CN108173259A - A kind of sinusoidal frequency method of estimation based on unit constraint least mean-square error - Google Patents
A kind of sinusoidal frequency method of estimation based on unit constraint least mean-square error Download PDFInfo
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- CN108173259A CN108173259A CN201711389872.1A CN201711389872A CN108173259A CN 108173259 A CN108173259 A CN 108173259A CN 201711389872 A CN201711389872 A CN 201711389872A CN 108173259 A CN108173259 A CN 108173259A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Power Engineering (AREA)
- Measuring Frequencies, Analyzing Spectra (AREA)
Abstract
The invention discloses it is a kind of based on unit constraint least mean-square error sinusoidal frequency method of estimation, including：(1) time-domain sampling is carried out to detected signal, obtains discrete-time signal x (n)；Wherein, the quantity of sampled point is N, and sample frequency is greater than or equal to Nyquist sampling frequency；(2) the discrete-time signal x (n) after sampling is obtained into x (n 1), x (n 2) and x (n 3) by delay；(3) object function of unit constraint least mean-square error is established：(4) object function in solution procedure (3), obtains frequency estimation
Description
Technical field
The present invention relates to frequency estimating methods more particularly to a kind of sinusoidal frequencies based on unit constraint least mean-square error
Method of estimation.
Background technology
Electric system is the mainstay of the national economy.With a large amount of non-linear, impact negative electrical charge access power grids, severe exacerbation
Electricity quality.The accurate estimation of the accurate estimation, especially frequency of harmonic wave and simple harmonic quantity wave parameter is to power quality deterioration problem
The premise administered.
The Frequency Estimation problem of sinusoidal signal in white Gaussian noise has very important researching value.At present both at home and abroad
It has proposed the method for many Frequency Estimations, has been broadly divided into frequency domain, time domain and time frequency analysis algorithm.Frequency domain method mostly be based on from
The direct Power estimation method of Fourier transformation (DFT) class, this method explicit physical meaning are dissipated, but there are energy leakages in DFT
And fence effect so that this method has larger error.Time domain analysis algorithm mainly carries out instantaneous frequency to signal and estimates
Meter, mainly has based on two major class algorithm of auto-correlation and linear prediction.Wherein, Pisarenko Harmonic Decompositions (PHD) algorithm and improvement
Pisarenko Harmonic Decompositions (RPHD) algorithm is used widely, although improved RPHD algorithms can realize it is progressive
Unbiasedness, but in the estimation performance of low-frequency range and not ideal enough.
With reaching its maturity for sampling technique, the numerical frequency of detected signal is frequently located in low frequency band, therefore we
It needs to obtain and estimates the better sinusoidal signal frequency method of estimation of performance in low-frequency range.
Invention content
Goal of the invention：In view of the problems of the existing technology the present invention, provides a kind of based on unit constraint lowest mean square mistake
The sinusoidal frequency method of estimation of difference.
Technical solution：Sinusoidal frequency method of estimation of the present invention based on unit constraint least mean-square error includes：
(1) time-domain sampling is carried out to detected signal, obtains discrete-time signal x (n)；Wherein, the quantity of sampled point is
N, sample frequency are greater than or equal to Nyquist sampling frequency；
(2) the discrete-time signal x (n) after sampling is obtained into x (n-1), x (n-2) and x (n-3) by delay；
(3) object function of unit constraint least mean-square error is established：
In formula, ω represents frequency to be estimated, e (n)=xT(n) ω, x (n)=[x (n), x (n-1), x (n-2), x (n-3)
]T, ω=[1,1-2cos (ω), 1-2cos (ω), 1]T；
(4) object function in solution procedure (3), obtains the estimated value of frequency to be estimated
In formula,A (n)=x (n)+x (n-3), b (n)=x
(n-1)+x(n-2)。
(5) it by Lagrange's equation, calculatesClosure varianceCarry out performance evaluation：
In formula, ω0Represent original signal actual frequency values, signal-to-noise ratio is sought in SNR () expressions.
Advantageous effect：Compared with prior art, the present invention its remarkable advantage is：
1st, the present invention is directly based upon time domain sampling point and carries out Frequency Estimation, does not need to carry out the conversion of frequency domain, and algorithm is simple,
Operation is simplified.
2nd, cost function of the invention is the least mean-square error function constrained based on unit, can provide progressive nothing in this way
Inclined estimation improves the accuracy of estimation；
3rd, the present invention can obtain Frequency Estimation the closed form and abbreviation of variance after approximating variances closed form,
Convenient for the variance estimated.
4th, Frequency Estimation of the invention can be obtained, therefore pass through number by adder, multiplier, delayer and its calculating
Circuit realizes that algorithm is simple, and operation is simplified, and is applicable to real time signal processing.
