A method and device for estimating multidimensional parameters of an array single snapshot under interference conditions

Abstract

The present application provides a method and device for estimating multidimensional parameters of an array in a single snapshot under interference conditions. The method comprises: first obtaining an array receiving signal under interference conditions; converting the source multidimensional parameter estimation problem into a multidimensional frequency estimation problem; then performing a multidimensional frequency rough estimation on the array receiving signal to obtain a multidimensional frequency rough estimation result; finally, calculating a frequency estimation result based on the multidimensional frequency rough estimation result and the multidimensional frequency fine estimation result, and converting the frequency estimation result into a parameter estimation result. It can be seen that this method does not require matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of a coherent source using only single snapshot data.

Description

Technical Field

[0001] The present application relates to the field of radar and reconnaissance technology, and in particular to a method and device for estimating multi-dimensional parameters of an array single snapshot under interference conditions. Background Art

[0002] Parameter estimation is a crucial task in radar and reconnaissance systems, directly impacting the array's ability to detect, track, and identify signal sources. Traditional array parameter estimation methods are mostly based on spatial methods. These methods collect a large number of independent and identically distributed (IID) samples to estimate the echo covariance matrix. Matrix decomposition techniques are then used to obtain the signal and noise subspaces, enabling super-resolution estimation of the source parameters. However, in practice, high-dimensional matrix decomposition consumes significant computational resources for large-scale array antenna systems, resulting in excessively high computational costs. Furthermore, due to the motion of the source / interference and the rapid scanning of the antenna beam, collecting a large number of IID samples becomes impractical, further limiting the practical application of spatial methods. Furthermore, when there is coherence between the signal sources, directly using subspace algorithms cannot accurately measure the parameters. Therefore, existing methods are computationally expensive, unsuitable for coherent signal sources, and struggle to meet real-time requirements. Summary of the Invention

[0003] The purpose of the embodiments of the present application is to provide a method and device for estimating multidimensional parameters of an array in a single snapshot under interference conditions, which can directly process multiple coherent received signals without the need for matrix decomposition and grid search, thereby achieving real-time, fast and accurate multidimensional parameter estimation.

[0004] In a first aspect, the present application provides a method for estimating multidimensional parameters of an array single snapshot under interference conditions, comprising:

[0005] Obtaining array received signals under interference conditions;

[0006] Converting the multi-dimensional parameter estimation problem of the signal source of the array receiving signal into a multi-dimensional frequency estimation problem;

[0007] Performing a multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result;

[0008] Performing a multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result;

[0009] Calculating a frequency estimation result based on the multidimensional frequency rough estimation result and the multidimensional frequency fine estimation result;

[0010] The frequency estimation result is converted into a parameter estimation result.

[0011] In the above implementation, the array received signal under interference conditions is first acquired; the source multidimensional parameter estimation problem is converted into a multidimensional frequency estimation problem; a coarse multidimensional frequency estimation is then performed on the array received signal to obtain a coarse multidimensional frequency estimation result; finally, based on the coarse and fine multidimensional frequency estimation results, a frequency estimation result is calculated and converted into a parameter estimation result. This method eliminates the need for matrix decomposition and grid search, and can quickly and accurately measure multiple dimensional parameters of a coherent source, such as distance, angle, and velocity, using only single snapshot data.

[0012] Furthermore, performing a multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result includes:

[0013] Performing a multidimensional fast Fourier transform on the array received signal based on the multidimensional frequency estimation problem to obtain a multidimensional spectrum matrix block;

[0014] Acquire the coordinates of the peak point of the signal spectrum according to the spectrum matrix block;

[0015] A multi-dimensional frequency rough estimation of the complex sine wave is performed according to the coordinates of the peak points of the signal spectrum to obtain a multi-dimensional frequency rough estimation result.

[0016] Furthermore, the multi-dimensional frequency rough estimation result is:

[0017]

[0018] in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; l k A positive integer representing the expansion factor.

[0019] Furthermore, performing multidimensional frequency fine estimation on the array received signal according to the multidimensional frequency coarse estimation result to obtain a multidimensional frequency fine estimation result includes:

[0020] Calculate the maximum number of iterations and offset based on the preset sampling length;

[0021] Determine the current iteration number;

[0022] Obtaining, according to the current number of iterations, a precise estimation value of the spectrum of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration;

[0023] Calculating spectrum leakage coefficients of multiple complex sinusoidal waves and multidimensional offset spectrum values ​​of multiple complex sinusoidal signals according to the multidimensional frequency coarse estimation result, the previous iterative spectrum precise estimation value, the offset, and the array received signal;

[0024] Calculating multidimensional offset spectrum leakage correction coefficients for the plurality of complex sinusoidal waves based on the complex amplitude coefficients of the plurality of complex sinusoidal waves of the previous iteration, the spectrum leakage coefficients of the plurality of complex sinusoidal waves, and the multidimensional offset spectrum values ​​of the plurality of complex sinusoidal signals;

[0025] Calculating a current frequency precision estimate based on the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sinusoidal waves and the previous iterative spectrum precision estimate;

[0026] Determine whether the current number of iterations reaches the maximum number of iterations;

[0027] If yes, the current frequency precise estimation value is determined as the multi-dimensional frequency precise estimation result.

[0028] Furthermore, the method further comprises:

[0029] When it is determined that the current number of iterations has not reached the maximum number of iterations, calculating the spectrum values ​​of the signal at a plurality of complex sinusoidal signal frequency estimation points according to the multidimensional frequency coarse estimation result and the spectrum precise estimation value of the previous iteration;

[0030] Calculating a spectrum leakage coefficient corresponding to the current number of iterations according to the multi-dimensional frequency rough estimation result;

[0031] Calculating the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values ​​of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves of the previous iteration;

[0032] The value of the current iteration number is increased by 1 to obtain a new current iteration number, and the process of determining the current iteration number is performed.

[0033] A second aspect of the present application provides a device for estimating multidimensional parameters of an array single snapshot under interference conditions, the device comprising:

[0034] an acquisition unit, configured to acquire an array receiving signal under interference conditions;

[0035] A first conversion unit is used to convert the problem of estimating the multidimensional parameters of the signal source of the array receiving signal into a problem of multidimensional frequency estimation;

[0036] a coarse estimation unit, configured to perform a coarse multidimensional frequency estimation on the array received signal based on the multidimensional frequency estimation problem, and obtain a coarse multidimensional frequency estimation result;

[0037] a fine estimation unit, configured to perform a multidimensional frequency fine estimation on the array received signal according to the multidimensional frequency coarse estimation result, to obtain a multidimensional frequency fine estimation result;

[0038] a calculation unit, configured to calculate a frequency estimation result based on the multidimensional frequency rough estimation result and the multidimensional frequency fine estimation result;

[0039] The second conversion unit is used to convert the frequency estimation result into a parameter estimation result.

