EP2304510A1 - Estimation of the impulse response of a system on the basis of binary observations - Google Patents

Abstract

The invention relates to a method of identifying an electronic or electromechanical system comprising the steps consisting in applying at least one noise signal (u) as input to said system, applying an output signal of said system to a one-bit analogue digital converter, acquiring a signal at the output of said converter, carrying out an estimation of the output of said system with the aid of means for performing an estimation (h) of the impulse response of said system, the estimation (h) of said impulse response comprising the iterative calculation of a plurality of nh elements (Jo, Ji, Jnh-1 ) of a given criterion (J) comprising respectively at least one term of correlation between said signal at the output of said converter and said noise signal.

Description

 ESTIMATING THE IMPULSE RESPONSE OF A SYSTEM FROM BINARY OBSERVATIONS

DESCRIPTION

TECHNICAL AREA

The invention relates to the identification of systems, in particular electronic devices for example such as filters, or electromechanical devices, for example in the form of MEMS.

The invention relates to a device and a method implementing an estimate of the output of a system by estimating its discrete time impulse response.

STATE OF THE PRIOR ART

In conventional system identification methods, quantization operations can be performed. These operations are usually modeled by adding white noise b to a signal y that is quantized: yquantifie = J + ^

This noise is lower as the number of bits on which the quantization is performed is high. Thus, to identify a system using a conventional method of identification, it is preferable to have a high resolution analog-to-digital converter (ADC). In this case, with a small number of measurements it is possible to dispense with the quantization noise.

In the case where a low precision CAN is used, a large number of measurement points may be necessary.

A very common classical method of identification is the least squares method. This method consists in producing a parametric model θ _[deal of the transfer function of the system and in minimizing the squared difference between measured values and estimated values at the output of the model H _θ , the input e of the system being otherwise known : h _dea i = argmm H ₁ Xe) - y quan Mtifi, e \\

In the case where the quantization noise is sufficiently weak, it is possible to assimilate the quantified signal y _quanafie to the real signal y. In this case, if the model H _θ is linear, the parametric model θ _ιdeal can be expressed analytically. The input e of the system which one wishes to identify is generally a white noise.

The least squares method has the disadvantage, in particular, that it requires the integration of a high resolution CAN converter.

In another method, called "KLV" (KLV for "Kessler Landau Voda") (FIG. 1), (block referenced 2), an identification of the transfer function H of a system placed in a feedback loop 1 is carried out. linear, with a comparator 3 with adjustable hysteresis. This comparator makes it possible to bring the system 2 into oscillation. One can deduce information on the system by the pace of these oscillations. A 1-bit ADC 4 is provided at the output of the system. The amplitude and frequency of the oscillations arising in the system can then be related to the value of the frequency response of the system using analytical relations. Each hysteresis value corresponds to one point of the frequency response curve.

Such a method has several disadvantages. First, the validity of the analytical relations used is based on an approximation known as the first harmonic of the comparator. Moreover, such a method requires a precise measurement of the amplitude and the phase of the oscillations, the amplitude measurement requiring a CAN of high resolution.

Another method called "OBT" (OBT for "Oscillation-Based Test"), similar to the KLV method, consists in inserting the system that one wishes to identify and having a transfer function H, in a nonlinear loop comprising a Comparator 6. The return gain (block referenced 7) is adjusted to observe oscillations preferably having a most sinusoidal shape possible. In this way, we can deduce using the hypothesis of the first harmonic, the parameters of the transfer function H using analytical relations, as for the KLV method.

This method also has the disadvantage that it requires an accurate measurement of the amplitude of oscillations at the input of the comparator, that is to say a CAN 5 high resolution (Figure 2).

An "MCL" (MCL for "Limit Cycle Measurement") identification method allows for precise determination of the natural frequency and damping of a second-order system using two frequency measurements. (Figures 3A and 3B).

A first measurement is made by placing the system to identify the transfer function H in a loop comprising a comparator 9 and a differentiator 8 (FIG. 3A).

A second measurement is performed by replacing in said loop the diverter 8 by an integrator 10 (Figure 3B).

It is thus possible to obtain a relationship between the frequency of the oscillations measured at the output of the comparator 6 and the value of the natural frequency and the damping of the system to be identified.

This method is based on two digital measurements, the frequency measurement being performed by counting the number of switches of the comparator for a given duration. This method has several disadvantages.

It is applicable only for integrating filters or analog or sampled differentiators. On the other hand, in the case of an implementation using a digital circuit, it is necessary to have a good resolution Digital Analog Converter (ADC) to inject the output of the system into the system. 'integrator. In the so-called "MCLC" method (MLCL for "Complex Limit Cycles Measurement"), the system to be identified 12 is placed in a nonlinear feedback loop comprising a sampled comparator 13 having a sampling period Ts, a digital filter programmable digital 14, and a DAC 15 (Figure 4).

Depending on the value chosen for the coefficients of the digital filter, binary oscillations or "limit cycles" may be observed at the output of comparator 13. These limit cycles differ from those observed by implementing the KLV method or the MCL method in that they have a period that is multiple of the sampling period Ts. The switching times of the comparator 13 correspond to sampling times. Thus, the measurement of a limit cycle corresponding to a set of coefficients of the programmable filter 14 is completely digital.

This method has the particular disadvantage of having to generate long limit cycles to implement it.

The KLV and MCL methods make it possible to establish, at the cost of an approximation, a relation between measured quantities and parameters that one seeks to determine.

The KLV and OBT methods require a high resolution ADC, while the MCL method requires a good DAC. These methods give insufficient results when sampling frequency is important. The MCLC method has performances independent of the sampling frequency, at the cost of a heavier treatment than that carried out with the other methods. Moreover, with such a method, good accuracy requires generation of long limit cycles, which can be problematic.

The use of the aforementioned closed-loop identification methods is particularly problematic in the case where the system to be identified is an electromechanical device in the form of a MEMS. The risk is not to be able to perform the identification at the right operating point, since the excitation of a MEMS on one of its modes tends to amplify very rapidly non-linear phenomena. To overcome this, an amplitude control loop (AGC) can be added to the identification system, which may require the use of a high precision ADC.

