Disclosure of Invention
The embodiment of the application aims to provide a method and a device for estimating multi-dimensional parameters of an array single snapshot under interference conditions, which can directly process a plurality of coherent received signals without matrix decomposition and grid search, thereby realizing real-time, rapid and accurate multi-dimensional parameter estimation.
The first aspect of the application provides a method for estimating multi-dimensional parameters of an array single snapshot under an interference condition, which comprises the following steps:
Acquiring an array receiving signal under an interference condition;
converting the information source multidimensional parameter estimation problem of the array receiving signals into a multidimensional frequency estimation problem;
Performing multi-dimensional frequency coarse estimation on the array receiving signals based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;
performing multi-dimensional frequency fine estimation on the array receiving signals according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result;
Calculating a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result;
And converting the frequency estimation result into a parameter estimation result.
In the implementation process, firstly, an array receiving signal under an interference condition is acquired, an information source multidimensional parameter estimation problem is converted into a multidimensional frequency estimation problem, then multidimensional frequency coarse estimation is carried out on the array receiving signal to obtain a multidimensional frequency coarse estimation result, finally, a frequency estimation result is calculated according to the multidimensional frequency coarse estimation result and the multidimensional frequency fine estimation result, and the frequency estimation result is converted into a parameter estimation result. Therefore, the method can rapidly and accurately measure a plurality of dimension parameters such as the distance, the angle, the speed and the like of the coherent information source by using only single snapshot data without matrix decomposition and grid search.
Further, the performing 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 includes:
performing multidimensional fast Fourier transform processing on the array receiving signals based on the multidimensional frequency estimation problem to obtain a multidimensional frequency spectrum matrix block;
Acquiring signal spectrum peak point coordinates according to the spectrum matrix block;
and carrying out multi-dimensional frequency rough estimation of the complex sine wave according to the signal spectrum peak point coordinates to obtain a multi-dimensional frequency rough estimation result.
Further, the multi-dimensional frequency coarse estimation result is:
Wherein, theAnd lk is a positive integer and represents a spreading factor.
Further, the performing multi-dimensional frequency fine estimation on the array receiving signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result includes:
Calculating the maximum iteration times and the offset according to the preset sampling length;
determining the current iteration times;
acquiring a last iteration frequency spectrum fine estimation value and complex amplitude coefficients of a plurality of complex sine waves of a last iteration according to the current iteration times;
Calculating the frequency spectrum leakage coefficients of a plurality of complex sine waves and the multidimensional offset frequency spectrum values of the complex sine signals according to the multidimensional frequency coarse estimation result, the last iteration frequency spectrum fine estimation value, the offset and the array receiving signals;
calculating the multi-dimensional offset spectrum leakage correction coefficients of the plurality of complex sine waves according to the complex amplitude coefficients of the plurality of complex sine waves in the last iteration, the spectrum leakage coefficients of the plurality of complex sine waves and the multi-dimensional offset spectrum values of the plurality of complex sine signals;
Calculating a current frequency fine estimation value according to the multi-dimensional offset spectrum leakage correction coefficients of the plurality of complex sine waves and the last iteration spectrum fine estimation value;
Judging whether the current iteration number reaches the maximum iteration number or not;
if yes, the frequency fine estimation value is determined to be a multi-dimensional frequency fine estimation result.
Further, the method further comprises:
When the current iteration times are judged to not reach the maximum iteration times, calculating the frequency spectrum values of the signals at a plurality of complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency coarse estimation result and the last iteration frequency spectrum fine estimation value;
according to the multi-dimensional frequency coarse estimation result, calculating a frequency spectrum leakage coefficient corresponding to the current iteration number;
Calculating complex amplitude coefficients of a plurality of complex sine waves corresponding to the current iteration times according to the frequency spectrum values of the signals at a plurality of complex sine signal frequency estimation points, the frequency spectrum leakage coefficients corresponding to the current iteration times and the complex amplitude coefficients of a plurality of complex sine waves of the previous iteration times;
And increasing the value of the current iteration number by 1 to serve as a new current iteration number, and executing the determination of the current iteration number.
The second aspect of the present application provides an apparatus for estimating a multi-dimensional parameter of an array single snapshot under an interference condition, the apparatus for estimating a multi-dimensional parameter of an array single snapshot under an interference condition comprising:
an acquisition unit for acquiring an array receiving signal under an interference condition;
the first conversion unit is used for converting the information source multidimensional parameter estimation problem of the array received signals into a multidimensional frequency estimation problem;
The coarse estimation unit is used for carrying out multi-dimensional frequency coarse estimation on the array received signals based on the multi-dimensional frequency estimation problem to obtain a multi-dimensional frequency coarse estimation result;
the fine estimation unit is used for carrying out multi-dimensional frequency fine estimation on the array receiving signals according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result;
the calculating unit is used for calculating a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result;
and the second conversion unit is used for converting the frequency estimation result into a parameter estimation result.