[0040] In the above implementation process, the acquisition unit first acquires the array received signal under interference conditions; the coarse estimation unit then performs a coarse multidimensional frequency estimation on the array received signal to obtain a coarse multidimensional frequency estimation result; and the fine estimation unit performs a fine multidimensional frequency estimation on the array received signal based on the coarse multidimensional frequency estimation result to obtain a fine multidimensional frequency estimation result; finally, the calculation unit calculates the frequency estimation result based on the coarse multidimensional frequency estimation result and the fine multidimensional frequency estimation result. This shows that the device can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of a coherent signal source using only single snapshot data without the need for matrix decomposition and grid search.

[0041] Furthermore, the rough estimation unit includes:

[0042] a signal conversion subunit, configured to perform a multidimensional fast Fourier transform on the array received signal based on the multidimensional frequency estimation problem to obtain a multidimensional spectrum matrix block;

[0043] an acquisition subunit, configured to acquire the coordinates of a signal spectrum peak point according to the spectrum matrix block;

[0044] The coarse estimation subunit is used to perform a coarse estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak point of the signal spectrum to obtain a coarse estimation result of the multi-dimensional frequency.

[0045] Furthermore, the multi-dimensional frequency rough estimation result is:

[0046]

[0047] in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; l k A positive integer representing the expansion factor.

[0048] Furthermore, the precise estimation unit includes:

[0049] A first calculation subunit, configured to calculate a maximum number of iterations and an offset according to a preset sampling length;

[0050] A first determining subunit, configured to determine a current number of iterations;

[0051] an acquisition subunit, configured to acquire, according to the current number of iterations, a precise spectrum estimate of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration;

[0052] A second calculation subunit is configured to calculate spectrum leakage coefficients of a plurality of complex sinusoidal waves and multidimensional offset spectrum values ​​of a plurality of complex sinusoidal signals based on the multidimensional frequency coarse estimation result, the spectrum precise estimation value of the previous iteration, the offset, and the array received signal;

[0053] The second calculation subunit is further configured to calculate multidimensional offset spectrum leakage correction coefficients of the plurality of complex sinusoidal waves based on the complex amplitude coefficients of the plurality of complex sinusoidal waves of the previous iteration, the spectrum leakage coefficients of the plurality of complex sinusoidal waves, and the multidimensional offset spectrum values ​​of the plurality of complex sinusoidal signals;

[0054] The second calculation subunit is further configured to calculate a current frequency precise estimation value based on the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the precise spectrum estimation value of the previous iteration;

[0055] A judging subunit, configured to judge whether the current number of iterations reaches the maximum number of iterations;

[0056] The second determining subunit is configured to determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result when it is determined that the maximum number of iterations has been reached.

[0057] Furthermore, the precise estimation unit further includes:

[0058] The third calculation subunit is further configured to calculate the spectrum values ​​of the signal at multiple complex sinusoidal signal frequency estimation points according to the multidimensional frequency coarse estimation result and the spectrum precise estimation value of the previous iteration when it is determined that the current number of iterations has not reached the maximum number of iterations;

[0059] The third calculation subunit is further configured to calculate a spectrum leakage coefficient corresponding to the current number of iterations based on the multi-dimensional frequency rough estimation result;

[0060] The third calculation subunit is further configured to calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number based on the spectrum values ​​of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves of the previous iteration;

[0061] The value increasing subunit is used to increase the value of the current iteration number by 1 as the new current iteration number, and trigger the first determining subunit to determine the current iteration number.

[0062] A third aspect of the present application provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the array single-snapshot multi-dimensional parameter estimation method under interference conditions described in any one of the first aspect of the present application.

[0063] A fourth aspect of the present application provides a computer-readable storage medium storing computer program instructions. When the computer program instructions are read and executed by a processor, the method for estimating multidimensional parameters of an array single snapshot under interference conditions described in any one of the first aspect of the present application is executed. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0065] Figure 1 A flowchart of a method for estimating multidimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application;

[0066] Figure 2 A schematic flow chart of another method for estimating multidimensional parameters of a single-snapshot array under interference conditions provided by an embodiment of the present application;

[0067] Figure 3 A schematic diagram of a three-dimensional frequency estimation result provided in an embodiment of the present application;

[0068] Figure 4 A schematic diagram of a 1-2 dimensional frequency estimation result provided in an embodiment of the present application;

[0069] Figure 5 A schematic diagram of a 1-3 dimensional frequency estimation result provided in an embodiment of the present application;

[0070] Figure 6 The estimated performance of the proposed algorithm at different numbers of iterations is shown;

[0071] Figure 7 The RMSE of the MKFE algorithm under different SNRs is shown;

[0072] Figure 8 The RMSE of the MKFE algorithm with different sampling lengths is shown;

[0073] Figure 9 Schematic diagram of FDA-MIMO array signal rearrangement for two-dimensional single-snapshot parameter estimation provided in an embodiment of the present application;

[0074] Figure 10 Schematic diagram of FDA-MIMO array signal rearrangement for three-dimensional single-snapshot parameter estimation provided in an embodiment of the present application;

[0075] Figure 11 Schematic diagram of 2D-FFT processing in the transmit and receive dimensions provided in an embodiment of the present application;

[0076] Figure 12 Schematic diagram of 3D-FFT processing for transmission, reception, and pulse dimensions provided in an embodiment of the present application;

[0077] Figure 13 shows the performance of the angle estimation algorithm;

[0078] Figure 14 The performance of the distance estimation algorithm is shown;

[0079] Figure 15 shows the performance of the angle estimation algorithm;

[0080] Figure 16 The performance of the distance estimation algorithm is shown;

[0081] Figure 17 shows the performance of the velocity estimation algorithm;

[0082] Figure 18 A schematic diagram of the structure of a device for estimating multi-dimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application;

[0083] Figure 19 This is a structural diagram of another device for estimating multi-dimensional parameters of an array single snapshot under interference conditions provided by an embodiment of the present application. DETAILED DESCRIPTION

[0084] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.

[0085] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and should not be understood as indicating or implying relative importance.

[0086] Example 1

[0087] Please see Figure 1 , Figure 1 The present embodiment provides a flowchart of a method for estimating multidimensional parameters of an array in a single snapshot under interference conditions. The method for estimating multidimensional parameters of an array in a single snapshot under interference conditions includes:

[0088] S101: Acquire an array receiving signal under interference conditions.