The aforementioned identification methods have the disadvantage of requiring an output analog to digital conversion of significant resolution, which complicates their implementation and poses cost problems.

There is the problem of finding a new identification method which does not have the disadvantages mentioned above. SUMMARY OF THE INVENTION

The present invention firstly relates to a method of system identification comprising the steps of:

to apply at least one noise signal at the input of said system,

applying an output signal y _k of said system to an analog-digital converter, in particular a 1-bit analog-digital converter,

acquiring a signal s _k at the output of said converter,

performing an estimate y _k of the output of said system using means for making an estimate h of the impulse response of said system, the estimate h of said impulse response comprising:

the iterative calculation of a plurality of nh (with nh an integer) elements Jo,..., Ji,, J _n hi of a given criterion J each comprising: at least one correlation term between said output signal of said converter and said input signal.

The output signal s _k is a binary data signal.

The method according to the invention makes it possible to carry out an identification without having to use a CAN of high resolution.

The input signal may be a noise signal. The system is a device or set of devices that can be described by a transfer function.

The system may be an electronic device, for example a filter, or a sigma-delta converter, or a telecommunications transmission channel, or a DC / DC converter.

According to another possibility, the system may be an electromechanical device, in particular in the form of a MEMS.

The given criterion J is also called "cost function".

The estimation of the impulse response may furthermore comprise: the application to said calculated elements of said given criterion of a so-called "passing" function, said passage function being predetermined as a function of said signal applied at the input of said system, and such that: with h _± an impulse response element h of said system and A ₁ an element of said impulse response estimate h of said one of a plurality of nh impulse response elements.

The estimate of the impulse response may include applying to the calculated elements of the given criterion a predetermined passage function f as a function of the input noise signal of the system, so as to obtain a plurality of elements h 1. .., h _lr -, hnh-i of said response estimate h impulse, said elements of said estimate being such that:

(ko, ..., A ₁ , ..., (f (Jo), ..., f (Jχ),, f (Jnh-1)).

According to one possibility, the input signal is a Gaussian noise signal.

In this case, the passage function follows a given relationship determined according to this type of noise.

In a case where the input signal is a Gaussian noise signal, said passage function f can follow the relation: f (J) = σ 'sin (( ^π / 2) (2 JI)), with: σ' ² = σ _b ² + σ _h ² where σ _b represents the ambient noise of the system to be identified modeled as a white noise

Gaussian additive at the output of the system and <3 _h ² = Σhf is

1 = 0 the quadratic sum of the different elements of the impulse response.

Alternatively, the input signal may be a white noise signal.

In this case, the passage function follows a given relationship determined according to this type of noise.

In the case where the input signal is a binary white noise signal, said transition function f may follow the relation:

f (J)

The estimate h of the impulse response may comprise: the transmission of the input signal u of the system through a chain of blocks each forming a delay function of order 1 or each having z ^"1 as a transfer function in z,

the acquisition of values u _k , ..., ut _-1 , Uk-nh-i of the output noise signal respectively of said blocks, said elements Jo,..., Ji,, j _n hi of said criterion J being calculated using said values u _k , ... ut _-1 , u _k - _n hi of the output noise signal respectively of said blocks.

The signal u is binary in the case of a binary white noise and on several levels in the case of Gaussian noise.

The values u _k , ..., u _k -i, u _k _ _n hi of the noise signal u are taken at different times k, k-1, ..., k-i, k-nh-1.

The calculation of said plurality of nh elements Jo,..., Ji,..., J _n hi of said given criterion J can comprise: the application of the signal s _k at the output of said converter taken at a given instant k and of a noise signal u _k _i, with (0 <i <nh) at the input of said system, delayed i times with respect to this given instant, to means forming an exclusive OR logic gate.

The calculation of said plurality of nh elements Jo,..., Ji,, J _n hi of said given criterion J may comprise:

the addition of a term depending on the result jk (n + 1) of said application of said exclusive OR function and a term of the function of cost calculated at time k-1 preceding said given instant.

According to a possibility of implementing the method, the acquisition of the signal s _k at the output of said converter can be performed for a given number N of samples, the calculation of the given criterion J being dependent on at least one coefficient λ predetermined, with (λ) ~ N, with N a given number of samples.

The method may comprise a modification of the value of said coefficient λ during said estimation h of said impulse response.

Variation of the coefficient λ can make it possible to modulate the precision and the speed of the estimation.

The estimate ' ^k of the response further comprises: calculating a convolution between the estimated impulse response' and the input signal u of noise.

A comparison of the output signal sk, and the estimate ^s k of this output signal can be performed over a given period of time to determine whether the estimate made is correct.

The modification of said coefficient λ can be carried out according to the evaluation of a second criterion Jt whose calculation is similar to that of the cost function J and which compares s _k and ⁵ _k -

Thus, the modification of said coefficient λ can be carried out according to the evaluation of a second criterion Jt, the evaluation of said second criterion Jt (n + 1) at a given time n + 1 being performed by iterative calculation comprising at least one XOR exclusive OR logic operation term between said output signal s _{k of} said converter and an estimate s _k of this signal, and a term dependent on said second criterion Jt (n) calculated at an instant n preceding the given instant.

The modification of the coefficient λ can be carried out as a function of the evaluation of said second criterion Jt and of the result of the application of a second function ft predetermined to said second criterion Jt.

The second function ft can be an affine function, such that: ft (Jt) = λ = CC * Jt + β (with α> 0 and β> 0) The coefficients CC and β can be chosen for example so that:

• λ tends to N when Jt tends to 0

• λ tends to 2 ⁶ when Jt tends to 1

The accuracy of the identification depends very little on the sampling frequency and has good robustness to the measurement noise.

Given the given identification accuracy, the method according to the invention requires fewer measurement points than the identification methods according to the prior art.

The method according to the invention does not rely on an approximation, whether it is a "white noise" or "first harmonic" type approximation, but on the minimization of a criterion which, without approximation, depends on the operation of 1-bit quantization performed by the analog-to-digital converter.

