JPH0296664A - Apparatus for estimating frequency and phase - Google Patents
Apparatus for estimating frequency and phaseInfo
- Publication number
- JPH0296664A JPH0296664A JP63250554A JP25055488A JPH0296664A JP H0296664 A JPH0296664 A JP H0296664A JP 63250554 A JP63250554 A JP 63250554A JP 25055488 A JP25055488 A JP 25055488A JP H0296664 A JPH0296664 A JP H0296664A
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- Prior art keywords
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- sine wave
- time
- frequency
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- 230000006870 function Effects 0.000 abstract description 14
- 238000000034 method Methods 0.000 abstract description 11
- 238000011156 evaluation Methods 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000006866 deterioration Effects 0.000 description 1
- 230000000630 rising effect Effects 0.000 description 1
- 230000017105 transposition Effects 0.000 description 1
Landscapes
- Measuring Phase Differences (AREA)
- Stabilization Of Oscillater, Synchronisation, Frequency Synthesizers (AREA)
Abstract
Description
【発明の詳細な説明】
（産業上の利用分野）
本発明は、雑音の重畳した正弦波から周波数と位相を推
定する周波数位相推定装置に関するものである。DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a frequency phase estimation device that estimates frequency and phase from a sine wave on which noise is superimposed.
（従来の技術）
従来技術として知られているものは、ＳｉｍｏｎＨａｙ
ｋｉｎ 著、 ”Ｉｎｔｒｏｄｕｃｔｉｏｎ ｔｏ
Ａｄ ａｐｔｆｖｅ Ｆｉｌｔｅｒ”（Ｍａｃｍｉｌｌ
ａｎ ｐｕｂｌｉｓｈｉｎｇ Ｃｏｍｐａｎｙ、 Ｎｅ
ｗ Ｙｏｒｋ、 １９８４年刊行）である。雑音の重畳
した信号に於て、位相方向に加わっている雑音成分にの
み着目し入力された正弦波の初期位相と周波数に対する
最適解を求める問題は、次の問題に帰着する。すなわち
、時刻ｉに於ける信号Ｓｉが
Ｓ、＝ Ａ、ｅｘｐＱ （θ。＋ｉω））但し、Ａ、＝
Ａ＋ｅａ、：ｅａ、は振幅方向の雑音と表される正弦波
に於てその位相θ１＝θｏ＋ｉωがこれに雑音（ｅ、）
が重畳し等測的に
θ； ＝ｅｏ ＋ ｌω＋ｅ。(Prior art) What is known as the prior art is Simon Hay
kin, “Introduction to
Ad aptfve Filter” (Macmill
a publishing company, Ne
York, published in 1984). In a signal on which noise is superimposed, the problem of finding the optimal solution for the initial phase and frequency of an input sine wave by focusing only on the noise component added in the phase direction results in the following problem. That is, the signal Si at time i is S, = A, expQ (θ.+iω)) However, A, =
A+ea, :ea is the noise in the amplitude direction of a sine wave whose phase θ1=θo+iω is the noise (e,)
are superimposed and isometrically θ; =eo + lω+e.
なる位相として観測されるとき、（ｅ、）による影響を
できるだけ受けないようにθ。とωを推定する問題であ
る。時刻１からｋまでの観測値を用い、推定誤差の分散
を最小にする方法として最小自乗法が良く知られている
。上記文献によれば最小自乗法を上記の問題に当てはめ
た場合には評価関数を５２８ｗ、ｅ、２
目ｌ
と定めていた。更に文献によれば重み付は関数Ｗ１とし
ては
ｗ、＝ｒｋ−１（ｒ＜１）
がよく知られていると述べている。上式に対して逐次回
帰法による周波数・位相推定（特願昭５９−２７７３６
５号明細書［周波数・位相推定装置Ｊ昭５９年ｙｔはＹ
の転置を表わす
を時刻ｋに於ける最適解として求めることができた。When observed as a phase of θ, avoid being affected by (e,) as much as possible. The problem is to estimate ω. The least squares method is well known as a method of minimizing the variance of estimation errors using observed values from time 1 to time k. According to the above literature, when the least squares method is applied to the above problem, the evaluation function is determined to be 528w, e, and 2th l. Furthermore, the literature states that the well-known weighting function W1 is w,=rk-1 (r<1). Frequency and phase estimation using the successive regression method for the above equation (Patent application No. 59-27736)
Specification No. 5 [Frequency/Phase Estimator J 1980 yt is Y
It was possible to find the optimal solution at time k, which represents the transposition of .
