A newton orthogonal matching pursuit method for single-target estimation scene of blind calibration

Abstract

The application discloses a Newton orthogonal matching detection method for a single-target estimation scene of blind calibration, which comprises the following steps: establishing an observation model, obtaining a target function G, setting preposed parameters and initialization, preliminarily estimating a frequency w and an intensity x, updating g and by using Newton correction, and outputting a target estimation result set. The application can be directly applied to detecting a single-target estimation scene under the condition of blind calibration, and can also be applied to an acoustic sensor array when the positions of a signal source and a receiving sensor are not known prior information.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing, specifically relating to a blind-calibrated Newton orthogonal matching detection method for single-target estimation scenarios. Background Technology

[0002] A key requirement for accurate operation of sensor arrays in various applications, such as beamforming or direction-of-arrival estimation, is the accurate calibration of their components. Unfortunately, due to real-world challenges (such as receiver temperature variations or frequency drift), model parameters often become erroneous, leading to relative changes in sensor gain and phase, which degrades estimation performance. While offline calibration (i.e., prior to operation and using known calibration signals at known locations whenever possible) is relatively straightforward, self-calibration or blind calibration remains a very challenging task.

[0003] Blind calibration plays a crucial role in the overall success of many applications. For example, in pushbroom cameras, variations between sensors within the device often cause striping in the image; some researchers have proposed blind calibration methods as an alternative to histogram matching. In acoustic sensor arrays, blind calibration is particularly important when the positions of the signal source and receiving sensors are not known prior information (a-priori). Furthermore, blind calibration is widely applied in environmental sensor networks, radio astronomy, and compressed sensing-based imaging sensors.

[0004] For unknown sensor gain and phase, Paulraj and Kaiath proposed a least-squares method; to jointly estimate the array and direction-of-arrival angles, Friedlander and Weiss proposed an eigenvalue method; Chong and See proposed a direct maximum likelihood method, where the maximum likelihood estimation is solved through an iterative algorithm, but it does not always converge. For uniform linear arrays, a maximum likelihood-optimal weighted least-squares blind calibration method has been proposed, which takes observed data as input and outputs calibrated data to estimate the response errors of angle, amplitude, and phase. Specifically:

[0005] Calculate the covariance matrix of the observed data; based on the covariance matrix from the previous step, calculate the maximum likelihood estimate of a weighted estimation error covariance matrix using a formula; construct a correlation measurement model using the formula; obtain the maximum likelihood-optimal weighted least squares estimation result using the formula; then obtain the maximum likelihood-optimal weighted least squares estimation results for amplitude and phase; finally output the calibrated data; however, these methods are all heuristic but not optimal.

[0006] Therefore, traditional algorithms can only use known calibration signals at known locations as much as possible before the operation process, making it difficult to handle self-calibration or blind calibration problems. Furthermore, some algorithms for blind calibration generally suffer from low convergence, high complexity, and low accuracy, and are not optimal. For example, the direct maximum likelihood method, which jointly estimates all unknown model parameters, leads to a multi-dimensional optimization problem without a closed-form expression and does not converge every time. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a Newton orthogonal matching pursuit algorithm for solving single-target blind calibration problems that is low in complexity, high in accuracy, can mitigate grid mismatch, and asymptotically optimal.

[0008] The technical solution of this invention is as follows:

[0009] A blind-calibrated Newton orthogonal matching detection method for single-object estimation scenarios includes the following steps:

[0010] Step 1: Establish a noisy observation model based on a uniform linear array;

[0011] Step 2: Based on the likelihood function corresponding to the mathematical model After processing, the objective function is obtained. ;

[0012] Step 3: Set the oversampling rate γ and the maximum number of iterations. Number of iterations Error limit , and Prerequisite parameters, set , ,initialization , ;

[0013] Step 4: Input the received array data Using oversampled discrete sets for frequency A preliminary estimate is made, and then the corresponding intensity is obtained. The estimated value;

[0014] Step 5: Fix , , ,use Starting from this point, we adopt Newton's correction update. When the first set condition is met, accept the current Newton correction result;

[0015] Step 6, based on And the updated Newton correction update When the second set condition is met, accept the current Newton correction result;

[0016] Step 7: Stop the iteration and output the target estimation result set.