In the case where the system to be identified is a MEMS or an integrated electronic circuit, the method of identification has advantages over the methods according to the prior art: that it can be implemented using a Can 1 bit sampled, which saves space and cost compared to methods requiring the use of high resolution ADC, can operate in open loop and does not disrupt the operating point of the system, that the Measurements are made near the system to be identified, a one-bit digital analog converter requiring few resources and area to be implemented, which minimizes measurement noise.

The invention also relates to an electronic or electromechanical system identification device, designed to implement an identification method as defined above.

The invention also relates to an electronic or electromechanical system identification device comprising:

means for generating a signal u of noise, intended to generate a noise signal at the input of said system,

- an analog-digital converter one bit, to which a signal y _k of output of the system is to be applied, means for producing an estimate y _k of the output of the system, using an estimate h of the impulse response of said system comprising:

first calculation means: to perform an iterative calculation of a plurality of nh

(with nh an integer) elements Jo, ..., Ji,, J _n hi of a given criterion J comprising at least one correlation term between said output signal of said converter and said noise signal.

A digital to analog converter may be provided to generate an analog excitation signal of the system.

The means for carrying out said estimate y _k of the output of the system may furthermore comprise: second calculation means, intended to apply to the elements Jo,..., Ji,, J _n hi calculated of said given criterion J, a function f predetermined passage according to the noise signal u _k transmitted at the input of said system, and such that: with hi an impulse response element h of said system and hi an element of said impulse response estimate h of said system.

The second calculation means may comprise one LUT or several LUTs.

The function f of passage can be applied using a LUT, connected as input, to multiplexer means, and output, to demultiplexer means.

According to one possible implementation, the noise signal uk may be a white noise signal.

The means for generating said noise signal uk may include a LFSR random sequence generator.

In the case where the input signal uk of the system is a white noise signal, said function f of passage can follow the relation:

f (J)

The impulse response estimation means may comprise: a chain of blocks respectively forming a first order delay function or having z ^"1 as a z transfer function, said chain being intended to receive said input signal u _k , and to emit values u _k , ... ut _-1 , u _k - _n hi of the delayed noise signal respectively output of said blocks.

The first calculation means may comprise means forming an exclusive OR logic gate, for performing an exclusive OR logic operation between said output signal sk of said comparator taken at a time k and said noise signal (uk-i, with 0 <i <nh) delayed by i with respect to said given instant.

The first calculation means may comprise adding means for adding the result of said logical operation to a term dependent on an element of said given criterion calculated previously. The acquisition of the signal s _k at the output of said converter can be carried out for a given number N of samples, the calculation of the criterion given by the first calculation means being dependent on at least one predetermined λ coefficient, 1+ λ being equal to said given number N.

The device may further comprise: means for modifying the coefficient value λ during said estimation of said impulse response.

The first calculation means may comprise means for applying said coefficient λ in the form of at least one shift register and / or means for applying a ratio l / (l + λ) in the form of at least one register shift.

According to another possibility, the first calculation means may comprise means making it possible to apply a ratio (1 / λ) in the form of at least one shift register.

The modification of the coefficient λ can be carried out according to the evaluation of a second criterion Jt. The calculation structure of the second criterion may be similar to that used to calculate the given criterion J.

The identification device may further include:

means for evaluating said second criterion Jt comprising at least one exclusive OR logic gate to perform a logical operation OR exclusive between said output signal s _{k of} said converter and an estimate s _k of this signal,

adder means, for adding the result of said logic operation between said output signal s _{k of} said converter and an estimate s _k of said signal, to a term dependent on an element of said second criterion calculated previously.

The modification of the coefficient λ can be carried out according to the evaluation of said second criterion Jt, for example by following the following relation: λ = α * Jt + β (with α> 0 and β> 0)

• With λ that tends to N when Jt tends to 0

• λ which tends for example to 2 ⁶ when Jt tends to 1

The means for carrying out said estimation ^k may comprise convolution calculation means, provided for performing the calculation of a convolution between the estimated impulse response and the noise input signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood on reading the description of exemplary embodiments given, purely by way of indication and in no way limiting, with reference to the appended drawings in which:

Figure 1 gives an example of a device for implementing a method system identification according to the prior art, called KLV method.

FIG. 2 represents an exemplary device for implementing a system identification method according to the prior art, called the OBT method.

FIGS. 3A-3B illustrate another example of a system identification method according to the prior art, called the MCL method.

FIG. 4 illustrates another example of a system identification method according to the prior art, called the MCLC method.

FIG. 5 illustrates an exemplary device for implementing a system identification method according to the invention.

FIG. 6 illustrates an example of an LSFR noise generator integrated into a device according to the invention.

FIG. 7 gives an exemplary curve representative of an impulse response of an HR filter.

FIGS. 8A-8B give examples of cost function calculation units integrated in a device according to the invention and in particular to a structure for estimating the output of a system to be identified using an estimation of the impulse response of this system.

FIG. 9 gives an example of LUT in a device according to the invention, for applying a function of transition between a cost function and a estimated impulse response estimation element.

FIGS. 10A-10B give examples of curves representative of predetermined passage functions respectively in the case of an input signal in the form of a Gaussian noise injected into a system to be identified, and in the case of a signal of FIG. input as a white noise.

FIG. 11 gives an example of an impulse response estimation calculation structure within a device according to the invention.

FIG. 12 gives an example of a convolution calculation structure between impulse response and an input signal of a system to be identified, integrated into an identification device according to the invention.

FIG. 13 illustrates an example of an impulse response estimation and output structure of a system, within a device according to the invention.

FIG. 14 gives a variant of a cost function calculation unit integrated into a device according to the invention and in particular to a structure for estimating the output of a system to be identified by means of an estimate of the response. impulse of this system.

FIG. 15 illustrates another example of an impulse response estimation structure of a system, within a device according to the invention. FIG. 16 gives another variant of a cost function calculation unit integrated into a device according to the invention, and in particular to a structure for estimating the output of a system to be identified by means of an estimate of the impulse response of this system.

FIG. 17 illustrates another example of an impulse response estimation structure of a system within a device according to the invention.

FIG. 18 illustrates another exemplary structure for estimating an impulse response LUT of a system, in a device according to the invention.

FIG. 19 illustrates another example of a one-stage estimation structure, of impulse response of a system, within a device according to the invention.