（発明が解決しようとする問題点）
この従来技術では、初期推定時に於て雑音により誤った
ベクトルで方向に推定を始めるとその後２■の不確定性
により最終的な推定値が誤ってしまう。この誤推定は問
題であり、基本的には時間的に古い情報を「忘れる」重
み付けをすれば良いことは明白であるが、従来技術のよ
うな重み付けでは特性の劣化を招いていた。これは上記
文献では指数重み付けを用いているが、指数重み付けは
非定常環境下でデータの統計的変動に追従するものであ
り、最近のデータに対しても情報が指数的に失われるた
めにこの問題には適していない。本発明はこれを時間関
数による固定的な重み付けを用いることにより解決しよ
うとしている。(Problems to be Solved by the Invention) In this prior art, if estimation is started in the direction of an incorrect vector due to noise at the time of initial estimation, the final estimated value will be incorrect thereafter due to the uncertainty of 2. This misestimation is a problem, and although it is clear that weighting should basically be used to "forget" temporally old information, weighting as in the prior art has led to deterioration of characteristics. This is because exponential weighting is used in the above literature, but exponential weighting follows statistical fluctuations in data in an unsteady environment, and information is lost exponentially even for recent data. Not suitable for the problem. The present invention attempts to solve this problem by using fixed weighting based on a time function.
（問題を解決するための手段）
本発明の周波数・位相推定装置は、正弦波あるいは雑音
の重畳した正弦波を入力とし、入力正弦波の初期位相と
周波数を推定する装置において、入力正弦波の初期位相
の推定値と入力正弦波の周波数の推定値から次時刻にお
ける正弦波の値を発生する手段と、該正弦波と入力信号
との位相誤差を検出する手段と、検出した位相誤差に時
間による関数で重み付けをする手段と、前記重み付けを
考慮し前記２つの推定値を導出するための第一及び第二
の時変係数を発生する係数発生手段と、前記重み付けさ
れた位相誤差に第一の時変係数を乗じた値により前記初
期位相の推定値を逐次的に更新する初期位相推定手段と
、前記重み付けされた位相誤差に第二の時変係数を乗じ
た値により前記周波数の推定値を逐次的に更新する周波
数推定手段とを含んで構成される。(Means for Solving the Problem) The frequency/phase estimating device of the present invention takes a sine wave or a sine wave superimposed with noise as an input, and estimates the initial phase and frequency of the input sine wave. means for generating the value of the sine wave at the next time from the estimated value of the initial phase and the estimated value of the frequency of the input sine wave; means for detecting the phase error between the sine wave and the input signal; coefficient generation means for generating first and second time-varying coefficients for deriving the two estimated values in consideration of the weighting; initial phase estimating means for sequentially updating the estimated value of the initial phase by a value obtained by multiplying the weighted phase error by a second time-varying coefficient; and an estimated value of the frequency by the value obtained by multiplying the weighted phase error by a second time-varying coefficient. and frequency estimating means for sequentially updating.
（作用）
本発明が対象とするのは、時刻ｉに於ける信号Ｓｉが
Ｓ、＝ Ａ、ｅｘｐ（ｊ（ｅｏ＋ ｉω））と表される
正弦波に於てその位相Ｏｉ＝θ。＋ｉωがこれに雑音（
ｅ、）が重畳し等測的に
θ１＝θ。＋ｉω十ｅｉ
なる位相として観測されるとき、θ。とωが未知パラメ
ータであり、（ｅｉ）による影響をできるだけ受けない
ように観測値θ、からθ。とωを推定する問題である。(Operation) The object of the present invention is that the signal Si at time i is a sine wave expressed as S, = A, exp (j (eo + iω)), and its phase Oi = θ. +iω adds noise to this (
e, ) are superimposed and isometrically θ1=θ. When observed as a phase of +iω10ei, θ. and ω are unknown parameters, and the observed value θ is changed from the observed value θ, so as not to be influenced by (ei) as much as possible. The problem is to estimate ω.