Description of the drawings
The realization block diagram of the frequency estimating methods of Fig. 1 present invention；
The Error Graph of Fig. 2 frequency estimating methods of the present invention；
Fig. 3 frequencies of the present invention are closed variance expression formula and figure are realized under sampled point N=20；
Fig. 4 frequencies of the present invention are closed variance expression formula and figure are realized under sampled point N=20；
Fig. 5 real data test charts of the present invention.
Specific embodiment
The present invention is specifically introduced by embodiment below.
WithFor signal, the specific derivation method of Frequency Estimation is provided, is imitated by Matlab
The validity of true verification frequency estimating methods of the present invention and the accuracy for being closed variance expression formula.Each simulation result is
500 independent estimations are averaged.
Single-frequency reality sinusoidal signal model is expressed as
WhereinTo have determined that unknown constant, respectively representation signal amplitude, frequency and
Phase.To it within observing time discretization, sample N number of sample value, obtained discrete sampling sequence is
Assuming that it is 0 to contain mean value in sinusoidal signal, variance isWhite Gaussian noise q (n), if x (n)=s (n)+q (n),
The sample value then once realized is
X (n)=s (n)+q (n) n=0,1 ..., N-1
There is very strong linear prediction characteristic to carry out Frequency Estimation in itself according to sinusoidal signal.According to without real sinusoidal letter of making an uproar
Number model, following equation can be obtained：
S (n)=2cos (ω0)s(n-1)-s(n-2)
Similar, it can obtain：
S (n-1)=2cos (ω0)s(n-2)-s(n-3)
Above-mentioned two formula is added, it is possible to obtain four following point Linear prediction models：
S (n)+s (n-1)+s (n-2)+s (n-3)=2cos (ω0)(s(n-1)+s(n-2))
Here it is the present invention is based on linear model.
Due to the addition of white Gaussian noise, defining error function is：
E (n)=a (n)+(1-2cos (ω)) b (n)
Here ω represents frequency to be estimated in a (n)=x (n)+x (n-3), b (n)=x (n-1)+x (n-2), formula e (n).
According to minimum mean square error criterion, can obtain cost function is：
By derivation, enableThe expression formula of the Frequency Estimation of a closure can be obtained：
HereRepresent the frequency estimation calculated.But this frequency estimation algorithm is unstable under noise
, i.e. Biased estimator.
In order to remove influence of the noise to four point Linear Frequency Estimations, the present invention is using unit constraint least mean-square error
E (n) is written as vector form by method first：
E (n)=xT(n)ω
Wherein, x (n)=[x (n), x (n-1), x (n-2), x (n-3)]TIt is input vector, ω=[1,1-2cos (ω),
1-2cos(ω),1]TIt is weight coefficient.Unit constraint Minimum Variance method target be：
Therefore, modification error function is
So as to obtain a modified cost function, and then obtain Frequency Estimation expression formula formula and be：
In formula,AndIt is by variance closure expression formula is calculated
By Fig. 1 it can be clearly seen that the numerical frequency in input sinusoidal signal changes between (0.2 π, 0.6 π)
When, the error of the frequency approach of frequency estimating methods of the present invention is respectively less than 10-3.Such error almost can be ignored, no
Only estimation is accurate, and estimated accuracy has very big stationarity.It is low in view of the complexity of algorithm simultaneously, suitable for frequency in real time
The application scenarios of rate estimation.
For preferably analytic variance, CRLB lower bounds are calculated：
Fig. 2 and Fig. 3 represents proposed frequency estimating methods under identical Signal to Noise Ratio (SNR)=20dB respectively, N=20 and N=
400 theoretical variance and actual emulation variance and CRLB circle.It can be seen from the figure that the theoretical variance in entire frequency (0, π)
It is all very identical with realized variance, and estimate that the increase of sampled point can make theoretical variance closer to actual emulation variance.But estimate
The increase of meter sampled point can make estimate variance far from CRLB variance inferior boundaries, it is clear that this result being not a desirable to.In practical application
In, in order to complete real-time estimation, the sampled data usually once estimated will not be too many, therefore can ensure that estimate variance approaches
CRLB lower bounds reach the estimation of near-optimization.
In order to further verify the superiority of proposed frequency estimation algorithm, using the sampled value of virtual voltage into line frequency
Estimation, the frequency of virtual voltage are about 50Hz, sample rate 1000Hz, and acquired results are as shown in Figure 4.RPHD is improved in Fig. 4
Pisarenko harmonic frequency algorithm for estimating is that the frequency based on continuous three point Linear prediction unit constraint least mean-square error is estimated
Calculating method.As can be seen from Figure 4 the present invention is substantially better than RPHD algorithms.
The sinusoidal frequency method of estimation of the present invention, passes through building for new linear prediction model it can be seen from above-mentioned example
The application of vertical and unit constraint least mean-square error improves the accuracy of Frequency Estimation.Meanwhile the frequency estimating methods are direct
It is carried out using time-domain sampling signal, avoids the conversion of frequency domain, algorithm complexity is low, convenient for hardware realization, can realize in real time
Frequency Estimation, application scenarios are extensive.