FIG. 20 illustrates an exemplary device for implementing a system identification method according to the invention, comprising a feedback loop for modifying the precision or the speed of the estimation of an impulse response during of this estimate.

FIG. 21 illustrates an example of means for modulating a calculation coefficient λ of a criterion J used for an impulse response estimation calculation in a method according to the invention.

Figure 22 illustrates an affine line representative of a relation connecting a criterion Jt and a coefficient λ involved in the calculation of a cost function.

FIG. 23 gives examples of representative curves for estimating impulse responses, obtained respectively, using a first device according to the invention without a feedback loop, and with the aid of a second device according to FIG. invention having a feedback loop.

FIGS. 24 and 25 respectively illustrate an exemplary identification device according to the invention in which the system to be identified is a filter, as well as an exemplary impulse response curve of this identification device.

Figure 26 gives examples of impulse response estimation curves determined using a simulation performed using the matlab software and an experiment carried out using a program written in VHDL and implemented. on an FPGA target.

FIG. 27 illustrates an example of a system in the form of an active filter, on which an identification method according to the invention has been implemented.

FIGS. 28 and 29 give examples of estimation curves of impulse response and gain of the filter of FIG. 27, obtained using an identification device according to the invention. Figure 30 gives an example of architecture for the implementation of an identification method according to the invention.

The different parts shown in the figures are not necessarily in a uniform scale, to make the figures more readable.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

An exemplary method according to the invention, of system identification and a device for implementing such a method, will now be given.

Such a method implements a treatment that will be called "BIMBO inline" (BIMBO for "Basic Identification Method using Binary Observations", "inline" meaning that the method uses an identification using binary signals called observations. and is performed in real time) and can be implemented for example using at least one digital signal processor (DSP), and / or at least one microprocessor and / or at least one circuit FPGA, and / or at least one computer.

In FIG. 5, an equivalent block diagram of a device making it possible to implement such a method is given.

The identification includes an estimation of the output of the system, using an estimate of the impulse response of this system. The system to be identified is a system that can be described by a transfer function.

The system to be identified may be for example an electronic device such as a filter, a sigma delta converter, a DC / DC converter, or a telecommunications transmission channel.

The system to be identified may for example be an electromechanical device, for example in the form of a MEMS.

First, a signal u is generated at the input of a system 100.

The signal u is preferably a discrete signal u _k with k representing a moment in discrete time. The signal u _k may be a spectrally rich signal such as a noise signal, in particular a Gaussian noise or a white noise.

In the case where the signal u is Gaussian white noise, a digital-to-analog converter can be used to generate the excitation of the observed system, the noise sign being used in the identification process.

In the case of binary white noise, a 0-order blocker may be used to drive the observed system 100 and as the input signal of the present structure.

The input signal u _k can be produced by a noise generator 110. A noise generator similar to those used in cryptography and which implements an LFSR (LFSR) method for the Linear Feedback Shift Register. linear feedback ") with a shift register can be used for example. With such a generator, some bits of a sequence undergo operations or transformations before being reinserted in a loop. Such a generator is intended to produce pseudo-random sequences. The generator may for example be an LFSR type 32 noise generator corresponding to the following primitive polynomial: l + x + x ³ + x ³⁰ .

An example of an LFSR generator is given in FIG. 6. This generator is formed of a series of blocks 111, 112, 113, 114 respectively having transfer functions in z equal to z ^"1 , z ^{~ 2} , z ^{~ 28} , z ^"1 . The generator also comprises a first adder 115, between the first block 111 and the second block 112, a second adder 116 between the second block 112 and the third block 113, a third adder 117 between the third block 113 and the fourth block 114, the output of the fourth block 114 being fed back to the input of each of the adders 115, 116, 117.

The method comprises several steps of acquiring the input and output signals of the system 100 to be characterized or identified.

The response signal y _k is then injected into means forming a comparator 120 at the output of which a sampled discrete output signal s _k is transmitted. The comparator 120 may be a CAN-I bit. This comparator 120 may be provided for applying a sign function S (). Such a sign function S () makes it possible to carry out the following processing: o = sign (x) and x> 0 we have o = 0

S i • o = sign (x) and x (0 then o = 1

It is sought to produce an estimate y _k of the output of the system 100, using means 130 in the form of a processing block or a processing module for implementing the BIMBO_inline method.

The means 130 may form an approximate parametric model of the unknown system 100. The method makes it possible to converge the approximate model as close as possible to the actual system 100 observed.

Estimation calculations h of the impulse response of the real system are implemented by the means 130, the estimated impulse response to correspond to that of the observed system, when the parametric model converges to the real system. The means 130 may be implemented for example using an FPGA. According to other possibilities, the means 130 can be implemented using a digital signal processor (DSP), and / or a microprocessor and / or a computer.

The calculations of the estimate h are made from the input signal u and the output signal s of the comparator 120, these signals u and s being injected at the input of the means 130. These signals s and u are also called " observations ". In this case, the observations are in the form of binary signals.

The means 130 thus produce at the output an estimate y _k of the output of the system 100, which is injected into a second comparator 140, for example in the form of a second 1-bit ADC, to apply the sign function to this estimate. The signal S _k = S (y _k ) with S () the sign function, can then be compared with the signal s _k from the first comparator 120.

It can be considered that the estimate of y _k achieved is satisfactory when s and s are equal over a significant period of time. By "significant" duration is meant here a period of at least 1000 times the sampling period, corresponding, for example, to a number N of observation samples of the order of 8,000 or 10,000.

The method according to the invention makes it possible to obtain an estimate y of the output of the system 100 observed by means of an estimate h of its impulse response.

Throughout the present description, the term "impulse response of a system" will be referred to as the time output of this system when it is stimulated by a pulse. In the case of a discrete signal, the impulse response can be considered as the response of the system to a Dirac pulse. The estimate of the impulse response of the system 100 may be defined by a set of discrete elements H ₁ .

In FIG. 7, an exemplary curve Ci representative of an impulse response of a discrete HR filter is given. In this figure, a number nh of elements of the impulse response is such that nh = 50. We can describe the set of nh elements an impulse response via a set of points

The treatment carried out by the means 130 aims to obtain the following relation:

(VVV ... ΛJ = VÎ) Λ'4 ... Λj

With Yi ₁ is an element of an impulse response and h _t an element of an estimated impulse response.