時刻１からｋまでの観測値を用い、推定誤差の分散を最
小にする方法として最小自乗法が良く知られている。最
小自乗法を上記の問題に当てはめた場合には評価関数を
従来技術で述べたように５２８ｗ、６１２
ｍｌ
と定義するが、ここで重み関数Ｗ、をｗ、ｒｋ−１の様
な関数ではなく、最近のデータに対して均等になるよう
な関数、例えば
ｗ、＝１−ｒｉ
や
但しＳは立ち上がり関数
で定義する。評価関数の篤及び訂に関する偏微分係数を
それぞれＯとおくと以下の方程式が得られる。The least squares method is well known as a method of minimizing the variance of estimation errors using observed values from time 1 to time k. When applying the least squares method to the above problem, the evaluation function is defined as 528w, 612ml as described in the prior art, but here the weighting function W, is not a function such as w, rk-1. , a function that is uniform for recent data, such as w, = 1-ri, where S is defined as a rising function. If we set the partial differential coefficients of the evaluation function regarding the depth and the degree to be O, the following equation is obtained.
と修正することになる。更に、
又は
０ｏとωの最小分散推定値は（１）式の解として求める
手段として逐次回帰法が知られている。それによれば時
刻ｉに於ける篤の推定値を篤ｌ、の推定値をｉ：３五と
すると時刻ｋにおいて
ここで（３）式の２行１列の行列Ｐｋ −１ｙｋで１行
１列の値が第一の時変係数で２行１列の値が第二の時変
係数となる。また（３）式右辺第２項の（・）の値を位
相誤差と呼ぶと、初期位相推定値θ。ｋは位相誤差に重
み関数Ｗ、を乗じ、更に時刻にと重み関数Ｗ、に依存す
る第一の時変係数を乗じ一時刻前の推定値θ。ｋ−１か
ら減することにより修正し、又周波数推定値ざｋは同じ
く位相誤差に重み関数Ｗ、を乗じ、更に時刻にと重み関
数Ｗコこ依存する第二の時変係数を乗じ一時刻前の推定
値δに−１から減することにより修正をするという構成
をとることにより（３）式が実現される。この方法によ
れば、毎時側その時点までの観測値を用いた最良の推定
が方程式を解く形で与えられるため、極めて短時間に最
適な推定値が得られる。This will be corrected. Furthermore, the successive regression method is known as a means for finding the minimum variance estimated value of 0o and ω as a solution to equation (1). According to this, if the estimated value of Atsushi at time i is Atsushi l, and the estimated value of Atsushi is i:35, then at time k, the matrix Pk - 1yk with 2 rows and 1 column of equation (3) has 1 row and 1 column. The value in the first time-varying coefficient is the first time-varying coefficient, and the value in the second row and the first column is the second time-varying coefficient. Also, if the value of (.) in the second term on the right side of equation (3) is called a phase error, it is the initial phase estimate θ. k is the estimated value θ one time ago obtained by multiplying the phase error by the weighting function W, and further multiplying the time by a first time-varying coefficient that depends on the weighting function W. The frequency estimate Z k is also calculated by multiplying the phase error by a weighting function W, and then multiplying the time by a second time-varying coefficient that depends on the weighting function W. Equation (3) is realized by correcting the previous estimated value δ by subtracting it from −1. According to this method, the best estimate using the observed values up to that point on each hour is given in the form of solving an equation, so the best estimate can be obtained in an extremely short time.
（実施例）
以下本発明の実施例について図面を参照して詳細に説明
する。第１図は本発明の実施例を示すブロック図である
。(Example) Examples of the present invention will be described in detail below with reference to the drawings. FIG. 1 is a block diagram showing an embodiment of the present invention.
雑音の重畳された正弦波信号はサンプルホールド１でサ
ンプルされ、ん０変換器２でディジタル化される。ディ
ジタル化された正弦波は、ディジタル位相検波器３に於
て、後述する手段により推定された周波数と位相に合致
した正弦波を発生する正弦波発生器４の発生する正弦波
と比較され、位相誤差が出力される。位相検波器の実現
手段は例えば文献（Ｗ、 Ｃ，Ｌｉｎｄｅｓｙ ”Ａ
５ｕｒｖｅｙ ｏｆ Ｄｉｇｉｔａｌ Ｐｈａｓｅ−Ｌ
ｏｃｋｅｄＬｏｏｐ” Ｐｒｏｃ、 ＩＥＥＥ、 ｖｏ
ｌ、 ６９． Ｎｏ、 ４．Ａｐｒｉｌ １９８１）に
詳しく示されている。The sine wave signal on which noise is superimposed is sampled by a sample hold 1 and digitized by a zero converter 2. The digitized sine wave is compared in a digital phase detector 3 with a sine wave generated by a sine wave generator 4 which generates a sine wave matching the frequency and phase estimated by means described later, and the phase is determined. The error is output. A method for realizing a phase detector is described, for example, in the literature (W. C. Lindesy “A
5urvey of Digital Phase-L
"ockedLoop" Proc, IEEE, vo
l, 69. No, 4. April 1981).
