CN113219248B - Signal component estimation method based on time domain waveform comparison - Google Patents
Signal component estimation method based on time domain waveform comparison Download PDFInfo
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Abstract
A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency of a signal component is known and only the initial phase of the signal component is estimated, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, … and N-1, and the sampling rate is set as f s It has a frequency f 0 Known, initial phase
An unknown signal component of interest; (2) solving the first phase
For the univariate optimization problem of the independent variable, will find
Is determined as the component of interest f 0 Corresponding initial phase
Is accurately estimated
A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency and the initial phase of a signal component are unknown, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, … and N-1, and the sampling rate is set as f s It has a frequency of f 0 At an initial phase of
The signal component of interest; (2) solving for a sum frequency f and an initial phase
Determining an optimal solution to the problem of binary function optimization of the independent variables as the frequency f of the component of interest 0 And an initial phase
Is accurately estimated
And
Description
Technical Field
The present application relates to a method of estimating an initial phase of a signal component if its frequency is known and a method of jointly estimating a signal component if both the frequency and the initial phase are unknown.
In some scenarios, the frequency of the signal component is accurate, constant and known, and its initial phase needs to be estimated, for example, in phase laser ranging, the time is indirectly calculated by estimating the initial phase difference between the transmitted signal and the received signal, so that the distance can be estimated according to the speed of light; for another example, when the frequency sweep method is used to perform system frequency response or impedance spectrum analysis, it is also the case that the frequency is known and the initial phase needs to be estimated accurately. In other scenarios, the frequency and phase of the signal components are unknown, for example, in ac grid connection of a power system, the frequency and initial phase of the grid-connected signal are required to be the same, and accurate estimation of both of them is required. The estimation of the frequency and initial phase of the signal component is also widely applied in many fields such as radar detection, biomedical electronics and the like. Accurate estimation of the signal component frequency and initial phase implies better performance of its application system.
In practice, the initial phase of a signal component is often also referred to simply as the phase.
Background
With respect to the initial phase estimate with known frequency. One basic method is: in the frequency domain, the phase of the fourier transform DTFT of the signal at a known frequency point is determined as an estimate of the initial phase of the signal component. Patent [1] also proposes an initial phase search estimation algorithm based on signal-to-spectrum comparison with known frequency. The initial phase of the system impulse response signal component can be embodied as the initial phase difference of the input and output same-frequency signals of the system. A first-order linear interpolation method [2] utilizes straight line approximation to replace a signal curve at a zero crossing point, an accurate zero crossing point can be calculated according to sampling values at two sides of the zero crossing point, and then an initial phase of the system is calculated according to the calculated time difference delta t of the zero crossing point of the input and output signals of the system; similarly, the second-order phase interpolation method utilizes a second-order polynomial to fit a signal curve at a zero-crossing point, and calculates according to three sampling points [2 ]; the cross-correlation method [3] calculates the cross-correlation of two paths of same-frequency signals x (t), y (t), and according to the principles that signals and noises are not correlated with each other, the cross-correlation function is only related to the initial phase difference of the two paths of signals at the zero point, so that the initial phase difference can be directly solved.
