
[0068] At this point, because the search angle is fixed Furthermore, a reference array element constraint is introduced, leaving only M-1 amplitude and phase error parameters as unknowns. To ensure a unique closed-form analytical solution to this quadratic optimization problem, the number of independent equations provided by the system must be greater than or equal to the number of unknowns; that is, the joint observation matrix must satisfy the full column rank condition, and the total number W of observation groups of the airborne uniform circular array must satisfy the theoretical identifiability condition of the system. .
[0069] Step 4) Perform a one-dimensional spectral search based on closed decoupling to obtain the estimated direction of arrival of the radiation source;
[0070] The amplitude and phase error Substituting the closed-form analytical solution back into the quadratic optimization objective function, we obtain the solution with respect to the angle. The problem of finding the minimum value of the objective function is transformed into finding the angle. Make Minimize (obtain the minimum value); to facilitate spectral peak search, the reciprocal of the objective function is defined as a one-dimensional spatial spectral function, i.e. ;
[0071] This successfully reduces the dimensionality of joint parameter estimation to a scalar search perspective only. A one-dimensional search is performed to find K angles that maximize the one-dimensional spatial spectral function, thereby obtaining estimates of the directions of arrival (DOAs) of the K radiation sources. ;
[0072] Step 5) Perform amplitude and phase error self-calibration calculation based on the direction of arrival estimate to obtain the final amplitude and phase error estimate for the entire array channel;
[0073] Based on the K specific directions of arrival estimates obtained in step 4), calculate their corresponding joint orthogonal projection matrices. And sum the K matrices to obtain the total matrix. , the total matrix Substituting these values into the constrained minimization problem solution model, the final amplitude and phase error estimates for the entire array channels are calculated. The solution model for the constraint and minimization problems is the same as before, where constraints refer to... The minimization problem-solving model refers to the quadratic optimization objective function. .
[0074] This completes the self-calibration of the airborne uniform circular array and the direction finding of the radiation source under unknown amplitude and phase errors.
[0075] Figure 3 This is a spatial spectrum comparison between the method described in this invention and the traditional algorithm under unknown amplitude and phase errors. The simulation parameters were set as follows: a uniform circular array with 5 elements, an array aperture of 0.25 m, two radiation source incident angles of 80° and 170° respectively, a signal-to-noise ratio of 20 dB, 800 snapshots, 4 rotations, and amplitude and phase error vectors corresponding to the 5 array elements. .Depend on Figure 3 It can be seen that when there is an unknown amplitude and phase error in the array, the traditional MUSIC algorithm cannot form obvious spectral peaks due to severe manifold mismatch and cannot distinguish the source at all. However, this invention utilizes the spatial diversity advantage introduced by rotation to achieve parameter correction in the blind environment, forming extremely high and sharp spectral peaks in the direction of the real source. The difference between the main lobe peak and the background noise is significant, and high-precision direction finding is successfully achieved.
[0076] Figure 4 This is a comparison chart of the actual and estimated values of the array amplitude and phase error obtained by the method described in this invention. Simulation parameter settings and... Figure 3 Consistent. For example... Figure 4 Comparison of amplitude error in (a) with Figure 4 As shown in the phase error comparison in (b), even with significant amplitude gain fluctuations and large phase deviations, this invention can accurately match the true value center for the estimated amplitude and phase errors of each channel of the entire array without prior correction or external auxiliary sources, thus achieving high-precision self-calibration separation of unknown amplitude and phase errors of the array.
[0077] Figure 5 This is a graph showing the root mean square error (RMSE) performance of the direction-of-arrival (DOA) estimation method described in this invention as a function of signal-to-noise ratio (SNR). Simulation parameters were set as follows: SNR range of -15dB to 30dB, and array amplitude error following a mean of 1 and a standard deviation of [value missing]. The phase error follows a Gaussian distribution with a mean of 0 and a standard deviation of 0. Gaussian distribution, with the remaining parameters being... Figure 3 Consistent. By Figure 5 As can be seen, after array self-calibration, the direction-of-arrival (DOA) estimation error of this invention exhibits a strictly linear decreasing trend in the semi-logarithmic coordinate system as the signal-to-noise ratio (SNR) increases. Especially in the medium-to-high SNR region, the estimation error of this invention has been reduced to an extremely low order of magnitude, and the overall direction-finding accuracy is significantly better than the traditional MUSIC algorithm, iterative WF algorithm, and N-ML algorithm, demonstrating excellent asymptotic consistency and direction-finding performance.
[0078] Figure 6 This is a comparison chart of the root mean square error of direction finding under different error conditions in actual scenarios using the method described in this invention. The measured parameters were set as follows: a five-element inverted uniform circular array with an array aperture of 0.25m, a transmitter frequency of 1883MHz, and scenarios including single-source and dual-source scenarios. Tests were conducted under both original strong phase error and weak phase error conditions after manual initial calibration. Figure 6 It can be seen that in harsh scenarios with strong initial phase errors or even dual signal sources at the same frequency, the traditional MUSIC algorithm fails completely due to severe array manifold mismatch, while iterative correction algorithms such as WF and N-ML also fail to converge normally due to the lack of accurate initial value guidance. In contrast, this invention adopts a closed decoupling mechanism, which does not rely on the initial error value at all. It can maintain an extremely low root mean square error in direction finding regardless of whether the error is strong or weak. In practical engineering applications, it has demonstrated extremely excellent direction finding robustness and computational stability.