In the implementation process, the acquisition unit acquires the array receiving signal under the interference condition, the coarse estimation unit performs multi-dimensional frequency coarse estimation on the array receiving signal to obtain a multi-dimensional frequency coarse estimation result, the fine estimation unit performs multi-dimensional frequency fine estimation on the array receiving signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result, and finally the calculation unit calculates the frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result. Therefore, the device can rapidly and accurately measure a plurality of dimension parameters such as the distance, the angle, the speed and the like of the coherent information source by using only single snapshot data without matrix decomposition and grid search.
Further, the rough estimation unit includes:
the signal transformation subunit is used for carrying out multidimensional fast Fourier transform processing on the array received signals based on the multidimensional frequency estimation problem to obtain a multidimensional frequency spectrum matrix block;
The acquisition subunit is used for acquiring signal spectrum peak point coordinates according to the spectrum matrix block;
and the coarse estimation subunit is used for carrying out multi-dimensional frequency coarse estimation of the complex sine wave according to the coordinates of the peak value points of the signal spectrum to obtain a multi-dimensional frequency coarse estimation result.
Further, the multi-dimensional frequency coarse estimation result is:
Wherein, theAnd lk is a positive integer and represents a spreading factor.
Further, the fine estimation unit includes:
The first calculating subunit is used for calculating the maximum iteration times and the offset according to the preset sampling length;
A first determining subunit, configured to determine a current iteration number;
The acquisition subunit is used for acquiring a last iteration frequency spectrum fine estimation value and complex amplitude coefficients of a plurality of complex sine waves in a last iteration according to the current iteration times;
The second calculating subunit is used for calculating the spectrum leakage coefficients of a plurality of complex sine waves and the multidimensional offset spectrum values of the complex sine signals according to the multidimensional frequency coarse estimation result, the last iteration spectrum fine estimation value, the offset and the array receiving signals;
the second calculating subunit is further configured to calculate a multi-dimensional offset spectrum leakage correction coefficient of the plurality of complex sine waves according to the complex amplitude coefficient of the plurality of complex sine waves in the last iteration, the spectrum leakage coefficient of the plurality of complex sine waves, and the multi-dimensional offset spectrum value of the plurality of complex sine signals;
The second calculating subunit is further configured to calculate a current frequency fine estimation value according to the multi-dimensional shifted spectrum leakage correction coefficients of the multiple complex sine waves and the last iteration spectrum fine estimation value;
a judging subunit, configured to judge whether the current iteration number reaches the maximum iteration number;
And the second determining subunit is used for determining the frequency fine estimation value as a multi-dimensional frequency fine estimation result when judging that the maximum iteration number is reached.
Further, the fine estimation unit further includes:
The third calculation subunit is further configured to calculate, when it is determined that the current iteration number does not reach the maximum iteration number, a spectrum value of the signal at a plurality of complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency coarse estimation result and the last iteration spectrum fine estimation value;
The third calculation subunit is further configured to calculate a spectrum leakage coefficient corresponding to the current iteration number according to the multi-dimensional frequency coarse estimation result;
The third calculation subunit is further configured to calculate complex amplitude coefficients of a plurality of complex sine waves corresponding to the current iteration number according to the spectrum values of the signals at the frequency estimation points of the plurality of complex sine signals, the spectrum leakage coefficients corresponding to the current iteration number, and the complex amplitude coefficients of the plurality of complex sine waves of the previous iteration;
And the numerical value increasing subunit is used for increasing the numerical value of the current iteration number by 1 to serve as a new current iteration number and triggering the first determining subunit to determine the current iteration number.
A third aspect of the present application provides an electronic device comprising a memory for storing a computer program and a processor for running the computer program to cause the electronic device to perform the method of array single snapshot multi-dimensional parameter estimation under interference conditions of any one of the first aspects of the present application.
A fourth aspect of the application provides a computer readable storage medium storing computer program instructions which, when read and executed by a processor, perform the method for estimating multi-dimensional parameters of an array snapshot under interference conditions as set forth in any of the first aspects of the application.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application.
It should be noted that like reference numerals and letters refer to like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures. Meanwhile, in the description of the present application, the terms "first", "second", and the like are used only to distinguish the description, and are not to be construed as indicating or implying relative importance.
Example 1
Referring to fig. 1, fig. 1 is a flowchart of a method for estimating multi-dimensional parameters of an array snapshot under an interference condition according to the present embodiment. The method for estimating the array single snapshot multidimensional parameters under the interference condition comprises the following steps:
s101, acquiring an array receiving signal under an interference condition.
S102, converting the information source multi-dimensional parameter estimation problem of the array receiving signals into a multi-dimensional frequency estimation problem.
S103, performing multi-dimensional frequency rough estimation on the array receiving signals based on the multi-dimensional frequency estimation problem to obtain multi-dimensional frequency rough estimation results.
S104, performing multi-dimensional frequency fine estimation on the array receiving signal according to the multi-dimensional frequency coarse estimation result to obtain a multi-dimensional frequency fine estimation result.
S105, calculating a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result.
S106, converting the frequency estimation result into a parameter estimation result.
In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, which is not limited in this embodiment.
In this embodiment, the execution body of the method may be an intelligent device such as a smart phone or a tablet computer, which is not limited in this embodiment.
Therefore, the array single snapshot multidimensional parameter estimation method under the interference condition described in the embodiment does not need matrix decomposition and grid search, and can rapidly and accurately measure a plurality of dimensional parameters such as distance, angle, speed and the like of a coherent information source by using single snapshot data.