[0089] S102: Convert the multi-dimensional parameter estimation problem of the signal source of the array receiving signal into a multi-dimensional frequency estimation problem.

[0090] S103 , performing multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result.

[0091] S104 , performing multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result.

[0092] S105 . Calculate a frequency estimation result based on the multi-dimensional frequency rough estimation result and the multi-dimensional frequency fine estimation result.

[0093] S106: Convert the frequency estimation result into a parameter estimation result.

[0094] In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, and this is not limited in this embodiment.

[0095] In this embodiment, the execution subject of the method may also be a smart device such as a smart phone, a tablet computer, etc., which is not limited in this embodiment.

[0096] It can be seen that the array single-snapshot multi-dimensional parameter estimation method under interference conditions described in this embodiment does not require matrix decomposition and grid search. It can quickly and accurately measure multi-dimensional parameters such as distance, angle, and speed of the coherent signal source using only single-snapshot data.

[0097] Example 2

[0098] Please see Figure 2 , Figure 2 The present embodiment provides a flowchart of a method for estimating multidimensional parameters of an array in a single snapshot under interference conditions. The method for estimating multidimensional parameters of an array in a single snapshot under interference conditions includes:

[0099] S201: Acquire an array receiving signal under interference conditions.

[0100] S202: Convert the multi-dimensional parameter estimation problem of the signal source of the array receiving signal into a multi-dimensional frequency estimation problem.

[0101] In this embodiment, it is assumed that the array received signal S is a complex signal composed of Q complex sine waves, each of which is determined by K frequencies. In the context of additive white Gaussian noise, the signal S can be modeled as:

[0102]

[0103] in, represents the frequency of the qth sine wave and the kth dimension, A q represents the complex amplitude coefficient of the qth sine wave, n(m1,...,m K ) represents Gaussian white noise signal;

[0104] According to the definition of formula (1.1), the received signal S can be re-expressed as the following vector form:

[0105]

[0106] in,

[0107] In this embodiment, a set of Vandermonde matrices is defined Its expression is:

[0108]

[0109] in, Represents a vector with a Vandermonde structure, which is expressed as:

[0110]

[0111] Using formula (1.3), formula (1.2) can be reconstructed as

[0112]

[0113] in, represents the Khatri-Rao product operation, n is assumed to have zero mean, and the covariance matrix The complex white Gaussian noise signal is Represents the noise power.

[0114] In this embodiment, the frequency estimation result obtained by performing K-dimensional frequency estimation based on the array received signal includes multi-dimensional estimated frequencies of multiple complex sine waves;

[0115] The Multiple Sinusoids KD Frequency Estimation (MKFE) algorithm is performed through two parts: rough estimation and fine estimation. Specifically, the qth sinusoidal signal and the frequency of the kth dimension are defined as Expressed as:

[0116]

[0117] in, is the estimated frequency of the qth sinusoidal signal and the kth dimension;

[0118] Defined as integer frequency, it represents the rough frequency estimation result;

[0119] Defined as the fractional-order residual frequency, it represents the frequency estimation result.

[0120] S203 , performing multi-dimensional fast Fourier transform processing on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional spectrum matrix block.

[0121] In this embodiment, the method can first perform a K-dimensional Fast Fourier Transform (FFT) operation on the received signal to obtain a K-dimensional spectrum matrix block P of the signal. K , whose expression is:

[0122]

[0123] Among them, n k =0, 1, ..., l k M k -1;

[0124] l k A positive integer representing the expansion factor, which is used to perform zero padding during K-dimensional FFT processing. The value range becomes [-0.5 / l k , 0.5 / l k ].

[0125] S204 : Obtain the coordinates of the peak points of the signal spectrum according to the spectrum matrix block.

[0126] In this embodiment, assuming that the input SNR is greater than the SNR threshold (DFT-based frequency estimation algorithms have a threshold effect. When the SNR exceeds the threshold, the root mean square error of the algorithm decreases rapidly and approaches the CRB), after performing K-dimensional FFT processing, the spectrum peak point of the signal can be obtained. The coordinates of the peak point are recorded as:

[0127]

[0128] S205 , performing a rough multi-dimensional frequency estimation of the complex sine wave according to the coordinates of the peak points of the signal spectrum to obtain a rough multi-dimensional frequency estimation result.

[0129] In this embodiment, the multi-dimensional frequency rough estimation result is:

[0130]

[0131] in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; l k A positive integer representing the expansion factor.

[0132] It should be noted that the threshold effect of DFT-based frequency estimation algorithms is determined by the algorithm estimation steps. DFT-based frequency estimation algorithms are divided into two parts: coarse estimation and fine estimation. The initial value of the fine estimation depends on the result of the coarse estimation. The coarse estimation part is implemented through FFT. If the SNR is low, the correct peak point of the signal cannot be condensed, and the correct initial value cannot be provided for the fine estimation, thus making it impossible to accurately estimate the signal frequency. Once the SNR exceeds a certain threshold, the peak point can be correctly condensed, providing the correct initial value for the fine estimation. Therefore, after the SNR exceeds a certain threshold, the estimation performance of the algorithm will improve rapidly. This threshold is also called the SNR breakdown threshold of the DFT-based algorithm. In practical applications, by performing zero padding, the SNR breakdown threshold of the algorithm can be effectively lowered, thereby improving the estimation performance of the algorithm under low SNR.

[0133] S206: Calculate the maximum number of iterations and the offset according to the preset sampling length.

[0134] In this embodiment, since the performance of the frequency estimation algorithm is affected by the number of iterations, in order to avoid the increase in computational complexity caused by too many iterations (which does not improve performance), the method proposes to calculate the maximum number of iterations I opt The algorithm is calculated as follows:

[0135]

[0136] in, Indicates rounding up.

[0137] In addition, the offset It is uncertain, and its value will affect the performance of the algorithm. Its value criteria are:

[0138]

[0139] In this embodiment, after determining the number of iterations I and the offset of the algorithm, After taking the value of , we can get the frequency estimation values ​​of Q complex sine waves in K dimensions.

[0140] S207: Determine the current number of iterations.

[0141] S208 . Obtain, according to the current iteration number, a precise spectrum estimation value of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration.

[0142] In this embodiment, for the fractional-order residual frequencies of Q complex sinusoidal waves of different dimensions, the method accurately estimates the frequencies one by one.