[0079] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.
Claims
1. A method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion, characterized in that, include: Step 1) Construct an array receiving data model of an airborne circular array under amplitude and phase error environment, control the airborne uniform circular array to perform mechanical step rotation, obtain array receiving data under multiple rotation observations, calculate the covariance matrix of array receiving data under each rotation observation and perform eigenvalue decomposition, and extract the noise subspace corresponding to each rotation observation. Step 2), construct a joint orthogonal projection matrix using the orthogonality of the noise subspace and the steering vector, and construct a quadratic optimization objective function containing the amplitude and phase errors to be estimated based on the joint orthogonal projection matrix; Step 3), introduce constraints to eliminate scale ambiguity, and derive the closed-form analytical solution of the amplitude and phase error using the Lagrange multiplier method; Step 4), substitute the analytical solution back into the quadratic optimization objective function, and obtain the estimated direction of arrival of the radiation source through one-dimensional spectral search; Step 5) Calculate the total joint orthogonal projection matrix based on the estimated direction of arrival, and solve the closed-form solution for the unknown amplitude and phase errors of all channels.
2. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 1, characterized in that, Step 1) The construction of the airborne circular array array receiving data model under amplitude and phase error environment specifically includes: Settings include A uniform circular array of omnidirectional elements is mounted on the UAV, with a radius of [missing information]. ; A far-field narrowband unknown radiation source is incident on a circular array, with a wavelength of [wavelength missing]. ; The steering vector under error-free conditions is expressed as: ,in, This represents the azimuth angle of the k-th radiation source. This represents the azimuth angle of the m-th array element relative to the reference array element. ; Considering the existence of unknown amplitude and phase errors in the array, the amplitude and phase error matrix of the array elements is defined as follows: ,in This represents the amplitude and phase error of the m-th array element relative to the reference array element. This represents the magnitude error of the m-th array element relative to the reference array element. This represents the phase error of the m-th array element relative to the reference array element; Define the direction of arrival vector ; The array received data model for the l-th snapshot is: ,in, For the number of snapshots, For array manifold matrix, For signal vectors, It is a complex vector of additive white Gaussian noise.
3. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 2, characterized in that, The signal vectors of the K far-field narrowband unknown radiation sources are independently and identically distributed, and are incoherent generalized statistical processes with a mean of zero; the additive white Gaussian noise complex vector is white in space, has a mean of 0, and is statistically independent of the radiation source signals.
4. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 2, characterized in that, In step 1), the airborne uniform circular array is rotated while the incident angle of the radiation source remains constant. From several angles, including the initial physical state, a total of [number] processes are carried out. The observation, i.e., the total number of observation groups is W, is used to obtain array received data under multiple rotation observations; For each rotation observation, calculate the covariance matrix of the array received data and perform eigenvalue decomposition: ,in, This represents a diagonal matrix consisting of K large eigenvalues, whose corresponding eigenvectors constitute the signal subspace. ; Indicates by The diagonal matrix formed by the smaller eigenvalues, and the corresponding eigenvectors constitute the noise subspace. ; The symbol for conjugate transpose; Extracting the noise subspace corresponding to the w-th rotation observation ,in .
5. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 4, characterized in that, The total number of observation groups W of the airborne uniform circular array satisfies: .
6. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 4, characterized in that, Step 2) utilizes the orthogonality between the noise subspace of each observation and the steering vector disturbed by amplitude and phase errors to search for any spatial angle. Construct a joint observation matrix by combining the conditions of W observations: ； in, For the w-th observation, the corresponding search angle Error-free guiding vector; Based on the joint observation matrix, the joint orthogonal projection matrix is constructed as follows: ; Constructing a framework for the search angle based on the joint orthogonal projection matrix. and the amplitude and phase error vector to be estimated The second-order optimization objective function .
7. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 6, characterized in that, Step 3) sets the amplitude error of the reference array element. Phase error This makes the first element of the amplitude and phase error To eliminate scale ambiguity, constraints are introduced: ,in, ; Construct the Lagrange function using the Lagrange multiplier method. ,in, For the Lagrange operator, derive the fixed search angle. At that time, the optimal amplitude and phase error closed-form analytical solution that minimizes the quadratic optimization objective function is found. .
8. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 7, characterized in that, In step 4), the closed-form analytical solution of the amplitude and phase error is substituted back into the quadratic optimization objective function to obtain the result regarding the angle. The problem of finding the minimum value, i.e., finding Make Minimize; Defined as a one-dimensional spatial spectral function; for scalar search angles A one-dimensional search is performed to find the K angles that maximize the one-dimensional spatial spectral function, thereby obtaining the estimated directions of arrival (DOAs) of the K radiation sources. .
9. The method for joint direction finding and amplitude / phase error estimation based on airborne circular array rotation measurement fusion according to claim 8, characterized in that, In step 5), the joint orthogonal projection matrix is calculated based on the K directions of arrival estimates. And add them together to obtain the total joint orthogonal projection matrix. The total joint orthogonal projection matrix Substituting into the constrained minimization problem solution model, the closed-form solution of the unknown amplitude and phase errors of all channels is calculated. .