Claims (2)
1. a kind of sinusoidal frequency method of estimation based on unit constraint least mean-square error, it is characterised in that this method includes：
(1) time-domain sampling is carried out to detected signal, obtains discrete-time signal x (n)；Wherein, the quantity of sampled point is N, is adopted
Sample frequency is greater than or equal to Nyquist sampling frequency；
(2) the discrete-time signal x (n) after sampling is obtained into x (n-1), x (n-2) and x (n-3) by delay；
(3) object function of unit constraint least mean-square error is established：
In formula, ω represents frequency to be estimated, e (n)=xT(n) ω, x (n)=[x (n), x (n-1), x (n-2), x (n-3)]T, ω
=[1,1-2cos (ω), 1-2cos (ω), 1]T；
(4) object function in solution procedure (3), obtains the estimated value of frequency to be estimated
In formula,A (n)=x (n)+x (n-3), b (n)=x (n-
1)+x(n-2)。
2. the sinusoidal frequency method of estimation according to claim 1 based on unit constraint least mean-square error, feature exist
In：It further includes
(5) it by Lagrange's equation, calculatesClosure varianceCarry out performance evaluation：
In formula, ω0Represent original signal actual frequency values, signal-to-noise ratio is sought in SNR () expressions.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102664841A (en) * | 2012-04-30 | 2012-09-12 | 电子科技大学 | Method for SC-FDE (single carrier-frequency domain equalization) system low complexity RLS self-adaption channel estimation |
| CN103795660A (en) * | 2014-02-11 | 2014-05-14 | 哈尔滨工程大学 | Double-stage frequency estimation method based on noise approximate processing |
| CN104502699A (en) * | 2014-12-13 | 2015-04-08 | 中国人民解放军后勤工程学院 | Frequency estimation method based on data prolongation and Hilbert conversion |
| CN105403858A (en) * | 2015-10-28 | 2016-03-16 | 上海电机学院 | Arrival time difference estimation method |
| US20160373025A1 (en) * | 2015-06-19 | 2016-12-22 | Sparq Systems Inc. | Adaptive control method for grid-connected inverters used with distributed power generation |
| WO2017026965A1 (en) * | 2015-08-12 | 2017-02-16 | Istanbul Teknik Universitesi Rektorlugu | Multiple input multiple output orthogonal frequency division multiplexing with index modulation, mimo-ofdm-im, communications system |
| CN107085140A (en) * | 2017-04-25 | 2017-08-22 | 东南大学 | Nonequilibrium system frequency estimating methods based on improved SmartDFT algorithms |
| CN107490722A (en) * | 2017-08-18 | 2017-12-19 | 南开大学 | A kind of frequency estimating methods of low signal-to-noise ratio real signal |
-
2017
- 2017-12-21 CN CN201711389872.1A patent/CN108173259B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102664841A (en) * | 2012-04-30 | 2012-09-12 | 电子科技大学 | Method for SC-FDE (single carrier-frequency domain equalization) system low complexity RLS self-adaption channel estimation |
| CN103795660A (en) * | 2014-02-11 | 2014-05-14 | 哈尔滨工程大学 | Double-stage frequency estimation method based on noise approximate processing |
| CN104502699A (en) * | 2014-12-13 | 2015-04-08 | 中国人民解放军后勤工程学院 | Frequency estimation method based on data prolongation and Hilbert conversion |
| US20160373025A1 (en) * | 2015-06-19 | 2016-12-22 | Sparq Systems Inc. | Adaptive control method for grid-connected inverters used with distributed power generation |
| WO2017026965A1 (en) * | 2015-08-12 | 2017-02-16 | Istanbul Teknik Universitesi Rektorlugu | Multiple input multiple output orthogonal frequency division multiplexing with index modulation, mimo-ofdm-im, communications system |
| CN105403858A (en) * | 2015-10-28 | 2016-03-16 | 上海电机学院 | Arrival time difference estimation method |
| CN107085140A (en) * | 2017-04-25 | 2017-08-22 | 东南大学 | Nonequilibrium system frequency estimating methods based on improved SmartDFT algorithms |
| CN107490722A (en) * | 2017-08-18 | 2017-12-19 | 南开大学 | A kind of frequency estimating methods of low signal-to-noise ratio real signal |
Non-Patent Citations (2)
| Title |
|---|
| H. C. SO ET AL.: "Reformulation of Pisarenko Harmonic Decomposition Method for Single-Tone Frequency Estimation", 《IEEE TRANSACTIONS ON SIGNAL PROCESSING》 * |
| YILI XIA ET AL.: "Complex-Valued Least Squares Frequency Estimation for Unbalanced Power Systems", 《IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT》 * |
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