Example 2
Referring to fig. 2, fig. 2 is a flowchart of a method for estimating multi-dimensional parameters of an array snapshot under an interference condition according to the present embodiment. The method for estimating the array single snapshot multidimensional parameters under the interference condition comprises the following steps:
s201, acquiring an array receiving signal under an interference condition.
S202, converting the information source multi-dimensional parameter estimation problem of the array receiving signals into a multi-dimensional frequency estimation problem.
In the present embodiment, it is assumed that the array reception signal S is a complex signal composed of Q complex sine waves, each of which is determined by K frequencies. In the context of an additive white gaussian noise signal, the signal S can be modeled as:
Wherein, theA frequency representing the qth sine wave and the kth dimension, aq representing the complex amplitude coefficient of the qth sine wave, and n (m1,...,mK) representing a gaussian white noise signal;
The received signal S can be re-represented as a vector form according to the definition of equation (1.1):
Wherein, the
In this embodiment, a set of Vandermonde matrices is definedThe expression is as follows:
Wherein, theA vector with a Vandermonde structure is represented by the expression:
using formula (1.3), formula (1.2) can be reconstructed as
Wherein, theRepresents the Khatri-Rao product operation,N is assumed to be zero-mean-compliant, covariance matrixIs a complex gaussian white noise signal of (c),Representing the noise power.
In this embodiment, the frequency estimation result obtained by performing K-dimensional frequency estimation based on the array reception signal includes multidimensional estimation frequencies of a plurality of complex sine waves;
The complex sinusoidal signal K-dimensional frequency estimation (Multiple Sinusoids K-D Frequency Estimation, MKFE) algorithm is implemented through two parts of coarse estimation and fine estimation. Specifically, the q-th sinusoidal signal and the frequency of the k-th dimension are definedExpressed as:
Wherein, theAn estimated frequency for the kth dimension, which is the qth sinusoidal signal;
Defining as integer frequency, and representing frequency rough estimation result;
and the frequency is defined as fractional order residual frequency, and represents the frequency fine estimation result.
S203, performing multidimensional fast Fourier transform processing on the array receiving signals based on the multidimensional frequency estimation problem to obtain a multidimensional frequency spectrum matrix block.
In this embodiment, the method may perform a K-dimensional fast fourier transform (Fast Fourier Transform, FFT) operation on the received signal, so as to obtain a K-dimensional spectrum matrix block PK of the signal, where the expression is:
wherein nk＝0,1,...,lkMk -1;
lk is a positive integer representing an extension factor for performing zero padding in the K-dimensional FFT processing, after performing zero paddingThe range of values becomes [ -0.5/lk,0.5/lk ].
S204, acquiring signal spectrum peak point coordinates according to the spectrum matrix block.
In this embodiment, assuming that the input SNR is greater than the SNR threshold (the DFT-like frequency estimation algorithm has a threshold effect, when the SNR exceeds the threshold, the root mean square error of the algorithm is rapidly reduced and approaches to CRB), after performing K-dimensional FFT processing, the spectrum peak point of the signal can be obtained, and the coordinates of the peak point are recorded as follows:
S205, performing multi-dimensional frequency rough estimation of the complex sine wave according to the coordinates of the peak points of the signal spectrum, and obtaining a multi-dimensional frequency rough estimation result.
In this embodiment, the result of the multi-dimensional frequency coarse estimation is:
Wherein, theAnd lk is a positive integer and represents a spreading factor.
The threshold effect of the DFT-type frequency estimation algorithm is determined by the step of algorithm estimation. The DFT frequency estimation algorithm is divided into a coarse estimation part and a fine estimation part, and the initial value of the fine estimation part depends on the result of the coarse estimation. The coarse estimation is implemented by FFT, if SNR is low, the correct peak point of the signal cannot be aggregated, the correct initial value cannot be provided for the fine estimation, and thus the signal frequency cannot be estimated accurately. And once the SNR exceeds a certain threshold, the peak points can be correctly aggregated to provide a correct initial value for the fine estimation. Therefore, the estimation performance of the algorithm increases rapidly after the SNR exceeds a certain threshold, also referred to as the SNR breakdown threshold of the DFT-like algorithm. In practical application, by executing zero padding, the SNR breakdown threshold of the algorithm can be effectively reduced, and the estimation performance of the algorithm under low SNR is improved.
S206, calculating the maximum iteration times and the offset according to the preset sampling length.
In this embodiment, since the performance of the frequency fine estimation algorithm is affected by the number of iterations. Therefore, in order to avoid the increase of computational complexity caused by excessive iterations (which does not improve the performance at this time), the method proposes an algorithm for calculating the maximum number of iterations Iopt, whose calculation expression is:
Wherein, theRepresenting an upward rounding.
Furthermore, the offsetIs uncertain, and its value affects the performance of the algorithm, and its value criterion is:
In the present embodiment, the number of iterations I and the offset of the algorithm are determinedAfter the value of (2), the frequency estimation values of K dimensions of Q complex sine waves can be obtained.
S207, determining the current iteration times.