[0017] Preferably, in step 1, the noisy observation model is modeled based on a uniform linear array ULA as follows:

[0018]

[0019] in This indicates noisy observations. Represents the set of complex numbers. Indicates the number of sensors. Indicates intensity. and There are two noise vectors. Represents a diagonal element as the corresponding A square matrix in which each element is a zero value in all other positions; ;

[0020] Indicates the amount of amplitude cancellation. Indicates the amount of phase cancellation. Represents positive real numbers. Each element , Indicates phase;

[0021] frequency , Indicates the spacing between array elements. Indicates wavelength. Indicates the azimuth angle.

[0022] Preferably, in step 1, for frequency ,Pick Then there is ;

[0023] By definition

[0024] Then there is , here Indicates the noise variance. Indicates to Squaring each element Indicates a complex Gaussian distribution. Let M represent a square matrix of order M, with 1s on the diagonal and 0s on the other sides.

[0025] The constraints are ( (representing a small numerical value)

[0026] , , .

[0027] Preferably, in step 2, the likelihood function corresponding to the mathematical model in step 1 is:

[0028]

[0029] Where || represents taking the absolute value, ;

[0030] Taking the logarithm of each term of the likelihood function of the observations, we have:

[0031]

[0032] Minimize the objective function:

[0033]

[0034] in,

[0035] .

[0036] Preferably, in step 4, by setting the oversampling grid according to the oversampling rate γ within the range of 0 to 2π, the following is obtained: 1 grid point frequency, using a finite discrete set Instead of infinite sets, frequency is obtained by maximizing the penalty function. The estimated value is then used to obtain its corresponding intensity. The estimated value.

[0037] Preferably, in step 5, based on the updated Newton correction update ,Right now

[0038]

[0039]

[0040]

[0041] .

[0042] Preferably, in step 5, the first condition for accepting the Newton correction is:

[0043] The following three sub-conditions must be met simultaneously:

[0044] a, The determinant of the Hansen matrix is ​​greater than 0;

[0045] b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value;

[0046] c. Updated Each component lies within (1- , 1+ ).

[0047] Preferably, in step 6, based on And the updated Newton correction update ,Right now

[0048]

[0049]

[0050] ;

[0051] This indicates the operation of taking the imaginary part. This indicates the operation of taking the real part.

[0052] Preferably, in step 6, the second condition for accepting the Newton correction is:

[0053] The following three sub-conditions must be met simultaneously:

[0054] a, The determinant of the Hansen matrix is ​​greater than 0;

[0055] b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value;

[0056] c. Updated Each component is located in ( , ).

[0057] Preferably, in steps 5 and 6, one of the following two conditions is met:

[0058] a. Number of iterations Reached the upper limit;

[0059] b. Before and after the update and The absolute value of the difference is less than The number of times reached Second-rate;

[0060] Stop the iteration and output the target estimation result set.

[0061] The beneficial effects of this invention are as follows:

[0062] 1. This invention uses Newton's gradient descent method to estimate the amplitude cancellation amount and phase cancellation amount, which effectively reduces the impact of grid mismatch problem and improves the frequency estimation accuracy;

[0063] 2. This invention utilizes the advantages of the Fast Fourier Transform to completely avoid the matrix inversion operation, thus significantly reducing computational complexity and facilitating chip implementation;

[0064] 3. This invention can jointly estimate frequency, intensity, amplitude cancellation amount and phase cancellation amount. Attached Figure Description

[0065] Figure 1 This is a flowchart of the Newton orthogonal matching detection method for a blind-calibrated single-target estimation scene according to the present invention. Detailed Implementation

[0066] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0067] This invention provides a Newton orthogonal matching pursuit algorithm, establishing an algorithm model and analysis framework. The detection step utilizes a penalty function to search for spectral peaks, finding the frequency corresponding to the maximum value of the penalty function as the grid division method for estimation. The framework analysis results determine the algorithm's Newton correction method for amplitude and phase cancellation. This algorithm can be used to solve blind calibration problems for single targets, and can jointly estimate frequency, intensity, amplitude cancellation, and phase cancellation.