[0143] In this embodiment, it is assumed that after the i-th iteration (i.e., the current number of iterations), the fractional order residual frequency estimate of the k-th dimension of the q-th complex sine wave has been obtained. (i.e. the last iterative spectrum estimate, initial value It is set to zero), and the frequency estimation result is expected to be updated in the next iteration.

[0144] In this embodiment, α r(i-1) Indicates the complex amplitude coefficient of the rth complex sine wave in the i-1th iteration (that is, the complex amplitude coefficient of multiple complex sine waves in the previous iteration, whose initial value α r(0) Set to 0).

[0145] S209 , calculating spectrum leakage coefficients of multiple complex sinusoidal waves and multidimensional offset spectrum values ​​of multiple complex sinusoidal signals according to the multidimensional frequency coarse estimation result, the spectrum precise estimation value of the previous iteration, the offset, and the array received signal.

[0146] In this embodiment, represents the spectrum leakage coefficient of the rth complex sine wave. The calculation expression is:

[0147]

[0148] In this embodiment, Indicates that the signal S is a complex sinusoidal signal in the qth dimension, and the kth dimension is offset The spectrum value after . Among them, The calculation expression is:

[0149]

[0150] S210 , calculating multidimensional shifted spectrum leakage correction coefficients of the multiple complex sinusoids based on the complex amplitude coefficients of the multiple complex sinusoids, the spectrum leakage coefficients of the multiple complex sinusoids, and the multidimensional shifted spectrum values ​​of the multiple complex sinusoids in the previous iteration.

[0151] In this embodiment, since the signal S contains Q complex sinusoids, when estimating the frequency of the qth complex sinusoid, the remaining Q-1 complex sinusoids will affect the estimation performance. Therefore, the spectrum leakage correction coefficient of the qth complex sinusoid is calculated as When , it is necessary to eliminate the remaining Q-1 source components, and the calculation expression is:

[0152]

[0153] Among them, αr(i-1) Indicates the complex amplitude coefficient of the rth complex sine wave in the i-1th iteration (that is, the complex amplitude coefficient of multiple complex sine waves in the previous iteration, whose initial value α r(0) Set to 0). represents the spectrum leakage coefficient of the rth complex sine wave. Indicates that the signal S is a complex sinusoidal signal in the qth dimension, and the kth dimension is offset The subsequent spectrum value.

[0154] S211 , calculating a current frequency precision estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the precision estimation value of the spectrum in the previous iteration.

[0155] Among them, according to the estimation result of the i-1th time (i.e., the precise value of the spectrum of the previous iteration), the calculation expression for the precise value of the frequency of the i-th iteration is:

[0156]

[0157] Among them, Re(·) represents the real part operation, Indicates that the qth complex sine wave is offset in the kth dimension The spectrum leakage correction coefficient after Represents the normalization coefficient.

[0158] The expression is

[0159]

[0160] in, Indicates the offset.

[0161] S212: Determine whether the current number of iterations reaches the maximum number of iterations. If so, execute step S213; if not, execute step S207.

[0162] In this embodiment, before executing step S207, the method may calculate the complex amplitude value α of each signal source in order to execute the next iteration. q(i) To update, it can be calculated using the maximum likelihood estimation, and the corresponding calculation expression is:

[0163]

[0164] in, It represents the spectrum value of signal s at the qth complex sinusoidal signal frequency estimation point after the i-th iteration, Represents the spectrum leakage coefficient after the i-th estimation.

[0165] The calculation expression is

[0166]

[0167] The calculation expression is

[0168]

[0169] As an optional implementation, when it is determined that the current number of iterations has not reached the maximum number of iterations, and before executing step S207, the method further includes:

[0170] (When it is determined that the current number of iterations has not reached the maximum number of iterations) calculating the spectrum values ​​of the signal at multiple complex sinusoidal signal frequency estimation points according to the multidimensional frequency coarse estimation result and the spectrum precise estimation value of the previous iteration;

[0171] According to the multi-dimensional frequency rough estimation result, the spectrum leakage coefficient corresponding to the current number of iterations is calculated (i.e., the spectrum leakage coefficient corresponding to the current number of iterations is calculated based on the above method). );

[0172] Calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values ​​of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves in the previous iteration;

[0173] The value of the current iteration number is increased by 1 to obtain the new current iteration number, and the current iteration number is determined (ie, step S207 is executed).

[0174] S213: Determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result.

[0175] S214. Calculate a frequency estimation result based on the multi-dimensional frequency rough estimation result and the multi-dimensional frequency fine estimation result.

[0176] S215: Convert the frequency estimation result into a parameter estimation result.

[0177] In this embodiment, the method can estimate the frequency and amplitude of different complex sinusoidal signals in sequence by repeating the above steps. As the number of iterations increases, the estimation error will gradually decrease, and the frequency estimation value will gradually converge to a stable result. Assuming that a total of I iterations are performed, the fractional order residual frequency estimation value of the kth dimension of the qth complex sinusoidal wave is obtained.

[0178] In summary, based on the results of rough and precise frequency estimation, the frequency estimate of the kth dimension of the qth complex sine wave is Expressed as:

[0179]

[0180] In summary, this method summarizes and gives the pseudo code of the multidimensional parameter estimation algorithm for a single-snapshot K-dimensional single-snapshot coherent signal source. The details are as follows:

[0181] Input: single snapshot multiple complex sinusoidal signal s, sampling length M k .

[0182] Initialization: Set I=I opt , l1≥1,...,l K ≥1,α 1(0) =...=α Q(0) =0,

[0183] Perform K-dimensional FFT through formula (1.7) to obtain the spectrum matrix block P K .

[0184]

[0185] The rough frequency estimate is obtained by formula (1.9):

[0186] For i=1,...,I ​​do

[0187] For q=1,...,Q do

[0188] Calculated by formula (1.12)

[0189] For k=1,...,K do

[0190] Calculated by formula (1.13)

[0191] Calculated by formula (1.14)

[0192] Calculate according to formula (1.15)

[0193] End

[0194] According to formula (1.18) and (1.19), calculate and

[0195] Update α according to formula (1.17) q(i) .

[0196] end

[0197] end

[0198] Output: Frequency estimation result

[0199] In this embodiment, numerical simulation is used to verify the performance of the proposed algorithm before implementation, and the performance of the proposed algorithm is compared with the Cramer-Rao bound of parameter estimation. Consider that the complex signal consists of two coherent sources, each of which is determined by three frequencies, and their frequencies are Since the purpose of the algorithm is mainly to estimate the frequency, for convenience, the amplitude coefficients A of the two sources are q All are set to 1. In subsequent simulations, set M1 = M2 = M3 = M, l1 = l2 = l3 = l, and use M and l to replace M. k and l k (k=1, 2, 3).