S208, obtaining a last iteration frequency spectrum fine estimation value and complex amplitude coefficients of a plurality of complex sine waves in the last iteration according to the current iteration times.
In this embodiment, for fractional order residual frequencies of different dimensions of Q complex sine waves, the method performs a fine estimation on the frequencies one by one.
In the present embodiment, it is assumed that after the ith iteration (i.e., the current number of iterations), a fractional order residual frequency estimate of the kth dimension of the qth complex sine wave has been obtained(I.e. the last iteration of the spectrum is accurate, the initial valueSet to zero) it is desirable to update the frequency estimation result in the next iteration.
In this embodiment, αr(i-1) represents the complex amplitude coefficient of the (i.e., the complex amplitude coefficients of the plurality of complex sinusoids of the previous iteration, whose initial value αr(0) is set to 0) th to 1 st iteration.
S209, calculating the spectrum leakage coefficients of the complex sine waves and the multidimensional offset spectrum values of the complex sine signals according to the multidimensional frequency coarse estimation result, the last iteration spectrum fine estimation value, the offset and the array receiving signals.
In the present embodiment of the present invention,Representing the spectral leakage coefficient of the r-th complex sine wave. Wherein, theThe calculated expression of (2) is:
In the present embodiment of the present invention,Representing the signal S at the qth complex sinusoidal signal, the kth dimension is offsetThe subsequent spectral values. Wherein, theThe calculated expression of (2) is:
S210, calculating the multi-dimensional offset spectrum leakage correction coefficients of the plurality of complex sine waves according to the complex amplitude coefficients of the plurality of complex sine waves, the spectrum leakage coefficients of the plurality of complex sine waves and the multi-dimensional offset spectrum values of the plurality of complex sine signals in the last iteration.
In this embodiment, since the signal S includes Q complex sine waves, when estimating the frequency of the Q-th complex sine wave, the remaining Q-1 complex sine waves affect the estimation performance. Thus, the spectral leakage correction coefficient of the qth complex sine wave is calculatedWhen the other Q-1 source components need to be eliminated, the calculation expression is as follows:
Where αr(i-1) represents the complex amplitude coefficient of the (i.e., the complex amplitude coefficients of the plurality of complex sinusoids of the last iteration, whose initial value αr(0) is set to 0) th iteration, the (r) th complex sinusoid.Representing the spectral leakage coefficient of the r-th complex sine wave.Representing the signal S at the qth complex sinusoidal signal, the kth dimension is offsetThe subsequent spectral values.
S211, calculating a current frequency fine estimation value according to the multi-dimensional offset spectrum leakage correction coefficients of the plurality of complex sine waves and the last iteration spectrum fine estimation value.
Wherein, according to the i-1 th estimation result(I.e. the last iteration frequency spectrum fine estimation value), the calculation expression of the ith iteration frequency fine estimation value is:
Wherein Re (. Cndot.) represents the operation of taking the real part,Indicating that the qth complex sine wave is shifted in the kth dimensionThe spectral leakage correction coefficients after that are calculated,Representing the normalized coefficient.
The expression of (2) is
Wherein, theRepresenting the offset.
S212, judging whether the current iteration number reaches the maximum iteration number, if so, executing the step S213, and if not, executing the step S207.
In this embodiment, before executing step S207, the method may update the complex amplitude value αq(i) of each source for executing the next iteration, which may be obtained by using the maximum likelihood estimation calculation, and the corresponding calculation expression is:
Wherein, theRepresenting the spectral value of the signal s at the frequency estimate of the qth complex sinusoidal signal after the ith iteration,Representing the spectral leakage coefficient after the i-th estimation.
The calculated expression of (2) is
The calculated expression of (2) is
As an alternative embodiment, when it is determined that the current iteration number does not reach the maximum iteration number, and before executing step S207, the method further includes:
Calculating the frequency spectrum values of the signals at a plurality of complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency coarse estimation result and the last iteration frequency spectrum fine estimation value (when the current iteration times are judged to not reach the maximum iteration times);
according to the multi-dimensional frequency coarse estimation result, calculating the frequency spectrum leakage coefficient corresponding to the current iteration number (namely calculating based on the mode);
Calculating complex amplitude coefficients of a plurality of complex sine waves corresponding to the current iteration times according to the frequency spectrum values of the signals at a plurality of complex sine signal frequency estimation points, the frequency spectrum leakage coefficients corresponding to the current iteration times and the complex amplitude coefficients of a plurality of complex sine waves of the last iteration;
The value of the current iteration number is incremented by 1 as a new current iteration number, and the determination of the current iteration number is performed (i.e., step S207 is performed).
S213, determining the current frequency fine estimation value as a multi-dimensional frequency fine estimation result.
S214, calculating a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result.
S215, converting the frequency estimation result into a parameter estimation result.
In this embodiment, the method may sequentially estimate the frequency and amplitude of different complex sinusoidal signals by repeating the above steps. Wherein, as the iteration number 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, a fractional order residual frequency estimate of the kth dimension of the qth complex sine wave is obtained
To sum up, according to the results of the coarse frequency estimation and the fine frequency estimation, the frequency estimation value of the kth dimension of the qth complex sine waveExpressed as:
In summary, the method summarizes pseudo codes of a single-snapshot K-dimension single-snapshot coherent source multidimensional parameter estimation algorithm. The method comprises the following steps:
And inputting a single-snapshot multi-complex sinusoidal signal s, and sampling the length Mk.