[0068] like Figure 1 As shown, the present invention provides a blind-calibrated Newton orthogonal matching detection method for single-target estimation scenarios, comprising the following steps:

[0069] Step 1: Establish a noisy observation model based on a uniform linear array;

[0070] Specifically, for a single signal ( (Indicates the number of signals), a single snapshot. ( In a scenario where the number of snapshots is considered, for a uniform linear array ULA, the amplitude and phase responses of each antenna are different and unknown. Therefore, the noisy observation model is modeled as follows:

[0071]

[0072] in This indicates noisy observations. Represents the set of complex numbers. Indicates the number of sensors. Indicates intensity. and There are two noise vectors. Represents a diagonal element as the corresponding A square matrix in which each element is a zero value in all other positions; ;

[0073] Indicates the amount of amplitude cancellation. Indicates the amount of phase cancellation. Represents positive real numbers. Each element , Indicates phase;

[0074] frequency , Indicates the spacing between array elements. Indicates wavelength. Indicates the azimuth angle.

[0075] Generally speaking, take Then there is ;

[0076] By definition Then there is , here Indicates the noise variance. Indicates to Squaring each element Indicates a complex Gaussian distribution. Let M represent a square matrix of order M, with 1s on the diagonal and 0s on the other sides.

[0077] The constraints are ( (representing a small numerical value);

[0078] , , .

[0079] The likelihood functions corresponding to the mathematical models in Step 2 and Step 1 are:

[0080]

[0081] Where || represents taking the absolute value, ;

[0082] Taking the logarithm of each term of the likelihood function of the observations, we have:

[0083]

[0084] Minimize the objective function:

[0085]

[0086] in,

[0087] .

[0088] objective function pair The derivative is:

[0089]

[0090] Setting the partial derivative to 0, we have:

[0091]

[0092] Will Substitution have to:

[0093]

[0094]

[0095] Therefore, the objective function is:

[0096]

[0097]

[0098] because , and These parameters are unrelated to frequency, so they can be discarded when detecting frequency.

[0099] Step 3: Set the oversampling rate γ and the maximum number of iterations. Number of iterations Error limit , and Prerequisite parameters such as the number of repetitions are set. , ,initialization , ;

[0100] Step 4: Input the received array data Using oversampled discrete sets for frequency A preliminary estimate is made, and then the corresponding intensity is obtained. Estimated values, detection and updates The process is as follows:

[0101] (1) Detection: By setting the oversampling grid according to the oversampling rate γ in the range of 0 to 2π, the following results were obtained. Grid frequency, using Find the grid frequency that maximizes the objective function as the output of the detection step, and record the detected frequency as... ,

[0102] ;

[0103] (2) Update Update its corresponding strength .

[0104] Specifically, the following formula is used:

[0105] .

[0106] Step 5: Fix , , ,use Starting from this point, we adopt Newton's correction update. The process is as follows:

[0107] Calculate the objective function term by term with respect to The gradient and Hansen's process are as follows ( (representing partial differentials)

[0108]

[0109]

[0110]

[0111] In the above formula, , ,

[0112] Then we have: ,

[0113] In the above formula, ,

[0114] ,

[0115] in,

[0116] ,

[0117] ,

[0118] Then we have:

[0119] .

[0120] In step 5, the current correction result is accepted if all three of the following conditions are met:

[0121] a, The determinant of the Hansen matrix is ​​greater than 0;

[0122] b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value;

[0123] c. Updated Each component lies within (1- , 1+ ).

[0124] In step 5, if one of the following two conditions is met,

[0125] a. Number of iterations Reached the upper limit;

[0126] b. Before and after the update and The absolute value of the difference is less than The number of times reached Second-rate;

[0127] That is, stop the iteration and start step 7.

[0128] Step 6: Based on And the updated Newton correction update The process is as follows:

[0129] The objective function remains the likelihood function.

[0130] ,

[0131] Then we have:

[0132]

[0133]

[0134] This indicates the operation of taking the imaginary part. This indicates the operation of taking the real part.

[0135] In step 6, the current correction result is accepted if all three of the following conditions are met:

[0136] a, The determinant of the Hansen matrix is ​​greater than 0;

[0137] b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value;

[0138] c. Updated Each component is located in ( , ).