An error between the y signal and the y estimate of this signal is called the prediction error. At a time n, the prediction error ε can be defined as follows: ε (n) = y (n) -y (n)

By successive iterations, the model implemented by the means 130 can be adjusted so as to correct the estimate y _k produced and thereby maximize the similarities between the signal S _k and its estimate.

S _k ⁼ s ⁽ y _k ⁾ •

This adjustment is carried out in particular by means of the calculation of a given criterion J carried out by the means 130. This criterion J, which will also be called "cost function", depends on a set of observations acquired up to a given time. instant n, with: j ⁽ n ⁾ = giM ... X4K ⁰ ) ... $ (n)> n)

In the present case, the output s () of comparator 120 is used to calculate said cost function. The cost function can therefore also be written: J (Xi) = g (s (0) _ _ _ s (4 <0) _ _ _ $ p), n)

To evaluate an impulse response, a cost function of the following general formula can be implemented:

The criterion J has a value between 0 and 1 and is minimal in a zone of the parameters space of the parametric model which one will call "zone of acceptability" of the approximate parametric model.

Two different examples of cost function calculations J, including a comparison term between the output signal s and the estimated output signal s, will now be given.

According to a first possibility, we can have S (y _k ) e [-1; 1] with S () the sign function. In this case, when: y _k > 0 => S (y _k ) = 1 y _k <0 => S (y _k ) = -1

Since the signals s and ^Sk are coded on one bit, we thus have the following relation: We note in this case:

With: JT = ^ll r Csu

2 2 A first example of unit 200 (FIG. 8A) integrated with the means 130 may be provided for implementing the iterative calculation of a cost function element Ji according to this first possibility. The means 130 with a unit impulse response model, so that the calculation of Ji comprises a correlation term between the signal s _k output of said converter and the noise signal:

With Ji an element of the cost function, and N a number of calculation points or observations, of the treatment performed. This result J ₁ will then be used to determine an i-th element Zz ₁ for estimating the impulse response of the observed system. The result Ji, which is a cost function element, corresponds to a correlation coefficient or a correlation term between the output signal s and the input signal u of the system 100. The cost function element J ₁ is determined by an iterative calculation comprising a correlation term between the signal s and the signal u.

In this example, the cost function element calculation unit J ₁ comprises means 202 forming an input multiplier from which an output signal s _k taken at a time k and a delayed input signal Uk _-1. of i are issued.

The unit 200 also comprises means 204 forming an adder at the output of the multiplier 202, as well as means 206 forming a filter. discrete delay of order 1, or a transfer function block in z equal to z ^"1 at the output of the adder.

The output of the block 206 is fed back to the input of the adder 204, while means 208 forming a divider by N (with N the number of samples or points of the iterative calculation on which the calculation is made) at the output of the adder 204. A loopback is thus formed such that an element Ji (n + 1) calculated at a given instant depends on a previously calculated element Ji (n).

At the output of the means 208, we obtain Csu a correlation between sk and s k:

Csu = -Y s, s, N ^ f ^kk

According to a second possibility of calculating the cost function, we can have S (y _k ) e [0; 1]

In this case, when: y _k > 0 => S (y _k ) = 0 y _k <0 => S (y _k ) = 1

However, the signals s and s can be coded in binary and are capable of adopting a state ^Λ 0 'or a state ^Λ l'.

We can implement the following calculation:

^J = -Σ ( ^s k- ^S k) ² = -Σ ^xor ( ^s k> ^S k)

A second example of unit 250 for calculating an element Ji of the cost function J according to this second possibility is given in FIG. 8B. This unit 250 may be provided to implement the following calculation:

With Ji an element of the cost function, and N a number of samples. The cost function element J ₁ is thus determined by an iterative calculation comprising a correlation term between the signal s and the noise signal u.

The unit 250 comprises means 252 forming an exclusive OR logic gate (XOR) at the input of which the output signal s _k of the comparator 120 at a time k and the input signal u _k-1 of the system 100 delayed by i, are issued.

Means 254 forming an adder are provided at the output of the XOR gate, while means 256 forming a first order delay filter or a transfer function block in z equal to z ^"1 are placed at the output of the XOR gate. adder 254, the output of the block 254 being fed back to the input of the adder 254. The cost function element J ₁ thus depends on a cost function element calculated at a previous instant. division by N (with N a number of samples) are also provided at the output of the unit 250 and deliver the result J ₁ corresponding to a correlation coefficient between the signal s and the signal u delayed by i sampling periods. this result J ₁ is then used to estimate the i ^"th element A ₁ of the impulse response of the observed system.

We define δ as a term term product of the impulse response elements (h ₀ , ..., h _lr ... _r h _nh _i) of the observed system and estimates (ho, ..., A ₁ ,,

 _nh ) elements of impulse responses.

A so-called "passing" function linking the

cost function J at δ, with δ = (hi a system impulse response element and hi an impulse response estimation element of the system) is also implemented and used by means 130.

The function of passage f is a function chosen, so as to make it possible to go from the computation of an element J ₁ of the cost function to a value of an element hi of the impulse response estimation, so that f ( J ₁ ) = hi. The passage function f is determined as a function of the input signal injected into the system 100.

The passage function f can be performed using at least one storage unit called LUT

(LUT for "Look Up Table"), which maps a value of J of cost function J to a value f (Ji) of element hi of impulse response estimation. An example of LUT 260 is given in FIG. 9. The LUT 260 is characterized in particular by its size and by a pitch Δ. The impulse response data are stored with a step Δ in the LUT, so that only certain values of images of the passage function are accessible: the values f (0), f (Δ), f (2 * Δ) The LUT 260 thus gives output values each corresponding to a range of cost function values J. According to one example, in the case where the input signal u is a Gaussian noise, the function f of passing from a cost function element to an impulse response element can respond to the following law:

With J the cost function and σ ' ² = σ _b ² + σ _h ² where σ _b represents the ambient noise of the system to be identified modeled as an additive Gaussian white noise in

out of the system and & l = Σh? the quadratic sum of the ι = o different elements of the impulse response.