The task of estimation is required both with respect to the frequency and the initial phase of the signal component. The general approach is to estimate the frequency and the initial phase of the signal component sequentially, that is, on the basis of a certain approximation, one parameter of the frequency or the initial phase is estimated, and then the other parameter is estimated accordingly. The classical frequency estimation method in the frequency domain can be classified as peak search based on the DTFT (discrete time Fourier transform) spectrum [5 ]][6]And spectral correction algorithms, such as iterative interpolation, enhanced iterative interpolation algorithms [ 7], for estimating the deviation of the frequency corresponding to the DFT peak from the true frequency][8][9]Sum-phase-difference method [10]][11]And the like. Patent application [12]]A signal component frequency accurate estimation method based on comparison of a constructed signal amplitude frequency spectrum and a signal amplitude frequency spectrum to be detected is provided, a signal is constructed by taking frequency f as a parameter, a correlation coefficient between a maximum constructed signal amplitude frequency spectrum and a signal amplitude frequency spectrum to be estimated is taken as an optimization target, and a frequency with the maximum correlation coefficient is given by binary search and taken as the frequency f of an interested component of the signal to be detected 0 Is accurately estimated
There are also some non-frequency domain parameter estimation algorithms, which do not require the computation of FFT and are therefore generally simpler and easier to implement. MUSIC method based on spatial spectral decomposition [13][14]The signal is divided into a signal space and a noise space through characteristic decomposition, and the parameters are estimated by utilizing the orthogonality of the noise space and the signal space. Similarly, the ESPRIT method using rotational invariance [15 ]]。
The frequency and initial phase joint estimation method means that one parameter is optimized and determined at a time and then the other parameter is determined, but two parameters are simultaneously optimized and simultaneously obtain an optimal value. The classical Prony algorithm [16] utilizes a series of linear combinations of complex exponential functions to express real signals to be measured, then constructs a polynomial, and solves parameters in the polynomial in a way of solving a linear equation set by a least square method so as to solve the frequency to be measured and the initial phase to be measured. Patent application [17] proposes a signal component frequency and initial phase joint search estimation algorithm based on whole spectrum comparison.
Reference documents:
[1] liu hong xing, Lu xing Cheng, Si Jiang Feng an accurate estimation method of the initial phase of the harmonic component of a signal [ p ]. Jiangsu province: CN108710029B, 2020-10-23.
[2] Study of phase measurements in the shengchun wave power system [ D ]. yanshan university, 2006.
[3] The sine signal initial phase detection method based on the multiple correlation method [ J ] the astronavigation measurement technology, 2011, 31 (004): 63-66.
[4]D.C.Rife，R.R.Boorstyn，Single-tone parameter estimation from discrete-time observations， IEEE Trans.Inform.Theory 20(1974)591-598.
[5]E.Aboutanios，A modified dichotomous search frequency estimator，IEEE Signal Process.Lett. 11(2004)186-188.
[6]Y.V.Zakharov，T.C.Tozer，Frequency estimator with dichotomous search of periodogram peak， Electron.Lett.35(1999)1608-1609.
[7]E.Aboutanios，B.Mulgrew，Iterative frequency estimation by interpolation on Fourier coefficients，IEEE Trans.Signal Process.53(2005)1237-1241.
[8]Xu C，Zhou L，Chen C，et al.A Low Computational Complexity Frequency Estimation Method with High Precision of Sinusoid Based on DFT[C].2017 4th International Conference on Information Science and Control Engineering(ICISCE).IEEE，2017.
[9]Y.Liu，Z.Nie，Z.Zhao，andQ.H.Liu，Generalization of iterative Fourier interpolation algorithm for single frequency estimation，Digital Signal Process.，21(2011)141-149.
[10] Phase difference correction for phase and frequency correction in spectral analysis [ J ] vibration engineering, 1999 (4): 454-459.
[11] Chicory, error analysis using FFT phase difference correction signal frequency and initial phase estimation [ J ] data acquisition and processing (1): 7-11.
[12] Liu hong xing, lu xing, si drastic peak a method for accurately estimating the frequency of signal components [ P ]. jiangsu province: CN108414833B, 2020-11-10.
[13]Schmidt R，Schmidt R O.Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas&Propagation，1986，34(3)：276-280.
[14]Stoica P，Eriksson A.MUSIC estimation of real-valued sine-wave frequencies[J].Signal Processing，1995，42(2)：139-146.
[15]Roy R，Kailath T.ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques[J].IEEE Transactions on Acoustics Speech and Signal Processing，1989， 37(7)：984-995.
[16]Hauer J.Initial results in Prony analysis of power system response signals[J].IEEE Transactions on Power Systems，1990，5(1)：80-89.
[17] Liuhong star, Maoyiwei, Severe peak, a joint estimation method of signal component frequency and initial phase [ P ]. Jiangsu province: CN112394223A, 2021-02-23.
Disclosure of Invention
Object of the Invention
A method for estimating the initial phase of a signal component under the condition that the frequency of the signal component is known is provided, and meanwhile, a method for jointly estimating the frequency and the initial phase under the condition that the frequency and the initial phase are unknown is provided, so that the estimation accuracy is improved.