Initialization-setting i=iopt,l1≥1,...,lK≥1,α1(0)＝...＝αQ(0)=0,
The K-dimensional FFT is performed by equation (1.7) to obtain a spectrum matrix block PK.
Obtaining a coarse frequency estimate by equation (1.9)
For i=1,...,I do
For q=1,...,Q do
Calculation by means of (1.12)
For k=1,...,K do
Calculation by means of (1.13)
Calculation by means of (1.14)
Calculated according to formula (1.15)
End
Calculated according to formulas (1.18) and (1.19), respectivelyAnd
Alphaq(i) is updated according to equation (1.17).
end
end
Output of frequency estimation results
In this embodiment, numerical simulation is used to verify the performance of the proposed algorithm before the method is implemented, and the performance of the proposed algorithm is compared with the Kramer boundary for parameter estimation. Consider that the complex signal is composed of two coherent sources, each of which is determined by three frequencies, respectivelySince the purpose of the algorithm is mainly frequency estimation, the amplitude coefficient aq of both sources is set to 1 for convenience. M1＝M2＝M3＝M,l1＝l2＝l3 = l was set in the subsequent simulations and Mk and lk were replaced with M and l (k = 1,2, 3).
The simulation utilizes RMSE of the frequency estimate to evaluate the performance of the algorithm, which is defined as:
Wherein, Nc =20000 represents the Monte Carlo simulation times,Representing the frequency estimate of the kth dimension of the nthc monte carlo simulation qth source.
In this embodiment, the process of verifying the validity of the algorithm is as follows:
Setting the sampling length m=17, the signal snr=10 dB, fig. 3, 4 and 5 show the frequency estimation results of two sources, wherein fig. 3 shows the three-dimensional frequency estimation result, fig. 4 shows the 1-2-dimensional frequency estimation result, and fig. 5 shows the 1-3-dimensional frequency estimation result. It can be seen from the figure that the proposed algorithm is able to accurately estimate the frequencies of the two sources in different dimensions, thereby verifying the effectiveness of the algorithm.
In this embodiment, to verify the validity of the optimal number of iterations, fig. 6 shows RMSE of the proposed algorithm at different numbers of iterations (i.e. fig. 6 shows the estimated performance of the proposed algorithm at different numbers of iterations). As can be seen from fig. 6, the MKFE algorithm can converge to Iopt =3 for all signal to noise values, thus proving the effectiveness of the algorithm. In addition, it can be found that increasing the iteration number does not improve the performance, but rather increases the computational complexity, so that in practical application, the iteration number does not need to be set too high.
In this embodiment, the performance of the algorithm at different sample lengths is verified as follows:
Setting the spreading factor l=3, fig. 7 gives the RMSE of MKFE algorithm at different SNRs, different sample lengths (i.e. fig. 7 shows the RMSE of MKFE algorithm at different SNRs). As shown in fig. 7, in the case where the signal-to-noise ratio is low, the estimation performance of MKFE algorithm is poor. When the signal-to-noise ratio exceeds the SNR threshold, the performance of MKFE algorithm approaches CRB, so that the frequency of the signal can be accurately estimated. For example, when the signal-to-noise ratio is greater than 2dB, the RMSE approximates the CRB, and the RMSE of MKFE algorithm is 1.7 times the CRB before conversion to dB. Furthermore, it was found that as the sample length increased from 17 to 48, the signal-to-noise threshold decreased from 4dB to 0dB.
Fig. 8 shows RMSE performance of MKFE algorithm at different sample lengths at different signal-to-noise ratios (i.e., fig. 8 shows RMSE of different sample lengths MKFE algorithm). As can be seen from fig. 8, the RMSE of MKFE algorithm is closer to CRB when snr=10 dB or snr=20 dB. Further, when snr=0 dB, if the sampling length M is less than 48, the estimation performance of the algorithm is poor. This is because a shorter sample length corresponds to a higher SNR breakdown threshold, resulting in poor RMSE performance for smaller sample numbers of scenes at low signal-to-noise ratios, consistent with the phenomenon of fig. 7.
In this embodiment, the execution subject of the method may be a computing device such as a computer or a server, which is not limited in this embodiment.
In this embodiment, the execution body of the method may be an intelligent device such as a smart phone or a tablet computer, which is not limited in this embodiment.
Therefore, the array single snapshot multidimensional parameter estimation method under the interference condition described in the embodiment does not need matrix decomposition and grid search, and can rapidly and accurately measure a plurality of dimensional parameters such as distance, angle, speed and the like of a coherent information source by using single snapshot data.
Example 3
This embodiment shows a process for implementing the method in an FDA-MIMO array. The problem of FDA-MIMO source multi-dimensional parameter estimation can be converted into the problem of multi-dimensional frequency estimation of complex sinusoidal signals. The transmit, receive and doppler frequencies are defined as:
f1=d sinθ/λ-2r△f/c
f2=d sinθ/λ
f3＝2v Tp/λ
Where d represents the element spacing, λ=c/f0 represents the signal wavelength, c represents the speed of light, f0 represents the carrier frequency of the first transmitting element, λ represents the signal wavelength, and Δf represents the frequency offset. Tp denotes a pulse repetition period. (r, θ, v) represents source distance, angle, and velocity.