正弦波発生器４は位相を入力としその値に対応した正弦
波の値を出力とする読みだし専用メモリ（ＲＯＭ）４４
、加算器４３、乗算器４２、時刻を発生するカウンタ４
１により構成することができ、後述する位相推定値と周
波数推定値をアドレスとして正弦波の標本値を出力する
。重み付は回路５は、カウンタ５４の時間経過に従い重
み付けの係数Ｗ、を係数発生器５１で発生させ前記位相
誤差にディジタル位相変換器３の出力に乗算器５２．５
３で重み付けする回路である。カウンタ４１．５４．８
２は本装置の動作開始時点から毎時側カウントアツプし
ている。これらのカウンタの値は等しいため共用する事
も可能である。The sine wave generator 4 has a read-only memory (ROM) 44 which inputs the phase and outputs a sine wave value corresponding to the phase.
, an adder 43, a multiplier 42, a counter 4 that generates time.
1, and outputs a sample value of a sine wave using a phase estimated value and a frequency estimated value, which will be described later, as addresses. The weighting circuit 5 generates a weighting coefficient W in a coefficient generator 51 according to the elapse of time of the counter 54, and multiplies the phase error by the output of the digital phase converter 3 in a multiplier 52.5.
This is a circuit that weights by 3. counter 41.54.8
2 has been counted up every hour since the start of operation of this device. Since the values of these counters are equal, they can also be shared.
係数発生器８は（３）式のＧ、７１ｙｋｅ計算し各々の
係数を発生ずる回路であり、カウンタ８２によって得ら
れる時刻と各時刻得られる重み付は係数とから逆行列計
算器８１によって逆行列を計算し、初期位相推定と周波
数推定の為のそれぞれ第１及び第２の係数を発生する。The coefficient generator 8 is a circuit that calculates G and 71yke in equation (3) and generates each coefficient, and the time obtained by the counter 82 and the weighting obtained at each time are inverted by the inverse matrix calculator 81 from the coefficients. and generate first and second coefficients for initial phase estimation and frequency estimation, respectively.
係数発生器８は毎時側逆行列の計算を行なうのでマイク
ロプロセッサ等により実現される。Since the coefficient generator 8 calculates the inverse matrix on an hourly side, it is realized by a microprocessor or the like.
初期位相推定器６は、重み付けされた位相誤差と第１の
係数を乗算器６２にて掛は合わせその値を初期位相推定
値を保持するレジスタ６１の内容と加算器６３に於て加
算し、初期位相推定値の更新値として再びレジスタに格
納する。The initial phase estimator 6 multiplies the weighted phase error and the first coefficient in a multiplier 62, adds the resulting value to the contents of the register 61 holding the initial phase estimate in an adder 63, It is stored in the register again as an updated value of the initial phase estimate.
周波数推定器７は、重み付けされた位相誤差と第２の係
数を乗算器７２にて掛は合わせ、その値を周波数推定値
を保持するレジスタ７１の内容と加算器７３に於て加算
し、周波数推定値の更新値として再びレジスタに格納す
る。更新された周波数推定値は正弦発生器４に於てカウ
ンタ４１の内容と乗算器４２で乗算され、更に初期位相
推定値と加算器４３で加算され、時刻ｋに於ける最適位
相推定値として読みだし専用メモリ４４に入力され正弦
波の値が出力される。尚、この読みだし専用メモリのア
ドレスの最大値を２Ｈに対応させておくことにより位相
推定値はモジュロ２ｎで行なわれる。以上により、入力
される雑音の重畳した正弦波から周波数と位相を逐次的
に最小分散推定をすることができる。推定値はそれぞれ
レジスタ６１．７１の内容として与えられる。The frequency estimator 7 multiplies the weighted phase error and the second coefficient in a multiplier 72, adds the resulting value to the contents of a register 71 that holds the frequency estimation value in an adder 73, and calculates the frequency. Store it in the register again as an updated estimated value. The updated frequency estimate is multiplied by the contents of the counter 41 in the sine generator 4 in a multiplier 42, and further added to the initial phase estimate in an adder 43, and read as the optimal phase estimate at time k. The signal is input to a dedicated memory 44, and the value of the sine wave is output. Incidentally, by making the maximum value of the address of this read-only memory correspond to 2H, the phase estimation value is performed modulo 2n. As described above, it is possible to successively estimate the minimum variance of the frequency and phase from the input sine wave on which noise is superimposed. The estimated values are given as the contents of registers 61, 71, respectively.