Technical scheme
A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency of a signal component is known and only the initial phase of the signal component is estimated, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, … and N-1, and the sampling rate is set to be f s Hz, it has a frequencyf 0 Known, initial phase of Hz
The signal component of interest with unknown radian, (2) solving for an initial phase
For the optimization problem of independent variables, the initial phase corresponding to the optimal solution
As initial phase of the component of interest
Is estimated value of
Wherein the optimization problem of step (2) can be defined as the maximization problem of formula (1) or the minimization problem of formula (2)
Wherein the content of the first and second substances,
constructed with f 0 Hz as frequency, in
Radian as initial phase with f s Hz is the sine wave sequence of the sampling rate, R is a correlation coefficient function, D is the norm of the difference value of the constructed normalized sine wave sequence and the normalized sequence to be estimated, and | is | · | | represents the norm of the sequence. The flow diagram of the method is shown in fig. 1.
The principle of the scheme is as follows: has already confirmed the frequencyFixed signal, initial phase
The change is equivalent to the control signal waveform moving back and forth on the time axis, when the initial phase of two same-frequency signals is equal, the time domain waveforms of the two signals will be completely correlated and have the maximum correlation coefficient, as shown in fig. 2, which is a graph
Respectively corresponding to two same-frequency signals.
Further study the value relationship between co-frequency signals with different phases. Is provided with a signal to be estimated
Radian, sampling frequency f s At 1kHz, a series of amplitudes A at 1 and initial phases are constructed
Structural signal of
Respectively calculating the signal x (n) to be estimated and the constructed signal
The correlation coefficient between them and the 1-norm of the waveform difference between them, the result is shown in fig. 3. It can be seen that only the signal is constructed
With respect to the signal to be estimated
When the correlation coefficients are equal, the maximum value of the correlation coefficient is 1, and the correlation coefficient is a single peak; likewise, the 1-norm of the difference between the two waveforms takes the minimum value of 0 only when the phases are equal.
A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency and the initial phase of a signal component are unknown and both the frequency and the initial phase need to be estimated, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, …, and N-1 sets the sampling rate to be f s Hz, it has a frequency of f 0 Hz, initial phase of
The signal component of interest in radians, (2) solving for a phase at frequency fHz and an initial phase
F sum to be obtained for the problem of binary function optimization of independent variables
Is determined as the component frequency of interest f 0 And an initial phase
Is estimated accurately
And
wherein the optimization problem solved in step 2 is defined as a maximization problem represented by formula (3) or a minimization problem represented by formula (4)
Wherein the content of the first and second substances,
constructed with fHz as frequency
Radian as initial phase with f s Hz is a sine wave sequence of a sampling rate, R is a correlation coefficient function, D is a norm of a difference value between a constructed normalized sine wave sequence and a normalized sequence to be estimated, | | · | | | represents the norm of the sequence, and the search range of f can be (0, f) s /2), initial phase
Has a search range of [0, 2 π]。
Similarly, a simulation experiment similar to that of fig. 2 is performed, and as shown in fig. 4, the frequency and phase of the constructed signal component are changed, and a search is performed, so that a unimodal convex function graph shown in fig. 4 can be obtained.
Specifically, the optimization can be performed by using a conjugate gradient method, and the specific steps are shown in table 1.
Table 1: conjugate gradient method combined solution optimization problem (setting binary function)
)
Advantageous effects
Experiment one: and verifying the effect of the initial phase estimation method based on the time domain waveform. Generation of a sine wave using MATLAB at different signal-to-noise levels
To simulate the signal to be measured, sampling frequency f s ＝1kHz，f 0 At [49Hz, 51Hz]Is randomly generated, A is the signal amplitude of [0.9, 1.1 ]]The length of the signal is about 3 cycles (N is 64), and the phase to be measured
At [0, 2 π]Randomly generated within the range, and omega (t) is Gaussian white noise. 10000 experiments were performed for each signal-to-noise level, and the root mean square error RMSE of 10000 experiments was used as a comparison index. The experiment is carried out by adopting the method and a second-order interpolation method, a cross-correlation method and a Prony method mentioned in the background technology as comparison methods respectively. The results obtained are shown in FIG. 5 and Table 2. The experiment shows that: under the condition of known frequency, the initial phase estimation method based on time domain waveform comparison provided by the application has an estimation effect obviously better than that of other methods under most conditions. When the signal-to-noise ratio is less than 0dB, the cross-correlation method weakens the influence of noise in a cross-correlation mode, so the effect is better at low signal-to-noise ratio, but the method of the application is only inferior to the method, and the estimation error of the method of the application is obviously smaller than that of other methods for the environment with the signal-to-noise ratio being more than 0 dB.
