United States Patent [19]
`Eatwell
`
`llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll!
`5,553,153
`Sep. 3, 1996
`
`USO05553153A
`[11] Patent Number:
`[45] Date of Patent:
`
`[54] NIETHOD AND SYSTEM FOR ON-LINE
`SYSTEM IDENTIFICATION
`
`[75] Inventor: Graham P. Eatwell, Cambridge, United
`Kingdom
`
`[73] Assignee: Noise Cancellation Technologies, Inc.,
`Linthicum, Md.
`
`[21] Appl. No.: 15,195
`[22] Filed:
`Feb. 10, 1993
`
`IEEE Transactions of Information Theory. “Polyphase
`Codes with Good Periodic Correlation Properties.” David
`Chu. Jul. 1972 pp. 531-535.
`
`Adaptive Signal Processing Bernard Widrow and Samuel
`Stearns. Prentice Hall, Inc. 1985, Table of Contents.
`
`Active Control of Sound. Nelson and Elliot. Academic Press.
`1992, Table of Contents.
`
`[51] Int. Cl.6 .................................................... .. A61F 11/06
`[52] U.S. Cl.
`381/71
`[58] Field of Search ........................................ .. 381/71, 94
`
`Primary Examiner—Curtis Kuntz
`Assistant Eyxaminer—Ping W. Lee
`
`[56]
`
`References Cited
`
`[57]
`
`ABSTRACT
`
`U.S. PATENT DOCUMENTS
`
`4,677,676
`4,953,217
`5,105,377
`5,278,913
`
`6/1987 Eriksson.
`8/1990 Twiney et a1. .......................... .. 381/71
`4/1992 Ziegler, Jr. ..... ..
`.. 381/71
`l/1994 Delfosse et a1. ........................ .. 381/71
`
`OTHER PUBLICATIONS
`
`This invention relates to an improved method of on-line
`system identi?cation for use with active control systems
`which requires less computation and reduces the problem of
`coe?icient jitter in the ?lters of the active control system by
`using a ?xed test signal which is designed to have a
`particular power spectrum.
`
`IBM J. Research and Development “Periodic Sequences
`with Optimal Properties for Channel Estimation and Fast
`Start Up Equalization” A. Milewski. pp. 426-430. Vol. 27
`No. 5 Sep. 1983.
`
`18 Claims, 4 Drawing Sheets
`
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`Sep. 3, 1996
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`U.S. Patent
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`Sep.3, 1996
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`

`
`1
`METHOD AND SYSTEM FOR ON-LINE
`SYSTEM IDENTIFICATION
`
`5,553,153
`
`BACKGROUND
`
`This invention relates to a technique for on-line system
`identi?cation primarily for use with active control systems.
`A review of systems for active control of sound is given in
`“Active Control of Sound” by P. A. Nelson and S. J. Elliott,
`Academic Press, London. Most of the control systems used
`for active control are adaptive systems, wherein the control
`ler characteristics or output is adjusted in response to
`measurements of the residual disturbance. If these adjust
`ments are to improve the performance of the system, then
`knowledge is required of how the system will respond to any
`changes. This invention relates to methods for obtaining that
`knowledge.
`Usually the system is characterized by the system impulse
`response, which is the time response at a particular control
`ler input caused by an impulse at a particular output. The
`response therefore includes the response of the input and
`output processes of the system, such as actuator response,
`sensor response, smoothing and anti-aliasing ?lter responses
`etc. For multichannel systems, which have more than one
`input and/or output, a matrix of impulse responses is
`required, one for each input/output pair. For a sampled data
`representation the impulse response between the j-th output
`and the i-th input at the n-th sample will be denoted by ail-(n).
`Equivalently, the system can be characterized by a matrix
`of transfer functions which correspond to the Fourier trans
`forms of the impulse responses. These are de?ned, for the
`k-th frequency, by
`
`(1)
`
`___
`N-l ,_
`119(k): Z a'1(n)-exp(2iknrt/N),
`n=0
`where the k-th frequency is (k/NT) Hz and T is the sampling
`period in seconds.
`The most common technique for system identi?cation is
`to send a test signal from the controller output and measure
`the response at the controller input. In order to discriminate
`against other noise in the system, a random test signal is
`normally used, and this is correlated with the response.
`Other noises which are not correlated with the test signal are
`rejected.
`In “Adaptive Signal Processing” by B. Widrow and S. D.
`Stearns, Prentice Hall, (1985), several adaptive schemes for
`system identi?cation (or plant modeling) are described.
`Provided that the test signal is uncorrelated with other
`system noise, the system identi?cation can continue while
`an active control system is in operation. In U.S. Pat. No.