By default we can choose σ '= l. We can then identify the impulse response of the system to the near gain.

In FIG. 10A, an example of a curve Cio representative of a function f of passage between the criterion J and the impulse response is given in one case, where the input signal u of the system 100 to be identified is transmitted in the form of a Gaussian noise.

According to another example, in the case where the input signal u is a white noise, the function of passage f of the cost function to the impulse response can respond to the following law:

Csu = -Y _t ^s k ^s k

NOT '

We have

By default, σ can be chosen equal to 1.

In FIG. 1B, another example of a curve C20 representative of a passage function f between the criterion J and the impulse response is given in the case where the input signal of the system 100 to be identified is a white noise.

In FIG. 11, an example of module integrated in the means 130 and having nh stages for performing a calculation of nh (with nh an integer greater than 1) elements of an estimate h of the impulse response of the system 100, is given.

This module firstly comprises a plurality of nh - 1 blocks forming a chain of discrete delay filters of order 1: 240i,..., 24O ₁ ,..., 240 _n hi each having a transfer function. z equals: z ^"1 .

At the input of the series of delay filters, the input signal u _k of the system 100 at a time k is transmitted, delayed signals Uk-i, ..., Uk-i, ..., u _n hi, are respectively output filters 240 ₁ , ... 240 ₁ , ..., 240 _nh _ ₁ .

A plurality of nh units 25Oo,..., 25O ₁ ,..., 250 _n hi of calculation of elements Jo,..., J ₁ ,..., Jnh-i of the cost function J similar to unit 250 previously described in connection with Figure 9B, are also provided. The 25OO units, ..., 25O _1, ..., 25O _n hi calculating cost function element each receive as input the output signal s _k from the comparator 120 at a time k and _k, respectively, the signals u , ..., u _k -i, Uk-i, ..., u _n hi corresponding to delayed input signal values of the system 100.

The structure also comprises a plurality of nh means 26Oo, 260i, ..., 26O ₁ ,..., 26O _n hi for applying the f () function. The passage function may be the one whose law has been given above, in the case where the input u is a white noise signal. The means 26Oo, 260i,..., 26O ₁ ,..., 26O _n hi may be in the form of nh LUTs of the type of that described with reference to FIG. 10, and receiving, respectively, input elements of cost functions. Jo, Ji, ..., J ₁ , ..., Jnh-i and outputting elements ho, , ..., h _ιf ..., h _n hi impulse response estimation.

From the impulse response estimate, it is possible to obtain an estimate y of the output y of the system 100. For this, the following calculation is implemented by the means 130:

A convolution operation between the estimate h of the impulse response and the binary input u of the observed system 100 is performed.

In FIG. 12, an example of module 270 integrated in the means 130 and making it possible to carry out this convolution operation is given. This module comprises a plurality of nh stages 270Q, 270i, ..., 27O ₁ , ..., 270 _n h- i respectively receiving at input signals u _k , u _k -i, ..., Uk-i, •••, Uk-nh ₊ i of input of the system at different times k, k-1, ..., ki, ..., k-nh + 1, and elements ho _,, ..., h _ιf ..., hnh-i of impulse response estimation.

Each stage of the module 270 comprises multiplying means 271 of the two inputs of the stage as well as means 273 for adding the output of the multiplication means 271 to an output of a preceding stage, in other words, to add the result of said multiplication to the result of a previous stage. The module 270 for carrying out the convolution operation outputs the estimate y of the output y of the system 100.

In FIG. 13, an example of a complete structure for delivering an estimate is shown.

This structure 230 comprises nh stages 231o, 231i, ..., 23I ₁ , ..., 231 _n hi the number of stages nh can be provided in particular according to the complexity of the system 100 to identify. The non-zero elements of the impulse response of the system are estimated. If we denote by no the number of non-zero elements of the impulse response, n ₀ and nh are such that nh> n ₀ .

This structure 230 comprises a filter of order 0 or a transfer function block in z: z ^~ °, as well as a plurality of nh-1 blocks 240i,..., 240 _n hi, having the function of transfer in z: z ^"1 or respectively forming a first order delay filter, these blocks being arranged in series or in a chain of blocks. The structure 230 also includes nh 25OO units, ..., 250 _n hi evaluation Jo elements, ..., J _n hi cost function, nh 26Oo units, ..., 260 _n hi LUTs to implement the function of passage f and to obtain estimation elements ho,..., h _n hi of impulse response, as well as nh units 27 Oo,..., 270 ₁ ,..., 270 _n hi to perform the operation of convolution and produce the estimate y.

In FIG. 14, another example of a cost function element calculation unit 300 making it possible to implement the calculation of an element of a cost function variant J 'that is different from the cost function J previously described, is given. The cost function element is determined by an iterative calculation including a correlation term between the system output signal and the system input signal.

The unit 300 comprises means 302 forming an exclusive OR logic gate (XOR) at the input of which is emitted an output s _k of the comparator 120 taken at a time k, and an input u _k-1 of the delayed system of i samples.

The unit 300 comprises means 304 forming an adder at the output of the XOR gate, means 306 forming a first order delay filter at the output of the adder 304 and the output of which is reinjected at the input of means 303 for applying a coefficient λ, the output of the means 303 for applying the coefficient λ being emitted at the input of the adder 304. The output of the adder is transmitted at the input of means 308 for dividing by (1 + λ). In output of the means 308, an element of said second cost function J 'is obtained.

The sum (1 + λ) corresponds to a number N of samples or computation points or observations.

In this example, the coefficient λ is also chosen such that (1 + λ) is equal to a power of 2, so that the means 308 for applying the coefficient l / (l + λ) are means for effecting an offset bits of their binary input. The means 308 may for example be in the form of a shift register. With respect to a unit such as those (referenced 200 and 250) described with reference to FIGS. 8A and 8B, this makes it possible to dispense with a divider and to simplify the implementation of the calculation.

The coefficient λ is also chosen so that λ is large in front of a (1 << λ). By λ "large" before 1 we mean that λ is greater than 2 ¹⁰ .