TABLE 2 under non-integer period sampling, different methods phase estimation root mean square error RMSE (rad)
Experiment two: and verifying the effectiveness of the frequency initial phase joint estimation based on the time domain waveform comparison. Design simulation experiment, frequency f 0 And phase
For measurement, the other experimental environments are the same as the experiment I. Experiments respectively take a method based on amplitude spectrum comparison (only frequency estimation comparison), iterative interpolation, enhanced iterative interpolation, a phase difference method, a Prony method and a parameter estimation theory lower CrLB limit in the background technology as a contrast, and 10000 Cramelo lower limits are carried out at each signal-to-noise ratio levelThe results of the experiments are shown in FIG. 6. The experiment shows that: when the frequency and the phase of the signal component are unknown, compared with other methods, the joint estimation algorithm based on time domain waveform comparison provided by the application can better approach to the CRLB no matter the frequency estimation or the phase estimation is carried out under any signal-to-noise level, and has a better estimation effect.
Drawings
Fig. 1 is a block diagram of a signal initial phase estimation process based on time domain waveform comparison according to the present invention.
Fig. 2 is a schematic diagram illustrating the principle of signal initial phase estimation based on time domain waveform comparison according to the present invention.
FIG. 3 is a schematic diagram of an initial phase estimation objective function based on time domain waveform comparison. Wherein (a) is a correlation coefficient objective function; (b) is the difference 1-norm objective function.
FIG. 4 shows a frequency-phase joint estimation objective function based on time-domain waveform comparison. The graphs (a) and (b) are a three-dimensional change surface graph and a two-dimensional contour graph of the 1-norm of the correlation coefficient and the difference in a coordinate system constituted by frequency and phase, respectively.
FIG. 5 is a comparison graph of the initial phase estimation effect of the present invention at different SNR.
FIG. 6 is a comparison graph of the effect of the frequency phase joint estimation under different SNR.
Detailed Description
A section of voltage signal x (t) 1.1-cos (2 pi t 50.1+ pi/4) + omega (t) with true frequency of 50.1Hz, initial phase pi/4 and length of 0.255s to be measured is arranged, omega (t) is Gaussian white noise, the signal-to-noise ratio is 45dB, and f is used s This is sampled at a sampling frequency of 1kHz to yield x (n). The initial phase estimation method based on time domain waveform comparison and the frequency and initial phase joint estimation method based on time domain waveform comparison are respectively adopted to estimate the parameters of the signals.
I. The initial phase estimation method based on time domain waveform comparison is implemented as follows:
(1) reading signals x (n); (2) by [0, 2 π](radian) as initial phase
To solve the optimization problem
Wherein, one for each time
Construction signal
Is obtained by 30 times of iteration based on dichotomy
And x (n) the initial phase with the largest correlation coefficient
Using the estimated value as the estimated value of the initial phase of the signal component to be estimated
The error is-2.2879X 10 -4 rad。
II, implementing a frequency initial phase joint estimation method based on time domain waveform comparison:
(1) reading signals x (n); (2) within a given range of parameters f e [49.1, 51.1 ] of the component of interest]，
Internally randomly generating a set of frequencies f and initial phases
As a starting point for a two-dimensional search, then, at f e [49.1, 51.1]，
Frequency f and initial phase of in-range transform
Searching by using conjugate gradient algorithm to solve optimization problem
Wherein, for each given set, the frequency f and the initial phase are searched
Construction signal
Through conjugate gradient iterative search, a group of frequency f and initial phase corresponding to the maximum correlation coefficient are obtained
Has a value of (50.1018, 0.7838), which is taken as the frequency estimate of the signal to be estimated
And phase estimation
The estimation errors are 0.0018Hz, -0.0016rad respectively, and the total estimation time is 0.012 s.