First, the transmission, reception, and Doppler frequencies of the qth source are defined as:
Wherein, theAndThe frequency coarse estimation result is expressed for integer frequency.AndThe fractional order residual frequency represents the frequency fine estimation result, and the value range is [ -0.5,0.5].
First, source parameter rough estimation is performed:
The single signals received by the array are rearranged first before the source parameters are roughly estimated. Under the condition of not considering the source speed, for the problem of the two-dimensional joint estimation of the source distance and the angle of the FDA-MIMO array, M1M2 multiplied by 1-dimensional single snapshot echo signalsThe rearrangement is the M1×M2 -dimensional matrix Y2, denoted as:
Wherein, theA reconstruction matrix representing the noise signal;
representing a transmit steering vector;
Representing the received steering vector.
For ease of understanding, fig. 9 shows a schematic diagram of how snapshot data, single snapshot data, and single snapshot reordered data in FDA-MIMO array two-dimensional parameter estimation (i.e., fig. 9 is a schematic diagram of FDA-MIMO array signal reordering for two-dimensional single snapshot parameter estimation).
For the problem of three-dimensional joint estimation of FDA-MIMO array source distance, angle and speed, M1M2M3 multiplied by 1-dimensional single snapshot echo signalsThe rearrangement is the M1×M2×M3 -dimensional matrix Y3, denoted as:
Wherein, theRepresenting a reconstructed matrix of the noise signal,Representation ofIs selected from the group consisting of a first element of (c),Representing the time-oriented vector.
Fig. 10 shows a schematic diagram of multi-snapshot data, single-snapshot data, and single-snapshot rearranged data in FDA-MIMO array three-dimensional parameter estimation (i.e., fig. 10 is a schematic diagram of FDA-MIMO array signal rearrangement for three-dimensional single-snapshot parameter estimation).
For FDA-MIMO arrays, both two-dimensional estimation and three-dimensional parameter estimation, the coarse estimation of the parameters of the algorithm is realized by FFT. And respectively replacing the signal S in the formula (1.7) with the rearranged received signals Y2 and Y3 to perform 2D-FFT and 3D-FFT calculation to respectively obtain a two-dimensional spectrum matrix block P2 and a three-dimensional spectrum matrix block P3 of the information source. Assuming that the input SNR is greater than the SNR threshold, then after 2D-FFT or 3D-FFT processing, the peak point of the source can be obtained.
Fig. 11 and 12 show two-dimensional or three-dimensional spectrograms of the echo signal after 2D-FFT and 3D-FFT processing, respectively, when the source peak point has been highlighted.
Specifically, FIG. 11 is a schematic diagram of a 2D-FFT processing in the transmit, receive dimension, and FIG. 12 is a schematic diagram of a 3D-FFT processing in the transmit, receive and pulse dimensions.
The coordinates of the q-th peak point in the spectrum matrix block are recorded as follows:
Wherein the size of K is determined by the problem addressed. K=2 if the problem of two-dimensional joint estimation of the source distance and the angle is solved, and K=3 if the problem of three-dimensional joint estimation of the source distance, the angle and the speed is solved.
After FFT processing, the frequency coarse estimation result of each dimension of the q-th source can be expressed as:
Secondly, carrying out information source parameter fine estimation:
For a multi-source scenario, the FDA-MIMO array received echoes can be considered as a superposition of multiple complex sinusoidal signals. And if K=2, the two-dimensional joint estimation scene of the multi-source single snapshot distance, the angle and the speed is obtained, and if K=3, the three-dimensional joint estimation scene of the multi-source single snapshot distance, the angle and the speed is obtained.
Based on the above, the method performs the following simulation experiment and result analysis:
Numerical simulation is used to verify the performance of the proposed algorithm and compare the performance of the proposed algorithm with the DFT search algorithm, the PARAFAC algorithm and the CRB. Because the algorithm flows adopted by the algorithm in the single-source scene and the multi-source scene are different, simulation experiments are respectively carried out on the single-source scene and the multi-source scene.
The simulation adopts a classical uniform frequency deviation FDA-MIMO array system, and the transmitting array and the receiving array both adopt uniform linear arrays with array element spacing of half wavelength. Table 1 gives the corresponding array simulation parameters. Setting an extension factor to perform zero paddingThe RMSE given by the simulation is the result after 20000 monte carlo simulations have been performed.