尚、プログラマブルな信号処理プロセッサで上記と等価
な動作を容易に実現することができることは明らかであ
る。It is clear that operations equivalent to the above can be easily realized using a programmable signal processor.
（発明の効果）
本発明によれば、従来技術よりも特性良くしかも正確に
周波数・位相を推定できるという効果がある。(Effects of the Invention) According to the present invention, there is an effect that the frequency and phase can be estimated more accurately and with better characteristics than the conventional technology.
第１図は本発明の実施例を示すブロック図である。図中
、
１１．・サンプルホールド、２・・・Ａ／Ｄ変換器、３
・・・位相検波器、４・・・正弦波発生器、５・・９重
み付は回路、６・・・初期位相推定器、７・・・周波数
推定器、８・・・係数発生器である。FIG. 1 is a block diagram showing an embodiment of the present invention. In the figure, 11.・Sample hold, 2...A/D converter, 3
...Phase detector, 4...Sine wave generator, 5...9 Weighting circuit, 6...Initial phase estimator, 7...Frequency estimator, 8...Coefficient generator be.
Claims (1)
正弦波の初期位相と周波数を推定する装置において、入
力正弦波の初期位相の推定値と入力正弦波の周波数の推
定値から次時刻における正弦波の値を発生する手段と、
該正弦波と入力信号との位相誤差を検出する手段と、検
出した位相誤差に時間による関数で重み付けをする手段
と、前記重み付けを考慮し前記２つの推定値を導出する
ための第一及び第二の時変係数を発生する係数発生手段
と、前記重み付けされた位相誤差に第一の時変係数を乗
じた値により前記初期位相の推定値を逐次的に更新する
初期位相推定手段と、前記重み付けされた位相誤差に第
二の時変係数を乗じた値により前記周波数の推定値を逐
次的に更新する周波数推定手段とを有することを特徴と
する周波数・位相推定装置。In a device that receives a sine wave or a sine wave with superimposed noise as input and estimates the initial phase and frequency of the input sine wave, the sine wave at the next time is calculated from the estimated initial phase of the input sine wave and the estimated frequency of the input sine wave. means for generating wave values;
means for detecting a phase error between the sine wave and the input signal; means for weighting the detected phase error by a function of time; and first and second means for deriving the two estimated values in consideration of the weighting. coefficient generating means for generating a second time-varying coefficient; initial phase estimating means for sequentially updating the estimated value of the initial phase by a value obtained by multiplying the weighted phase error by a first time-varying coefficient; A frequency/phase estimating device comprising: frequency estimating means for sequentially updating the estimated value of the frequency by a value obtained by multiplying the weighted phase error by a second time-varying coefficient.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63250554A JP2527011B2 (en) | 1988-10-03 | 1988-10-03 | Frequency / phase estimation device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63250554A JP2527011B2 (en) | 1988-10-03 | 1988-10-03 | Frequency / phase estimation device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH0296664A true JPH0296664A (en) | 1990-04-09 |
| JP2527011B2 JP2527011B2 (en) | 1996-08-21 |
Family
ID=17209639
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP63250554A Expired - Lifetime JP2527011B2 (en) | 1988-10-03 | 1988-10-03 | Frequency / phase estimation device |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2527011B2 (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008136443A1 (en) * | 2007-04-26 | 2008-11-13 | The University Of Tokyo | Sine wave parameter estimation method |
| CN113219248A (en) * | 2021-05-07 | 2021-08-06 | 南京大学 | Signal component estimation method based on time domain waveform comparison |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS61154317A (en) * | 1984-12-27 | 1986-07-14 | Nec Corp | Frequency and phase estimating device |
-
1988
- 1988-10-03 JP JP63250554A patent/JP2527011B2/en not_active Expired - Lifetime
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS61154317A (en) * | 1984-12-27 | 1986-07-14 | Nec Corp | Frequency and phase estimating device |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008136443A1 (en) * | 2007-04-26 | 2008-11-13 | The University Of Tokyo | Sine wave parameter estimation method |
| JP5553334B2 (en) * | 2007-04-26 | 2014-07-16 | 国立大学法人 東京大学 | Sinusoidal parameter estimation method |
| CN113219248A (en) * | 2021-05-07 | 2021-08-06 | 南京大学 | Signal component estimation method based on time domain waveform comparison |
| CN113219248B (en) * | 2021-05-07 | 2022-09-20 | 南京大学 | Signal component estimation method based on time domain waveform comparison |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2527011B2 (en) | 1996-08-21 |
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