[0139] In step 6, if one of the following two conditions is met,

[0140] a. Number of iterations Reached the upper limit;

[0141] b. Before and after the update and The absolute value of the difference is less than The number of times reached Second-rate;

[0142] That is, stop the iteration and start step 7.

[0143] Step 7: Stop the iteration and output the target estimation result set.

[0144] This invention can be directly applied to single-target estimation scenarios under blind calibration conditions. Furthermore, it can also be applied to acoustic sensor arrays when the positions of the signal source and receiving sensor are not known prior information.

[0145] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

Claims

1. A blind-calibrated Newton orthogonal matching detection method for single-object estimation scenes, characterized in that, Includes the following steps: Step 1: Establish a noisy observation model based on a uniform linear array; In step 1, for a uniform linear array in a scenario with a single signal and a single snapshot, the amplitude and phase responses of each antenna are different and unknown. The noisy observation model is then modeled as follows: in This indicates noisy observations. Represents the set of complex numbers. Indicates the number of sensors. Indicates intensity. and There are two noise vectors. Represents a diagonal element as the corresponding A square matrix in which each element is a zero value in all other positions; ; Indicates the amount of amplitude cancellation. Indicates the amount of phase cancellation. Represents positive real numbers. Each element , Indicates phase; frequency , Indicates the spacing between array elements. Indicates wavelength. Indicates azimuth; Step 2: Based on the likelihood function corresponding to the mathematical model After processing, the objective function is obtained. ; In step 2, the likelihood function corresponding to the mathematical model in step 1 is: Where || represents taking the absolute value, ; Taking the logarithm of each term of the likelihood function of the observations, we have: Minimize the objective function: in, ； Step 3: Set the oversampling rate γ and the maximum number of iterations. Number of iterations Error limit , and ,set up , ,initialization , ; Step 4: Input the received array data Using oversampled discrete sets for frequency A preliminary estimate is made, and then the corresponding intensity is obtained. The estimated value; Step 5: Fix , , ,use Starting from this point, we adopt Newton's correction update. When the first set condition is met, accept the current Newton correction result; In step 5, based on the updated Newton correction update ,Right now ， ， ； In step 5, the first condition for accepting the Newton correction is: The following three sub-conditions must be met simultaneously: a, The determinant of the Hansen matrix is ​​greater than 0; b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value; c. Updated Each component lies within (1- , 1+ ); Step 6, based on And the updated Newton correction update When the second set condition is met, accept the current Newton correction result; In step 6, Newton correction is used for updating. ,Right now ， ， ； This indicates the operation of taking the imaginary part. This indicates the operation of taking the real part; In step 6, the second condition for accepting Newton's correction is: The following three sub-conditions must be met simultaneously: a, The determinant of the Hansen matrix is ​​greater than 0; b. Updated The value of the corresponding penalty function is less than that before the update. The corresponding value; c. Updated Each component is located in ( , ); Step 7: Stop the iteration and output the target estimation result set.

2. The Newton orthogonal matching detection method for blind-calibrated single-target estimation scenarios according to claim 1, characterized in that: In step 1, for frequency ,Pick Then there is ; By definition , Then there is , here Indicates the noise variance. Indicates to Squaring each element Indicates a complex Gaussian distribution. Let M represent a square matrix of order M, with 1s on the diagonal and 0s on the other sides. The constraints are: , , .

3. The Newton orthogonal matching detection method for blind-calibrated single-target estimation scenarios according to claim 2, characterized in that: In step 4, by setting the oversampling grid according to the oversampling rate γ within the range of 0 to 2π, the following was obtained: 1 grid point frequency, using a finite discrete set Instead of infinite sets, the frequency is obtained by maximizing the penalty function. The estimated value is then used to obtain its corresponding intensity. The estimated value.

4. The Newton orthogonal matching detection method for blind-calibrated single-object estimation scenarios according to claim 3, characterized in that: In steps 5 and 6, if one of the following two conditions is met, a. Number of iterations Reached the upper limit; b. Before and after the update and The absolute value of the difference is less than The number of times reached Second-rate; Stop the iteration and output the target estimation result set.

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