TABLE 1 FDA-MIMO array System parameters
| Parameters (parameters) | Sign symbol | Numerical value |
| Reference carrier frequency | f0 | 10GHz |
| Wavelength of | λ | 0.03m |
| Array element spacing | d | 0.015m |
| Frequency offset | Δf | 1500Hz |
| Pulse repetition period | Tp | 50μs |
Experiment 1 RMSE for two-dimensional parameter estimation
For the two-dimensional parameter estimation problem, consider that two coherent sources are located at (0.5 km, -10 °), (1.5 km,20 °) respectively. Since the performance of the DFT search algorithm is affected by the discrete quantisation numbers, the RMSE performance of the algorithm is simulated for discrete quantisation numbers nθ and nr of 512 and 1024, respectively. Fig. 13 and 14 show RMSE performance of different algorithms as a function of SNR for antenna dimensions 24 and 48, respectively, in a multi-source scenario (i.e., fig. 13 shows the performance of the angle estimation algorithm and fig. 14 shows the performance of the distance estimation algorithm).
Comparing the proposed algorithm with the DFT search algorithm, it can be seen from fig. 13 and 14 that the proposed algorithm has better estimation performance than the DFT search algorithm. In particular, the SNR breakdown threshold of the proposed algorithm is significantly smaller than that of the DFT search algorithm, which means that the algorithm can obtain better estimation accuracy in a low signal-to-noise scenario. It can also be seen from fig. 13 and 14 that the performance of the DFT search algorithm is affected by the discrete quantizations nθ and nr of the angle and distance dimensions. This is because the algorithm is a grid search algorithm, and increasing the discrete quantization number can improve the operation performance of the algorithm, but this also results in an increase in the operation complexity of the algorithm. In contrast, the proposed algorithm does not require grid searching when performing fine estimation and has better estimation performance.
Experiment 2 RMSE for three-dimensional parameter estimation
For the three-dimensional parameter estimation problem, two coherent source parameters are set to be (20 DEG, 5km,100 m/s), (-10 DEG, 0.5km,50 m/s) respectively. Considering that no mature FDA-MIMO array single snapshot coherent source three-dimensional parameter estimation algorithm exists in the prior published document, the disclosed PARAFAC algorithm is compared with the proposed algorithm in the experiment. Because the PARAFAC method is a multi-snapshot algorithm, coherent source parameter estimation cannot be performed under a single snapshot condition. Therefore, two incoherent information sources are arranged in an experiment of the PARAFAC algorithm, and simulation shows the estimation performance of the PARAFAC algorithm when sampling data are respectively 5 snapshots and 20 snapshots. Fig. 15, 16, and 17 show RMSE performance of different algorithms as a function of SNR for antenna dimensions 24 and 48, respectively, in a multi-source scenario (i.e., fig. 15 shows the performance of the angle estimation algorithm, fig. 16 shows the performance of the distance estimation algorithm, and fig. 17 shows the performance of the velocity estimation algorithm).
For distance estimation, the estimation performance of the proposed algorithm is better than that of the 5 snapshot PARAFAC algorithm, and is substantially identical to that of the PARAFAC algorithm at 20 snapshots (it should be noted that the CRB given here is obtained based on a single snapshot, so that the estimation performance of the PARAFAC algorithm may be lower at a higher number of snapshots than the CRB). For speed estimation, the estimation performance of the proposed algorithm is better than that of the PARAFAC algorithm under 5 or 20 shots. In particular, the proposed algorithm has better distance and speed estimation performance under low signal-to-noise ratio conditions.
Therefore, the array single-snapshot multidimensional parameter estimation method under the interference condition described in the embodiment is implemented, matrix decomposition and grid search are not needed, and the single-snapshot data are only utilized to rapidly and accurately measure a plurality of dimensional parameters such as distance, angle, speed and the like of a coherent information source.
Example 4
Referring to fig. 18, fig. 18 is a schematic structural diagram of an array single snapshot multidimensional parameter estimation device under an interference condition according to the present embodiment. As shown in fig. 18, the device for estimating multi-dimensional parameters of single snapshot of the array under the interference condition comprises:
An acquisition unit 310, configured to acquire an array reception signal under an interference condition;
a first converting unit 320, configured to convert a source multi-dimensional parameter estimation problem of the array received signal into a multi-dimensional frequency estimation problem;
a coarse estimation unit 330, configured to perform multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem, so as to obtain a multi-dimensional frequency coarse estimation result;
a fine estimation unit 340, configured to perform multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result, so as to obtain a multi-dimensional frequency fine estimation result;
A calculating unit 350, configured to calculate a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result;
the second converting unit 360 is configured to convert the frequency estimation result into a parameter estimation result.
In this embodiment, the explanation of the array single snapshot multidimensional parameter estimation device under the interference condition may refer to the description in embodiment 1 or embodiment 2, and the description is not repeated in this embodiment.
Therefore, the array single-snapshot multidimensional parameter estimation device under the interference condition described in the embodiment is implemented, matrix decomposition and grid search are not needed, and a plurality of dimensional parameters such as distance, angle and speed of a coherent information source can be rapidly and accurately measured by using single-snapshot data.