[0200] The simulation uses the RMSE of frequency estimation to evaluate the performance of the algorithm, which is defined as:

[0201]

[0202] Among them, N c =20000 represents the number of Monte Carlo simulations, Indicates the nth c The frequency estimate of the k-th dimension of the q-th source is obtained by Monte Carlo simulation.

[0203] In this embodiment, the process of verifying the validity of the algorithm is as follows:

[0204] Set the sampling length M = 17, signal SNR = 10dB, Figure 3 、 Figure 4 and Figure 5 The frequency estimation results of two sources are given, among which, Figure 3 shows the three-dimensional frequency estimation results, Figure 4 The 1-2 dimension frequency estimation results are shown. Figure 5 The frequency estimation results of 1-3 dimensions are shown. As can be seen from the figure, the proposed algorithm can accurately estimate the frequencies of the two sources in different dimensions, thereby verifying the effectiveness of the algorithm.

[0205] In this embodiment, in order to verify the effectiveness of the optimal number of iterations, Figure 6 The RMSE of the proposed algorithm at different iteration times is given. Figure 6 shows the estimated performance of the proposed algorithm under different numbers of iterations). Figure 6 It can be seen that for all SNR values, the MKFE algorithm converges to I opt =3, thus proving the effectiveness of the algorithm. In addition, it can be found that increasing the number of iterations does not improve performance, but increases computational complexity. Therefore, in practical applications, it is not necessary to set too high a number of iterations.

[0206] In this embodiment, the performance of the algorithm under different sampling lengths is verified as follows:

[0207] Set the expansion factor l = 3, Figure 7 The RMSE of the MKFE algorithm at different SNR and different sampling lengths (i.e. Figure 7 Figure 2 shows the RMSE of the MKFE algorithm under different SNRs. Figure 7 As shown in the figure, the MKFE algorithm performs poorly when the signal-to-noise ratio is low. When the signal-to-noise ratio exceeds the SNR threshold, the MKFE algorithm approaches the CRB algorithm in performance, accurately estimating the signal frequency. For example, when the signal-to-noise ratio is greater than 2dB, the RMSE is similar to that of the CRB algorithm. Before conversion to dB, the MKFE algorithm's RMSE is 1.7 times that of the CRB algorithm. Furthermore, it can be seen that as the sample length increases from 17 to 48, the SNR threshold decreases from 4dB to 0dB.

[0208] Figure 8 The RMSE performance of the MKFE algorithm at different sampling lengths under different signal-to-noise ratios is given (i.e. Figure 8 Figure 2 shows the RMSE of the MKFE algorithm for different sampling lengths. Figure 8 It can be found that when SNR = 10dB or SNR = 20dB, the RMSE of the MKFE algorithm is closer to CRB. In addition, when SNR = 0dB, if the sampling length M is less than 48, the estimation performance of the algorithm is poor. This is because a shorter sampling length corresponds to a higher SNR breakdown threshold, which leads to poor RMSE performance in scenarios with a small number of samples under low SNR conditions, which is consistent with the Figure 7 The phenomenon is consistent.

[0209] In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, and this is not limited in this embodiment.

[0210] In this embodiment, the execution subject of the method may also be a smart device such as a smart phone, a tablet computer, etc., which is not limited in this embodiment.

[0211] It can be seen that the array single-snapshot multi-dimensional parameter estimation method under interference conditions described in this embodiment does not require matrix decomposition and grid search. It can quickly and accurately measure multi-dimensional parameters such as distance, angle, and speed of the coherent signal source using only single-snapshot data.

[0212] Example 3

[0213] This embodiment illustrates a method for implementing this method in an FDA-MIMO array. The multidimensional parameter estimation problem for the FDA-MIMO signal source can be transformed into a multidimensional frequency estimation problem for a complex sinusoidal signal. The transmit, receive, and Doppler frequencies are defined as:

[0214] f1=d sinθ / λ-2r△f / c

[0215] f2=d sinθ / λ

[0216] f3=2v T p / λ

[0217] Where d represents the array element spacing, λ = c / f0 represents the signal wavelength, c represents the speed of light, f0 represents the carrier frequency of the first transmitting array element, λ represents the signal wavelength, and Δf represents the frequency offset. p represents the pulse repetition period. (r, θ, v) represents the source distance, angle, and velocity.

[0218] First, the transmission, reception and Doppler frequencies of the qth source are defined as:

[0219]

[0220] in, and is an integer frequency, which represents the rough frequency estimation result. and is the fractional residual frequency, which represents the frequency estimation result, and its value range is [-0.5, 0.5].

[0221] First, perform a rough estimation of the source parameters:

[0222] Before making a rough estimation of the signal source parameters, the single signals received by the array are first rearranged. Without considering the signal source speed, for the two-dimensional joint estimation of the signal source distance and angle of the FDA-MIMO array, the M1M2×1 dimensional single snapshot echo signal is Rearrange it into an M1×M2 dimensional matrix Y2, expressed as:

[0223]

[0224] in, Reconstructed matrix representing the noise signal;

[0225] represents the launch steering vector;

[0226] Represents the receive steering vector.

[0227] For ease of understanding, Figure 9The schematic diagram of multi-snapshot data, single-snapshot data and single-snapshot rearranged data in FDA-MIMO array two-dimensional parameter estimation is given (i.e. Figure 9 (Schematic diagram of FDA-MIMO array signal rearrangement for two-dimensional single-snapshot parameter estimation).

[0228] For the FDA-MIMO array source distance, angle and velocity three-dimensional joint estimation problem, the M1M2M3×1 dimensional single snapshot echo signal is transformed into Rearranged into an M1×M2×M3 dimensional matrix Y3, expressed as:

[0229]

[0230] in, represents the reconstruction matrix of the noise signal, express The first element of represents a time-oriented vector.

[0231] Figure 10 The schematic diagram of multi-snapshot data, single-snapshot data and single-snapshot rearranged data in FDA-MIMO array three-dimensional parameter estimation is given (i.e. Figure 10 (Schematic diagram of FDA-MIMO array signal rearrangement for three-dimensional single-snapshot parameter estimation).

[0232] For FDA-MIMO arrays, whether it is two-dimensional or three-dimensional parameter estimation, the algorithm's rough parameter estimation is achieved through FFT. The signal S in Equation (1.7) is replaced by the rearranged received signals Y2 and Y3, respectively, and 2D-FFT and 3D-FFT calculations are performed to obtain the two-dimensional spectrum matrix block P2 and the three-dimensional spectrum matrix block P3 of the signal source, respectively. Assuming that the input SNR is greater than the SNR threshold, the peak point of the signal source can be obtained after 2D-FFT or 3D-FFT processing.