The coefficient λ can be flexible, possibly modulable during the identification process.

The cost function variant J 'implemented by the unit 300 can follow the following relation:

J ' _k (n + 1) = (l * j _k (n) + λ * J' _k (n)) / (l + λ)

with jk (n) the output of means 302 forming a logic gate XOR, λ the coefficient whose sum with the unit corresponds to a number N of computation points or samples.

,, _{ι Λ} _ j (n) + λj (n - 1) + λ ² j (n - 2) + ... + λ ^N - ¹ j (n - N + 1)

^{J [n + [)} - i _{+ λ}

When λ is chosen such that κ <λ, we have J '(n) ≈J (n), the cost function J being substantially equal to the variant J' of cost function.

In Fig. 15, a variant of structure 330 provided for outputting an estimate of y is shown. This structure 330 differs from that previously described in connection with FIG. 13, by the calculation of the cost function, and comprises nh units 3OOo,..., 30O ₁ ,..., 300 _n h of evaluation of cost function elements J 'such as that (referenced 300) which has just been described with reference to FIG. 14.

In FIG. 16, another example of a calculation unit 350 for implementing the calculation of an element J '' _k of another variant of cost function J '' is given.

This unit 350 comprises means 352 forming an exclusive OR logic gate (XOR) at the input of which an output s _k of the comparator 120 is transmitted at a time k, and an input signal u _k -i of the system 100.

The unit 350 also comprises means 353a making it possible to apply a ratio (1 / λ) to the output pk (n) of the gate XOR, as well as means 354 forming an adder at the output of the means 353a, means 356 forming a first-order delay filter at the output of the adder 354 and the output of which is reinjected at the input of means 353b making it possible to apply a ratio (1 / λ), the output of the means 353b and the filter 356 being emitted at the input of the adder 354. At the output of the adder 354, an element of said second variant of cost function J "is obtained.

The sum (1 + λ) of the coefficient λ and the unit corresponds to a number N of calculation points.

In this example, the coefficient λ is chosen equal to a power of 2: λ = 2 ^A b.

The means 353a and 353b are also able to shift their binary input, each to apply the ratio 1 / λ, which amounts to applying a shift of b bits to the right.

With respect to the structure 300 described in connection with FIG. 15, this makes it possible to dispense with multipliers.

This other variant of calculation unit 350 is implemented with a coefficient λ chosen so that λ large in front of 1 (1 << λ). By λ "large" is meant that λ is greater than at least 2 ¹⁰ .

k 1+ λ 1+ λ 1+ λ Considering the limited development of order 2, we have the following relation:

When λ is chosen such that κ <λ, we have J '' (n) ≈J (n), the cost function J being substantially equal to the cost function variant J ''.

In Fig. 17, a variant of structure 430 for providing an estimate of y is shown. This structure 430 differs from that previously described in connection with FIG. 14, by the calculation of the cost function, and comprises nh units 35Oo,..., 35O ₁ ,..., 35O _n hi evaluation of cost function elements J '' such as that (referenced 350) which has just been described with reference to FIG.

Another example of structure 530 intended to deliver an estimate y of the output of the system 100 is given in FIG. 18. In this example, the means for applying a function f for passing a cost function element Ji to a element / zi impulse response, differ from those structures 230, 330 previously described in connection with Figures 13 and 15. In this example, the number of LUT is greatly reduced compared to that of structures 230 and 330. We go from nh LUTs, ie from one LUT per floor, to a single LUT for the nh floors of the structure.

For this, the first multiplexer means 362 are provided at the output of nh 350Q units ..., 35O _1, 350 _n hi calculating the cost function J '' such as that (referenced 350) described in connection with Figure 16.

Based on a selection signal sent by a control module 365, the first multiplexer means 362 outputs one of a plurality of their inputs.

At the output of the first multiplexer means 362, there are means 360, for example in the form of a LUT, for applying the function f of the passage.

Demultiplexer means 364 are provided at the output of the LUT 360. The input of the second demultiplexer means 364 is transmitted to one of its outputs selected by a selection signal delivered by the control module 365. The outputs of the demultiplexer means 364 respectively deliver elements hθ, ... hi, hnh-1 of impulse response estimation.

The control module 365 is thus provided to transmit selection signals to the multiplexer means 362, and to the demultiplexer means 364, so as to ensure proper routing of the estimated impulse response values.

The structure 430 also includes the nh units 270o, 270i, ..., 27O ₁ ,..., 27O _n hi for carrying out the convolution operation leading to the estimate y.

The operation of one or other of the structures 230, 330, 430, 530 has heretofore been presented with a given number of stages nh. This number nh corresponds to a number of elements of the impulse response that one seeks to identify, and can be modified or adapted. The number of elements nh of the impulse response that can be identified can be chosen according to the complexity of the system 100 and the sampling frequency fs. The number nh of elements to be identified is greater than the number of non-zero elements n0 of the impulse response of the observed system: so that nh> nθ. This number nh depends on system characteristics 100, such as damping, and the sampling frequency fs. The higher the oversampling, the higher the number of stages nh will be expected for a given damping. The choice of the number nh is done in a way that respects Shannon's theorem. In the case for example, where the system to be identified is an electric oscillator, the sampling frequency fs may be provided, such that fs> 2 * fc with fc is the cut-off frequency of the oscillator.

The number nh of stages is preferably small in front of λ, the coefficient of the cost function calculation units. For example, λ is at least ²⁸ times larger than nh and λ can be between 2 ¹⁰ and ²⁰ .

Another example of structure 630 intended to deliver an estimate is given in FIG.

In this structure 630, a parallelization of the nh stages has been performed, so that the structure 630 has a stage.

For this, at the output of the 240i, ..., 240 _n hi delay filters, multiplexing means are provided. 545 controlled by a control signal from a control module 565.

At the output of the multiplexing means 545, a unit 550 for calculating the elements of a cost function J "is provided. This stage differs from that (referenced 350) previously described in connection with FIG. 16, in that the means 356 forming a transfer function delay filter in z equal to z ^"1 , are replaced by a module 556 comprising means memory 557, means forming a multiplexer 558 connected to the memory, and means forming a demultiplexer 559 connected to the memory, the memory 557 is provided for storing values of elements I 'o, ... j'' _lr ..., J'' _nh _χ of cost function J''.