Claims (2)
1. A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency of a signal component is known and the initial phase of the signal component needs to be estimated, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, … and N-1, and the sampling rate is set as f s Hz, it has a frequency f 0 Known, initial phase
An unknown signal component of interest; (2) solving the first phase
For the optimization problem of independent variables, the initial phase corresponding to the optimal solution is used as the initial phase of the interested component
Is estimated by
Wherein the optimization problem of step (2) can be defined as the maximization problem of formula (1) or the minimization problem of formula (2)
Wherein the content of the first and second substances,
constructed with f 0 Hz as frequency, in
Radian as initial phase with f s Hz is a sine wave sequence of the sampling rate, R is a correlation coefficient function, D is a norm of the difference value of the constructed normalized sine wave sequence and the normalized sequence to be estimated, and | | · | | represents the norm of the sequence.
2. A signal component estimation method based on time domain waveform comparison aims at the condition that the frequency and the phase of a signal component are unknown and both the frequency and the phase of the signal component need to be estimated, and comprises the following steps of (1) reading a signal sampling sequence x (N) to be estimated, wherein N is 0, 1, … and N-1, and the sampling rate is set to be f s Hz, it has a frequency of f 0 At an initial phase of
The signal component of interest; (2) solving for a sum frequency f and an initial phase
F and to be solved for the problem of binary function optimization of the independent variables
Is determined as the component frequency of interest f 0 And an initial phase
Is accurately estimated
And
wherein the optimization problem solved in step (2) is defined as a maximization problem represented by formula (3) or a minimization problem represented by formula (4)
Wherein the content of the first and second substances,
constructed with f Hz as frequency
Radian as initial phase with f s Hz is sine wave sequence of sampling rate, R is correlation coefficient function, D is constructed normalized sine wave sequence andnormalizing the norm of the difference value of the sequence to be estimated, | | · | |, which represents the norm of the sequence, and the search range of f is (0, f) s /2), initial phase
Has a search range of [0, 2 π]。
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0296664A (en) * | 1988-10-03 | 1990-04-09 | Nec Corp | Apparatus for estimating frequency and phase |
| CN104142425A (en) * | 2014-07-13 | 2014-11-12 | 中国人民解放军后勤工程学院 | Phase matching method for sinusoidal signal frequency estimation |
| JP2015004584A (en) * | 2013-06-20 | 2015-01-08 | アンリツ株式会社 | Sampling waveform measurement device and sampling waveform measurement method |
| CN108414833A (en) * | 2018-03-07 | 2018-08-17 | 南京大学 | A kind of precise Estimation Method of signal component frequency |
| CN108710029A (en) * | 2018-07-02 | 2018-10-26 | 南京大学 | A kind of precise Estimation Method of signal harmonic component initial phase |
| CN112394223A (en) * | 2020-11-10 | 2021-02-23 | 南京大学 | Joint estimation method for signal component frequency and initial phase |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0296664A (en) * | 1988-10-03 | 1990-04-09 | Nec Corp | Apparatus for estimating frequency and phase |
| JP2015004584A (en) * | 2013-06-20 | 2015-01-08 | アンリツ株式会社 | Sampling waveform measurement device and sampling waveform measurement method |
| CN104142425A (en) * | 2014-07-13 | 2014-11-12 | 中国人民解放军后勤工程学院 | Phase matching method for sinusoidal signal frequency estimation |
| CN108414833A (en) * | 2018-03-07 | 2018-08-17 | 南京大学 | A kind of precise Estimation Method of signal component frequency |
| CN108710029A (en) * | 2018-07-02 | 2018-10-26 | 南京大学 | A kind of precise Estimation Method of signal harmonic component initial phase |
| CN112394223A (en) * | 2020-11-10 | 2021-02-23 | 南京大学 | Joint estimation method for signal component frequency and initial phase |
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