[0233] Figure 11 and Figure 12 The two-dimensional or three-dimensional spectrum diagrams of the echo signal after 2D-FFT and 3D-FFT processing are respectively given, and the peak point of the signal source has been highlighted.

[0234] Specifically, Figure 11 Schematic diagram of 2D-FFT processing in the transmit and receive dimensions; Figure 12 Schematic diagram of 3D-FFT processing in the transmit, receive and pulse dimensions.

[0235] Among them, the coordinates of the qth peak point in the spectrum matrix block are:

[0236]

[0237] The value of K is determined by the problem being solved. If the problem is a two-dimensional joint estimation of source distance and angle, then K = 2; if the problem is a three-dimensional joint estimation of source distance, angle, and velocity, then K = 3.

[0238] After FFT processing, the rough frequency estimation result of each dimension of the qth signal source can be expressed as:

[0239]

[0240] Secondly, perform precise estimation of the source parameters:

[0241] In multi-source scenarios, the echo received by the FDA-MIMO array can be viewed as a superposition of multiple complex sinusoidal signals. If K = 2, this is a two-dimensional joint estimation of range and angle from a single snapshot from multiple sources; if K = 3, this is a three-dimensional joint estimation of range, angle, and velocity from a single snapshot from multiple sources.

[0242] Based on the above content, this method conducts the following simulation experiments and results analysis:

[0243] Numerical simulations are used to verify the performance of the proposed algorithm and compare it with the DFT search algorithm, PARAFAC algorithm, and CRB algorithm. Since the algorithm uses different algorithmic processes in single-source and multi-source scenarios, simulation experiments are conducted separately for single-source and multi-source scenarios.

[0244] The simulation uses a classic uniform frequency offset FDA-MIMO array system. Both the transmitting array and the receiving array use uniform linear arrays with an element spacing of half a wavelength. Table 1 shows the corresponding array simulation parameters. Set the expansion factor for zero padding. The RMSE given by the simulation is the result of performing 20,000 Monte Carlo simulations.

[0245] Table 1 FDA-MIMO array system parameters

[0246] parameter symbol Numerical Reference carrier frequency <![CDATA[f0]]> 10GHz wavelength λ 0.03m Element spacing d 0.015m Frequency offset Δf 1500Hz Pulse repetition period <![CDATA[T p ]]> <![CDATA[50 μs ]]>

[0247] Experiment 1: RMSE of 2D Parameter Estimation

[0248] For the two-dimensional parameter estimation problem, consider two coherent signal sources located at (0.5km, -10°) and (1.5km, 20°). Since the performance of the DFT search algorithm is affected by the discrete quantization number, the discrete quantization number n is simulated. θ and n r RMSE performance of the algorithm when the value is 512 and 1024. Figure 13 and Figure 14 The RMSE performance of different algorithms with SNR changes in the multi-source scenario with antenna dimensions of 24 and 48 are given (i.e. Figure 13 shows the performance of the angle estimation algorithm, Figure 14 shows the performance of the distance estimation algorithm).

[0249] Comparing the proposed algorithm with the DFT search algorithm, Figure 13 and Figure 14 It can be seen that the estimation performance of the proposed algorithm is better than that of the DFT search algorithm. Specifically, the SNR breakdown threshold of the proposed algorithm is significantly lower than that of the DFT search algorithm, which means that the algorithm can achieve better estimation accuracy in low signal-to-noise ratio scenarios. Figure 13 and Figure 14 It can also be found that the performance of the DFT search algorithm is affected by the discrete quantization number n of the angle dimension and the distance dimension. θ and n r This is because the algorithm is a grid search algorithm. Increasing the discrete quantization number can improve the algorithm's computational performance, but this also leads to an increase in the algorithm's computational complexity. In contrast, the proposed algorithm does not require a grid search when performing fine estimation and has better estimation performance.

[0250] Experiment 2: RMSE of 3D Parameter Estimation

[0251] For the three-dimensional parameter estimation problem, two coherent signal source parameters were set to (20°, 5 km, 100 m / s) and (-10°, 0.5 km, 50 m / s). Considering that there are no mature algorithms for estimating the three-dimensional parameters of a single-snap coherent signal source in the existing literature for FDA-MIMO arrays, this experiment compares the published PARAFAC algorithm with the proposed algorithm. Since PARAFAC is a multi-snap algorithm, it cannot estimate coherent signal source parameters under single-snap conditions. Therefore, two incoherent signal sources were set in the PARAFAC algorithm experiment. Simulations show the estimation performance of the PARAFAC algorithm when the sampling data consists of 5 and 20 snapshots, respectively. Figure 15 、 Figure 16 、 Figure 17 The RMSE performance of different algorithms with SNR changes in the multi-source scenario with antenna dimensions of 24 and 48 are given (i.e., Figure 15 shows the performance of the angle estimation algorithm, Figure 16 shows the performance of the distance estimation algorithm, Figure 17 shows the performance of the velocity estimation algorithm).

[0252] For distance estimation, the proposed algorithm outperforms the PARAFAC algorithm with 5 snapshots and is essentially consistent with the performance of the PARAFAC algorithm with 20 snapshots. (It should be noted that the CRB presented here is based on a single snapshot, so the PARAFAC algorithm may perform worse than the CRB algorithm with a large number of snapshots.) For velocity estimation, the proposed algorithm outperforms the PARAFAC algorithm with 5 or 20 snapshots. In particular, the proposed algorithm exhibits superior distance and velocity estimation performance under low signal-to-noise ratio conditions.

[0253] It can be seen that the single-snapshot multi-dimensional parameter estimation method for an array under interference conditions described in this embodiment can quickly and accurately measure multiple dimensional parameters of a coherent signal source, such as distance, angle, and speed, using only single-snapshot data, without the need for matrix decomposition and grid search.

[0254] Example 4

[0255] Please see Figure 18 , Figure 18 This is a schematic diagram of the structure of a device for estimating multi-dimensional parameters of a single snapshot of an array under interference conditions provided by this embodiment. Figure 18 As shown, the array single snapshot multi-dimensional parameter estimation device under the interference condition includes:

[0256] An acquisition unit 310 is configured to acquire an array received signal under interference conditions;

[0257] A first conversion unit 320 is configured to convert a multidimensional parameter estimation problem of a signal source of an array receiving signal into a multidimensional frequency estimation problem;

[0258] A coarse estimation unit 330 is configured to perform a multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;

[0259] A fine estimation unit 340 is configured to perform a multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency fine estimation result;

[0260] A calculation unit 350 is configured to calculate a frequency estimation result based on the multi-dimensional frequency rough estimation result and the multi-dimensional frequency fine estimation result;

[0261] The second conversion unit 360 is configured to convert the frequency estimation result into a parameter estimation result.