`4,677,676 by L. J. Eriksson this is described for a single
`channel active control system in a duct. This system is
`typical of the prior art and is summarized in FIGS. 1 and 2.
`FIG. 1 shows the system identi?cation system and control
`system in a duct or pipe. FIG. 2 shows the equivalent block
`diagram. These correspond to FIGS. 19 and 20 in the
`original document.
`It is not recognized in Eriksson that the residual signal (44
`in the Figures) used to adapt the control ?lters is contami
`nated by the test signal. This will cause the system to try to
`adapt to cancel the test signal-resulting in a random
`variation or ‘jitter’ in the ?lter coe?icients. This results in a
`reduced performance.
`A further aspect of Eriksson and similar approaches is that
`on-line system identi?cation is an adaptive ?lter and at each
`sampling interval every coe?icient of the impulse response
`
`10
`
`15
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`65
`
`2
`is updated. This is a computationally expensive operation
`and, since the signal processor has ?xed processing power,
`this will slow down the maximum sampling rate of the
`controller and reduce its performance. Another aspect of
`Eriksson and similar approaches is that a random test signal
`(or noise source) is used.
`
`SUMMARY OF THE INVENTION
`
`This invention relates to an improved method and system
`of on-line system identi?cation which requires less compu
`tation and removes the problem of coei?cient jitter.
`In contrast to the prior art, which describes the use of a
`random, uncorrelated test signal, the system of this invention
`uses a ?xed test signal. The use of a ?xed test signal reduces
`the computational requirement of the system identi?cation.
`The model of the system response can be updated using an
`accumulated response signal or an accumulated error signal.
`In another aspect of the invention, a means is provided for
`estimating the effect of the test signal and subtracting this
`from the residual (error) signal used to adapt the control
`system. This greatly reduces the problem of coe?icient or
`weight jitter.
`In another aspect of the invention, the system identi?ca
`tion is performed at a rate which is different to the rate of the
`control ?lters.
`Accordingly, it is an object of this invention to provide an
`improved method of on-line system identi?cation which
`requires less computation and removes the problem of
`coe?icient jitter.
`Another object of this invention is to use a ?xed test signal
`to reduce the number of computations required in a system
`identi?cation.
`A still further object of this invention is to estimate the test
`signal effect and subtract that from the error signal in
`adapting the control system.
`These and other objects of this invention will become
`apparent when reference is had to the accompanying draw
`ings in which
`FIG. 1 is a diagrammatic view of the circuitry of US. Pat.
`No. 4,677,676,
`FIG. 2 is a diagrammatic view of the circuitry of U.S. Pat.
`No. 4,677,676,
`FIG. 3 is a diagrammatic view of the control system of
`this invention incorporating on-line system identi?cation,
`FIG. 4 is a diagrammatic view of the system identi?cation
`circuit using accumulated response, and
`FIG. 5 is a diagrammatic view of the circuit using
`accumulated error.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`The system identi?cation system of this invention is
`primarily for use with sampled data systems (either analog
`or digital).
`The invention will be described with reference to a single
`channel system, although it can be easily extended to
`multichannel systems.
`By way of explanation, we will ?rst consider the case
`where the system can be modeled by a Finite Impulse
`Response (FIR) ?lter with coe?icients a(n).
`
`SAMSUNG 1027-0006
`
`

`
`3
`The response at sample n to a test signal produced from
`the sequence of controller outputs, y(n), is
`
`M-l
`
`'
`
`(2)
`
`Where M is the number of coe?icients in the ?lter and d(n)
`is the component of the response not due to the test signal,
`y(n). (d(n) also contains any unmodeled response.
`The Least Squares estimate of the system impulse
`response can be obtained by correlating the response, u, with
`the output signal, this gives the cross-correlation
`
`where the angled brackets <.> denote the expected value.
`The last term can be ignored provided that the test signal is
`uncorrelated with the noise d(n). Equation (3) is a matrix
`equation for the coe?‘icients a(m) which can be solved
`directly or iteratively. The LMS iterative solution is given by
`
`20
`
`5,553,153
`
`4
`arbitrary. They can be chosen to minimize the peak value of
`the signal, for example. Two articles describing this are
`“Polyphase Codes with Good Periodic Correlation Proper
`ties", by D. C. Chu, IEEE Transactions on Information
`Theory, July 1972, pp 531-532, and “Periodic Sequences
`with Optimal Properties for Channel Estimation and Fast
`Start-Up Equalization”, by A. Milewski, IBM Journal of
`Research and Development, Vol. 5, No. 5, Sept. 1983, pp
`426—43l. Alternatively, the coe?icients ej can be chosen to
`shape the spectrum of the test signal so as to make it less
`noticeable or to give a more uniform signal to noise ratio.