Example 5
Referring to fig. 19, fig. 19 is a schematic structural diagram of an array single snapshot multidimensional parameter estimation device under an interference condition according to the present embodiment. As shown in fig. 19, the array single snapshot multidimensional parameter estimation device under the interference condition includes:
An acquisition unit 310, configured to acquire an array reception signal under an interference condition;
a first converting unit 320, configured to convert a source multi-dimensional parameter estimation problem of the array received signal into a multi-dimensional frequency estimation problem;
a coarse estimation unit 330, configured to perform multi-dimensional frequency coarse estimation on the array received signal based on the multi-dimensional frequency estimation problem, so as to obtain a multi-dimensional frequency coarse estimation result;
a fine estimation unit 340, configured to perform multi-dimensional frequency fine estimation on the array received signal according to the multi-dimensional frequency coarse estimation result, so as to obtain a multi-dimensional frequency fine estimation result;
A calculating unit 350, configured to calculate a frequency estimation result according to the multi-dimensional frequency coarse estimation result and the multi-dimensional frequency fine estimation result;
the second converting unit 360 is configured to convert the frequency estimation result into a parameter estimation result.
As an alternative embodiment, the rough estimation unit 330 includes:
The signal transformation subunit 331 is configured to perform multidimensional fast fourier transform processing on the array received signal to obtain a multidimensional spectrum matrix block;
an acquisition subunit 332, configured to acquire signal spectrum peak point coordinates according to the spectrum matrix block;
the coarse estimation subunit 333 is configured to perform multi-dimensional frequency coarse estimation of the complex sine wave according to the coordinates of the peak points of the signal spectrum, so as to obtain a multi-dimensional frequency coarse estimation result.
In this embodiment, the result of the multi-dimensional frequency coarse estimation is:
Wherein, theAnd lk is a positive integer and represents a spreading factor.
As an alternative embodiment, the fine estimation unit 340 includes:
A first calculating subunit 341, configured to calculate a maximum iteration number and an offset according to a preset sampling length;
a first determining subunit 342, configured to determine a current iteration number;
An obtaining subunit 343, configured to obtain, according to the current iteration number, the last iteration spectrum fine estimation value and complex amplitude coefficients of a plurality of complex sine waves in the last iteration;
A second calculating subunit 344, configured to calculate, according to the multi-dimensional frequency coarse estimation result, the last iteration spectrum fine estimation value, the offset, and the array receiving signal, the spectrum leakage coefficients of the plurality of complex sine waves and the multi-dimensional offset spectrum values of the plurality of complex sine signals;
The second calculating subunit 344 is further configured to calculate a multi-dimensional offset spectral leakage correction coefficient of the plurality of complex sine waves according to the complex amplitude coefficient of the plurality of complex sine waves, the spectral leakage coefficient of the plurality of complex sine waves, and the multi-dimensional offset spectral value of the plurality of complex sine signals in the previous iteration;
The second calculating subunit 344 is further configured to calculate a current frequency fine estimation value according to the multi-dimensional offset spectrum leakage correction coefficients of the plurality of complex sine waves and the last iteration spectrum fine estimation value;
a judging subunit 345, configured to judge whether the current iteration number reaches the maximum iteration number;
and a second determining subunit 346, configured to determine the current frequency fine estimation value as a multi-dimensional frequency fine estimation result when it is determined that the maximum number of iterations is reached.
As an alternative embodiment, the fine estimation unit 340 further includes:
A third calculating subunit 347, configured to calculate, when it is determined that the current iteration number does not reach the maximum iteration number, a spectrum value of the signal at a plurality of complex sinusoidal signal frequency estimation points according to the multi-dimensional frequency coarse estimation result and the last iteration spectrum fine estimation value;
The third calculation subunit 347 is further configured to calculate a spectrum leakage coefficient corresponding to the current iteration number according to the multi-dimensional frequency coarse estimation result;
The third calculation subunit 347 is further configured to calculate complex amplitude coefficients of the plurality of complex sine waves corresponding to the current iteration number according to the spectrum values of the signals at the frequency estimation points of the plurality of complex sine signals, the spectrum leakage coefficients corresponding to the current iteration number, and the complex amplitude coefficients of the plurality of complex sine waves of the previous iteration;
the value increasing subunit 348 is configured to increase the value of the current iteration number by 1 as the new current iteration number, and trigger the first determining subunit 342 to determine the current iteration number.
In this embodiment, the explanation of the array single snapshot multidimensional parameter estimation device under the interference condition may refer to the description in embodiment 1 or embodiment 2, and the description is not repeated in this embodiment.
Therefore, the array single-snapshot multidimensional parameter estimation device under the interference condition described in the embodiment is implemented, matrix decomposition and grid search are not needed, and a plurality of dimensional parameters such as distance, angle and speed of a coherent information source can be rapidly and accurately measured by using single-snapshot data.
The embodiment of the application provides an electronic device, which comprises a memory and a processor, wherein the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to execute the method for estimating the single snapshot multidimensional parameters under the interference condition in the embodiment 1 or the embodiment 2 of the application.
The embodiment of the application provides a computer readable storage medium storing computer program instructions which, when read and executed by a processor, perform the method for estimating multi-dimensional parameters of an array single snapshot under interference conditions in embodiment 1 or embodiment 2 of the application.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners. The apparatus embodiments described above are merely illustrative, for example, of the flowcharts and block diagrams in the figures that illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, functional modules in the embodiments of the present application may be integrated together to form a single part, or each module may exist alone, or two or more modules may be integrated to form a single part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application. The storage medium includes a U disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, an optical disk, or other various media capable of storing program codes.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and variations will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application. It should be noted that like reference numerals and letters refer to like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.