[0262] In this embodiment, the explanation of the array single-snapshot multi-dimensional parameter estimation device under interference conditions can refer to the description in Example 1 or Example 2, which will not be repeated in this embodiment.

[0263] It can be seen that the array single-snapshot multi-dimensional parameter estimation device under interference conditions described in this embodiment can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of a coherent signal source using only single-snapshot data without the need for matrix decomposition and grid search.

[0264] Example 5

[0265] Please see Figure 19 , Figure 19 This is a schematic diagram of the structure of a device for estimating multi-dimensional parameters of a single snapshot of an array under interference conditions provided by this embodiment. Figure 19 As shown, the array single snapshot multi-dimensional parameter estimation device under the interference condition includes:

[0266] An acquisition unit 310 is configured to acquire an array received signal under interference conditions;

[0267] A first conversion unit 320 is configured to convert a multidimensional parameter estimation problem of a signal source of an array receiving signal into a multidimensional frequency estimation problem;

[0268] A coarse estimation unit 330 is configured to perform a multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;

[0269] A fine estimation unit 340 is configured to perform a multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency rough estimation result to obtain a multi-dimensional frequency fine estimation result;

[0270] A calculation unit 350 is configured to calculate a frequency estimation result based on the multi-dimensional frequency rough estimation result and the multi-dimensional frequency fine estimation result;

[0271] The second conversion unit 360 is configured to convert the frequency estimation result into a parameter estimation result.

[0272] As an optional implementation, the coarse estimation unit 330 includes:

[0273] The signal conversion subunit 331 is used to perform multi-dimensional fast Fourier transform processing on the array received signal to obtain a multi-dimensional spectrum matrix block;

[0274] An acquisition subunit 332 is configured to acquire the coordinates of a signal spectrum peak point according to the spectrum matrix block;

[0275] The coarse estimation subunit 333 is used to perform a coarse estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak points of the signal spectrum to obtain a coarse estimation result of the multi-dimensional frequency.

[0276] In this embodiment, the multi-dimensional frequency rough estimation result is:

[0277]

[0278] in, represents the K-dimensional frequency rough estimation result of Q complex sine waves; l k A positive integer representing the expansion factor.

[0279] As an optional implementation, the precise estimation unit 340 includes:

[0280] A first calculation subunit 341 is configured to calculate a maximum number of iterations and an offset according to a preset sampling length;

[0281] A first determining subunit 342 is configured to determine a current number of iterations;

[0282] An acquisition subunit 343 is configured to acquire, according to the current iteration number, a precise spectrum estimation value of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration;

[0283] The second calculation subunit 344 is used to calculate the spectrum leakage coefficients of the multiple complex sinusoidal waves and the multidimensional offset spectrum values ​​of the multiple complex sinusoidal signals based on the multidimensional frequency coarse estimation result, the fine spectrum estimation value of the previous iteration, the offset and the array received signal;

[0284] The second calculation subunit 344 is further configured to calculate multi-dimensional shifted spectral leakage correction coefficients for the plurality of complex sinusoidal waves based on the complex amplitude coefficients of the plurality of complex sinusoidal waves in the previous iteration, the spectral leakage coefficients of the plurality of complex sinusoidal waves, and the multi-dimensional shifted spectral values ​​of the plurality of complex sinusoidal signals;

[0285] The second calculation subunit 344 is further configured to calculate a current frequency precision estimation value based on the multi-dimensional shifted spectrum leakage correction coefficients of the plurality of complex sinusoidal waves and the precision estimation value of the spectrum from the previous iteration;

[0286] The judging subunit 345 is used to judge whether the current number of iterations has reached the maximum number of iterations;

[0287] The second determining subunit 346 is configured to determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result when it is determined that the maximum number of iterations has been reached.

[0288] As an optional implementation, the precise estimation unit 340 further includes:

[0289] The third calculation subunit 347 is configured to calculate the spectrum values ​​of the signal at multiple complex sinusoidal signal frequency estimation points based on the multi-dimensional frequency coarse estimation result and the spectrum fine estimation value of the previous iteration when it is determined that the current iteration number has not reached the maximum iteration number;

[0290] The third calculation subunit 347 is further configured to calculate the spectrum leakage coefficient corresponding to the current iteration number according to the multi-dimensional frequency rough estimation result;

[0291] The third calculation subunit 347 is further configured to calculate the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number based on the spectrum values ​​of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves in the previous iteration;

[0292] The value increasing subunit 348 is configured to increase the value of the current iteration number by 1 to serve as the new current iteration number, and trigger the first determining subunit 342 to determine the current iteration number.

[0293] In this embodiment, the explanation of the array single-snapshot multi-dimensional parameter estimation device under interference conditions can refer to the description in Example 1 or Example 2, which will not be repeated in this embodiment.

[0294] It can be seen that the array single-snapshot multi-dimensional parameter estimation device under interference conditions described in this embodiment can quickly and accurately measure multiple dimensional parameters such as distance, angle, and speed of a coherent signal source using only single-snapshot data without the need for matrix decomposition and grid search.

[0295] An embodiment of the present application provides an electronic device, including a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the array single-snapshot multi-dimensional parameter estimation method under interference conditions in Example 1 or Example 2 of the present application.

[0296] An embodiment of the present application provides a computer-readable storage medium storing computer program instructions. When the computer program instructions are read and executed by a processor, the method for estimating multidimensional parameters of a single-snapshot array under interference conditions in embodiment 1 or embodiment 2 of the present application is executed.

[0297] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions and operations of the devices, methods and computer program products according to the multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of the code, and the module, program segment or a part of the code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0298] In addition, the functional modules in each embodiment of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0299] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0300] The foregoing is merely an embodiment of the present application and is not intended to limit the scope of protection of the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included within the scope of protection of the present application. It should be noted that similar reference numerals and letters represent similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined or explained in subsequent figures.