`According to one aspect of this invention an impulsive
`test signal is used. This test signal is zero unless n is a
`multiple of M, in which case y(n)=+/—L. Here L is the level
`of the test signal and the sign of the signal is varied in a
`random or prescribed manner. This signal is obtained by
`setting all of the phase angles in equation (9) to zero.
`In equation (2) only one value of y(n~m) is non-zero, at
`m=k say, so the input is
`
`where a,-(k) is the estimate of the k-th term in the impulse
`response at the i-th iteration and where r(n) is the estimated
`response to the test signal given by
`
`25
`
`As indicated by the “+” symbol shown in FIG. 5, u(n) is
`always added to r(n) signal to produce e(n). The estimate of
`a(k) can then be adjusted using
`
`M-1
`r(n) — M220 (a(m) - y(n — m),
`
`(5)
`
`and u is a positive convergence parameter.
`In the stochastic or noisy LMS adaption algorithm the
`correlations are estimated over a single sample, and the
`angled brackets in equation (4) can be removed to give
`
`or, if the test signal is a random sequence with an autocor
`relation which is a delta function,
`
`35
`
`where e(n) is the difference between the actual response and
`the expected response
`
`The algorithm in (6) is described in the “Adaptive Signal
`Processing” article, for example, and a similar approach is
`used in Eriksson’s patent. At each step (i), the response r(n)
`must be calculated, which requires M multiplications and
`additions, and all M coe?icients are adjusted which requires
`a further M multiplications and additions.
`According to one aspect of the invention, a test signal is
`used which satis?es
`
`45
`
`50
`
`>
`
`(8)
`
`L2 if m = 0
`Mil ( ) (
`n n — m :
`n=0 y y
`0
`otherwise
`This condition relates to the circular autocorrelation of the
`test signal.
`A test signal of this form is called ‘block white’ since a
`?nite Fourier transform of the signal over M points will
`result in a ?at spectrum. It is said to be ‘delta-correlated’
`since its autocorrelation over a block of M samples, as
`expressed by (8), is zero except at one point. One way of
`constructing such a sequence is to use
`
`where eJ=1/2 if j=0 or j=M/2 and 61:1 otherwise. The phase
`angles ¢j are zero for j=0 and j=Ml2 otherwise they are
`
`55
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`60
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`65
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`Only one coe?icient of the impulse response is being
`updated at each sample time. This requires 2 multiplications
`and additions, compared to the 2><M multiplications and
`additions of previous methods.
`.
`The update can be performed in every sample interval if
`required. Alternatively, the update can be performed at a
`slower rate. The update can be done as a background task,
`where the update rate is determined by the processing power
`of the system identi?cation circuit shown in FIG. 4.
`One embodiment of the system described by equations
`(1 2) and (13) and incorporated into an active control system,
`is shown in FIG. 3. In contrast to the prior art, the signal e(n)
`is used to adapt the control system rather then the signal
`u(n). This reduces the problem of weight jitter.
`Alternatively, the system can be estimated using the
`general block white signal. This same signal is sent out
`repeatedly, except that the sign is changed in some random
`or predetermined manner in order to decorrelate the test
`signal with any other signals. Additionally, or alternatively,
`the test signal can be delayed by varying amounts to aid
`decorrelation. Preferably, this delay is a whole number of
`sample periods. It can be achieved either by varying the
`number of samples (the gap) between each block of mea~
`surements, or by starting the test signal from a dilferent point
`within the block. Account is taken of this delay when the
`response to the signal is accumulated.
`If the sign of the test signal is changed, then two blocks
`of the signal are sent out with the same sign, and measure
`
`SAMSUNG 1027-0007
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`

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`5,553,153
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`5
`ments are only made in the second block. This ensures that
`real convolutions can be replaced by circular convolutions
`and so use can be made of the property in equation (8).
`Limiting the length of the block to exactly M points, so
`that it has the same length as the model ?lter, means that a
`maximum amount of time is spent measuring (which makes
`adaption to changes quicker) and a minimum of storage is
`required.
`The response at the controller input is accumulated, with
`the appropriate sign and/or delay, and then used to adapt the
`model of the system. One embodiment of this approach is
`shown in FIG. 4 and will now be described in more detail.
`' Variable delay is not used in this example.
`We de?ne a number sj which is 0 if the sign has changed
`from one block to the next and otherwise is equal to +/—l
`depending on the sign of the j-th block. We denote the
`accumulated response at the n-th point in the block by U(n).