[0301] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

[0302] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

Claims

1. A method for estimating multidimensional parameters of an array in a single snapshot under interference conditions, characterized in that: include: Obtaining array received signals under interference conditions; Converting the multi-dimensional parameter estimation problem of the signal source of the array receiving signal into a multi-dimensional frequency estimation problem; Performing a multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result; Performing a multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result; Calculating a frequency estimation result based on the multidimensional frequency rough estimation result and the multidimensional frequency fine estimation result; converting the frequency estimation result into a parameter estimation result; The performing multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result to obtain the multi-dimensional frequency fine estimation result includes: Calculate the maximum number of iterations and offset based on the preset sampling length; Determine the current iteration number; Obtaining, according to the current number of iterations, a precise estimation value of the spectrum of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration; Calculating spectrum leakage coefficients of multiple complex sinusoidal waves and multidimensional offset spectrum values ​​of multiple complex sinusoidal signals according to the multidimensional frequency coarse estimation result, the previous iterative spectrum precise estimation value, the offset, and the array received signal; Calculating multidimensional offset spectrum leakage correction coefficients for the plurality of complex sinusoidal waves based on the complex amplitude coefficients of the plurality of complex sinusoidal waves of the previous iteration, the spectrum leakage coefficients of the plurality of complex sinusoidal waves, and the multidimensional offset spectrum values ​​of the plurality of complex sinusoidal signals; Calculating a current frequency precision estimate based on the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sinusoidal waves and the previous iterative spectrum precision estimate; Determine whether the current number of iterations reaches the maximum number of iterations; If yes, the current frequency precise estimation value is determined as the multi-dimensional frequency precise estimation result.

2. The method for estimating multidimensional parameters of an array in a single snapshot under interference conditions according to claim 1, characterized in that: The performing a multi-dimensional frequency rough estimation on the array received signal based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency rough estimation result includes: Performing a multidimensional fast Fourier transform on the array received signal based on the multidimensional frequency estimation problem to obtain a multidimensional spectrum matrix block; Acquire the coordinates of the peak point of the signal spectrum according to the spectrum matrix block; A multi-dimensional frequency rough estimation of the complex sine wave is performed according to the coordinates of the peak points of the signal spectrum to obtain a multi-dimensional frequency rough estimation result.

3. The method for estimating multidimensional parameters of an array in a single snapshot under interference conditions according to claim 2, characterized in that: The multi-dimensional frequency rough estimation result is: ； in, Represents the K-dimensional frequency rough estimation result of Q complex sine waves; A positive integer representing the expansion factor.

4. The method for estimating multidimensional parameters of an array in a single snapshot under interference conditions according to claim 1, characterized in that: The method further comprises: When it is determined that the current number of iterations has not reached the maximum number of iterations, calculating the spectrum values ​​of the signal at a plurality of complex sinusoidal signal frequency estimation points according to the multidimensional frequency coarse estimation result and the spectrum precise estimation value of the previous iteration; Calculating a spectrum leakage coefficient corresponding to the current number of iterations according to the multi-dimensional frequency rough estimation result; Calculating the complex amplitude coefficients of the multiple complex sine waves corresponding to the current iteration number according to the spectrum values ​​of the signal at the multiple complex sine signal frequency estimation points, the spectrum leakage coefficient corresponding to the current iteration number, and the complex amplitude coefficients of the multiple complex sine waves of the previous iteration; The value of the current iteration number is increased by 1 to obtain the new current iteration number, and the process of determining the current iteration number is performed.

5. A device for estimating multidimensional parameters of an array in a single snapshot under interference conditions, characterized in that: The array single-snapshot multi-dimensional parameter estimation device under interference conditions comprises: an acquisition unit, configured to acquire an array receiving signal under interference conditions; A first conversion unit is used to convert the problem of estimating the multidimensional parameters of the signal source of the array receiving signal into a problem of multidimensional frequency estimation; a coarse estimation unit, configured to perform a coarse multidimensional frequency estimation on the array received signal based on the multidimensional frequency estimation problem, and obtain a coarse multidimensional frequency estimation result; a fine estimation unit, configured to perform a multidimensional frequency fine estimation on the array received signal according to the multidimensional frequency coarse estimation result, to obtain a multidimensional frequency fine estimation result; a calculation unit, configured to calculate a frequency estimation result based on the multidimensional frequency rough estimation result and the multidimensional frequency fine estimation result; A second conversion unit, configured to convert the frequency estimation result into a parameter estimation result; Wherein, the precise estimation unit comprises: A first calculation subunit, configured to calculate a maximum number of iterations and an offset according to a preset sampling length; A first determining subunit, configured to determine a current number of iterations; an acquisition subunit, configured to acquire, according to the current number of iterations, a precise spectrum estimate of the previous iteration and complex amplitude coefficients of multiple complex sine waves of the previous iteration; A second calculation subunit is configured to calculate spectrum leakage coefficients of a plurality of complex sinusoidal waves and multidimensional offset spectrum values ​​of a plurality of complex sinusoidal signals based on the multidimensional frequency coarse estimation result, the spectrum precise estimation value of the previous iteration, the offset, and the array received signal; The second calculation subunit is further configured to calculate multidimensional offset spectrum leakage correction coefficients of the plurality of complex sinusoidal waves based on the complex amplitude coefficients of the plurality of complex sinusoidal waves of the previous iteration, the spectrum leakage coefficients of the plurality of complex sinusoidal waves, and the multidimensional offset spectrum values ​​of the plurality of complex sinusoidal signals; The second calculation subunit is further configured to calculate a current frequency precise estimation value based on the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the precise spectrum estimation value of the previous iteration; A judging subunit, configured to judge whether the current number of iterations reaches the maximum number of iterations; The second determining subunit is configured to determine the current frequency precise estimation value as the multi-dimensional frequency precise estimation result when it is determined that the maximum number of iterations has been reached.

6. The device for estimating multidimensional parameters of an array in a single snapshot under interference conditions according to claim 5, characterized in that: The rough estimation unit includes: a signal conversion subunit, configured to perform a multidimensional fast Fourier transform on the array received signal based on the multidimensional frequency estimation problem to obtain a multidimensional spectrum matrix block; an acquisition subunit, configured to acquire the coordinates of a signal spectrum peak point according to the spectrum matrix block; The coarse estimation subunit is used to perform a coarse estimation of the multi-dimensional frequency of the complex sine wave according to the coordinates of the peak point of the signal spectrum to obtain a coarse estimation result of the multi-dimensional frequency.

7. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the array single-snapshot multi-dimensional parameter estimation method under interference conditions according to any one of claims 1 to 4.

8. A readable storage medium, characterized in that: The readable storage medium stores computer program instructions, and when the computer program instructions are read and executed by a processor, the method for estimating multi-dimensional parameters of an array single snapshot under interference conditions according to any one of claims 1 to 4 is executed.

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