`We denote by uj(n) the value of the input at the n-th point in
`the j-th block. U(n) can be accumulated over N consecutive
`blocks of M samples. Using equation (2) this gives
`
`from which
`
`The coe?icients a(n) can be found from an inverse transform
`of (19), or the Fourier coe?icients can be used directly.
`The amplitudes ej can be chosen so that the power
`spectrum of the response to the test signal and the power
`spectrum of the residual noise have a ?xed ratio. For
`example, with L=1,
`
`[E,,|2=7t.ti(k)|2 /|E(k)|2+min(k)
`
`(20)
`
`where 7L is a positive factor and min(k) is a low-level
`spectrum which can be included to ensure that the test signal
`is not zero in any frequency band and that any quantization
`errors in the digital system do not have too large an effect.
`The estimates of the modulus of the residual signal r(k)
`can be obtained recursively to cope with changing signal
`statistics.
`Alternatively, the coef?cients ej can be chosen so that the
`response to the test signal is white, but the power level, L,
`can be chosen to be proportional to the power in the residual
`signal. Alternatively, the coefficients can be chosen to give
`any other desired frequency spectrum.
`The averaging process used in the above techniques
`allows for small test signals to be used, which reduces the
`effects of weight jitter in the cancellation ?lters.
`In an alternative approach, the e?°ect of the test signal is
`subtracted from the response signal.
`This new signal is used for the adaption of the cancella
`tion ?lters and is accumulated for use in the adaption of the
`system model. One embodiment of this approach is shown
`in FIG. 5.
`For the adaption of the model, the diiference between the
`expected response and the actual response is accumulated.
`This gives an accumulated error de?ned by
`
`(15)
`
`is the ‘corrected’ error signal at the n-th point in the j-th
`block and is used for the adaption. The accumulated error
`signal is related to the difference between the actual impulse
`response and the current estimate, since
`
`where a,-(m) is the current estimate of the impulse response,
`which is used to calculate r(m).
`Correlating the accumulated error E(n) with the test signal
`gives
`
`20
`
`25
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`35
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`45
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`50
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`55
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`U( )
`
`n =
`
`Nil
`( )
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`1.20 J
`J
`
`(14)
`
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`= "50 m5‘) “(#1) win-('1 — m) + "50 s,- - dJ-(n),
`
`_ NMil
`_
`mzo a(m) - y(n — m),
`
`where
`
`N-l
`N‘: )3 iii!
`1:0
`
`is the number of non-zero accumulations made and y(n) is
`the ?xed test sequence.
`There are two ways in WhlCl’l the accumulated response
`U(n) can be used to calculate the coe?icients a(m). The ?rst
`way is to correlate U with the test signal. This gives
`
`.
`
`.
`
`where
`
`The correlation and update can be done in the processor as
`a background task or by a separate processor.
`The level, L, of the test signal can be chosen with
`reference to the power in the residual signal, or the power in
`the cancellation signal and/or the response of the system.
`Additionally, or alternatively, it can be chosen with refer
`ence to quantization errors in the digital system.
`The other way of calculating a(k) is via a Discrete Fourier
`transform of the accumulated values U(n) as shown in FIG.
`4. This approach can also be used even when the coe?icients
`of the test sequence, ej in equation (9), are not chosen to give
`a ?at spectrum.
`The Fourier transform of (14) gives
`
`SAMSUNG 1027-0008
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`

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`7
`and the update equation for the impulse response is
`
`5,553,153
`
`8
`characterized in that the compensation signals substan
`tially cancel the components of the input signal due to
`the test signals.
`2. An active noise or vibration control system as in claim
`1 and including means for delaying the residual signals by
`the same amount as the test signals and inverting the residual
`signals whenever the test signals the inverted so as to
`produce delayed or inverted residual signals.
`3. An active noise or vibration control system as in claim
`2, said control system including accumulation means for
`accumulating said delayed or inverted residual signals so as
`to produce accumulated residual signals.
`4. An active noise or vibration control system as in claim
`3 wherein the compensation ?lter means is adapted in
`response to said accumulated residual signals and said ?xed
`test signal.
`5. An active noise or vibration control system as in claim
`4 wherein the compensation ?lter means is adapted in
`response to the product of said accumulated residual signals
`and said ?xed test signal.
`6. An active noise or vibration control system as in claim
`1 and including means for delaying the input signals by the
`same amount as the test signals and inverting the input
`signals whenever the test signals are inverted so as to
`produce delayed or inverted input signals.
`7. An active noise or vibration control system as in claim
`6, said control system including accumulation means for
`accumulating said delayed or inverted input signal so as to
`produce accumulated input signal.
`8. An active noise or vibration control system as in claim
`7 wherein predicted responses to said ?xed test signal are
`produced by passing said test signals through said compen~
`sation ?lter means and wherein the compensation ?lter
`means is adapted in response to said accumulated input
`signals and the predicted responses.
`9. An active noise or vibration control system as in claim
`8 wherein the compensation ?lter means is adapted in
`response to a Fourier Transform of said accumulated input
`signals and a Fourier transform of said test signals.
`10. An active noise or vibration control system as in claim
`8 wherein the compensation ?lter means is adapted in
`response to said accumulated input signals, said ?xed test
`signal and said predicted responses.
`11. An active noise or vibration control system as in claim
`1 wherein said ?xed test signal, y(n) at time sample n,
`satis?es
`
`M—1
`Z
`
`_ =
`
`n=0 y(n))’(n m) { 0
`
`L2 if m = 0
`
`otherwise
`
`wherein M is the length of said ?xed test signal and L is a
`constant.
`12. An active noise or vibration control system as in claim
`1 wherein said ?xed test signal, y(n) satis?es
`
`where M is the length of said ?xed test signal and L is a
`constant.
`13. An active noise or vibration control system as in claim
`1 wherein one compensation ?lter means is used to couple
`each actuator output with each sensor input.
`14. An active noise or vibration control system as in claim
`1 wherein said compensation ?lter means is a Finite Impulse
`Response ?lter.
`
`where 0<p<2 and u is chosen with reference to the ratio of
`the test signal level to the noise level.
`The corresponding frequency domain update is
`
`ai+1(k)=Ei(k)+(P/N')E (Io/i000
`
`(26)
`
`This update is performed only once every N blocks of M
`points, and so for N>1 it represents a considerable saving
`over the previous methods. The update can be performed as
`a background task.
`The signal e(n) is used to update the coef?cients of the
`control ?lter. This is in contrast to previous methods which
`use the signal u(n) and so try to adapt to cancel the test
`signal.
`Some physical systems are more efficiently modeled as
`recursive ?lters rather than FIR ?lters. The response at the
`input is then modeled by
`
`20
`
`where b(p) are the coefficients of the feedback ?lter and r(n)
`is given by equation (5). The total number of computations
`involved in calculating the estimated response to the test
`signal can often be reduced by using this type of ?lter.
`The techniques for adapting this type of ?lter are well
`known (see “Adaptive Signal Processing”, Widrow and
`Stearns, for example). These techniques can easily be modi
`?ed to use test signals of the type described above.
`Having described the invention it will be obvious to those
`of ordinary skill in the art that many modi?cations‘ and
`' changes can be made without departing from the scope of
`the appended claims in which
`I claim:
`1. An active noise or vibration control system with on-line
`system identi?cation for identifying the response of a physi
`cal system, said control system comprising
`control means producing control signals, said control
`means including control adaption means responsive to
`residual signals,
`test signal generating means for generating test signals,
`wherein the test signal generating means includes
`means for delaying or inverting a ?xed test signal of
`length determined by the response time of the physical
`system, including actuator means and sensing means,
`said actuation means responsive to a combination of the
`control signals and the test signals and producing a
`canceling noise or vibration, one component of which
`counters or partially counters an unwanted ?rst noise or
`vibration,
`said sensing means responsive to the combination of said
`canceling noise or vibration and said ?rst noise or
`vibration and producing input signals,
`compensation ?lter means responsive to said test signals
`and producing compensation signals, said compensa
`tion ?lter means including a ?lter adaption means
`responsive to said test signals and said residual signals
`and con?gured to minimize the correlation between the
`residual signals and the test signals,
`signal subtraction means for subtracting said compensa
`tion signals from said input signals to produce said
`residual signals,
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`SAMSUNG 1027-0009
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`5,553,153
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`15. An active noise or vibration control system as in claim
`1 wherein said compensation ?lter means is an In?nite
`Impulse Response or recursive ?lter.
`16. An active noise or Vibration control system as in claim
`1 wherein said compensation ?lter means is a Lattice ?lter.
`17. An active noise or vibration control system as in claim
`1 wherein said compensation ?lter means is adapted less
`frequently than said control means.
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`5
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`10
`18. An active noise or vibration control system as in claim
`1 wherein the control adaption means and the compensation
`?lter adaption means operate at a different rate to the control
`means and the adaption rate of said compensation ?lter
`means is determined by the processing power of said active
`noise control system.
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`SAMSUNG 1027-0010