For the purpose of calculating an element J '' (n + 1) of the cost function, a previously or previously calculated cost function element J '' (n) is extracted from the memory 557 and output from the multiplexer 558 to be inputted to an adder and means for applying a ratio (1 / λ).

The multiplexer 558 and the demultiplexer 559 are controlled by signals transmitted by the control module 565.

Once calculated, an element of the cost function is sent to the input of the demultiplexer means 559, in order to be placed in the memory 557.

At the output of the computing stage of J '', there is placed a LUT 560 provided to receive a cost function element J '' i and to output a corresponding impulse response element / zi. This element hi. The impulse response may be transmitted to a multiplexer 580 connected to a memory 582 and stored in said memory 582.

A convolution calculation module 570 is also provided at the output of the LUT 560. This module 570 comprises means 571 forming a multiplier for multiplying the output of the LUT 560 delivering an impulse response estimating element hi, at the output of the multiplexer means 545 supplying a system input signal u among the signals Uk,..., Uk-i,... u _n hi • adder forming means 572 are provided for effecting an addition of the output of the multiplier and a multiplexer 574. The output of the adder is fed back to the input of the multiplexer 574 after passing through a delay filter 575. The multiplexer 574 is also controlled by the control block 565.

At the output of the adder, an estimate y is obtained.

The value of the coefficient λ can be modified, possibly during the identification process.

The choice of a low λ coefficient, for example less than ²⁸ , makes it possible to give significant weight to new samples, and to obtain a treatment in which speed is preferred over accuracy.

The choice of a high λ coefficient (with b> 2 ¹⁵ ) makes it possible to favor precision over speed. It is therefore possible to change the parameter λ during the identification process, as a function of the progress of the estimation of the impulse response.

Another example of a device for implementing an identification method according to the invention is given in FIG.

With such a device, the coefficient λ involved in the calculation of the cost function J is changed during processing.

Feedback or feedback is implemented at a structure 730 receiving the input signal u from the system and the output signal of the comparator 120 and provided to provide an estimate of y. The structure 730 may be one of those 330, 430, 530, 630 described above, with a control block 680 output.

The control block 680 may comprise a calculation unit 689 comprising components similar to those of the calculation unit described with reference to FIG. 16. The block 680 receives as input the output signal of the comparator 120 at a time k , and the estimate sk coming out of the comparator 140.

The control block 680 can comprise means 683 forming an exclusive OR logic gate (XOR) at the input of which the signals sk and sk are emitted.

The stage 689 also comprises means 684 making it possible to apply a ratio (1 / λ), for example using at least one shift register, to the output of the XOR gate, as well as means 686 forming an adder at the output of the means 684, means 687 forming a first-order delay filter and transfer function z ^"1 at the output of the adder 686 and the output of which is reinjected at the input of means 685 making it possible to apply a ratio (1 / λ), by example using at least one shift register, the output of the means 685 and the filter 687 being emitted at the input of the adder 686.

Thus, the computing stage 689 implements the calculation of a second criterion Jt to estimate the error on s _k with respect to Sk, with Jt such that:

Jt {k) ≈-VX0R {s {k), s {k)) (N: the number of

calculation points equal to 1 + λ)

The value of the coefficient λ is controlled as a function of the value obtained from J _t . A function f _t is then applied to determine a control law such that:

In the case of Figure 16, we have λ = 2 ^b . The modification of λ returns to a modification of b, one can thus find a function ft such that:

The function f _t can be applied via a LUT 688.

According to one variant, the control of the coefficient λ can be performed from the function J _t , while dispensing with the use of a LUT 680.

We can implement a linear relation between the parameter λ and J _t . FIG. 21 shows an example of means 780 for applying a linear command, corresponding to the equation: λ = α * Jt + β where β ≠ O to avoid the case λ = 0. It is then possible to replace the LUT by these means 780 which include means 781 for multiplication and adding means 782.

In FIG. 22, an example of a line C10 representative of a linear control of the coefficient λ is given.

Figure 23 shows the contribution of the feedback and control block 630. In this figure, a first curve C200 is representative of the evolution of the estimate of the impulse response performed without feedback. A second curve C202 is representative of the evolution of the estimate of the impulse response performed with a feedback loop provided with the control block 680.

Another example of a device according to the invention is given in FIG.

This device comprises a noise generator 110, for example a pseudo-random type LFSR signal generator of 32 order, which can deliver for example an amplitude signal between 0 and 3 volts. At the output of the generator 110, a level shifter 802 circuit ("level shifter" according to the English terminology) is provided and can deliver a signal for example between -0.5 volts and 0.5 volts. The device also comprises a first buffer circuit 810 at the input of a system 1000 to identify, and a second buffer circuit 820 at the output of the system 1000. A comparator 120 is provided at the output of the second buffer circuit 820 and delivers the signal s to means 830, for example one of the structures 130, 230, 330 previously described. , to estimate the output of the system 1000. The means 830 also receive a noise signal u from the generator. The means 830 can be implemented for example using an FPGA.

In this example, the system 1000 may be a resonant second-order RLC filter whose transfer function H follows the following relationship:

The resonant frequency of the filter may be of the order of 1500 Hz, while the sampling frequency fs chosen is 5 kHz. Such a system 1000 may have an impulse response of the shape of the curve C3oo-

An example of a program implemented using the Matlab tool, for the implementation of an impulse response estimate following the invention is given in the appendix. This program comprises a function, whose inputs are the input signal u and the output signal s, the number of stages nh, the coefficient value λ and the number of points nb_pts of calculation in parameters. This function returns a hhat datum, corresponding to the estimate h of the impulse response h of the observed system.

The implementation of the BIMBO inline method can be carried out by a microcomputer comprising a calculation section with all the electronic components, software or other, necessary for the treatment. Thus, for example, the microcomputer includes in particular at least one programmable processor, and at least one memory for this treatment.

The processor may be, for example, a microprocessor, a DSP, or a CPU processor. The memory may be, for example, a hard disk, a ROM, a compact optical disk, a DRAM dynamic random access memory or any other type of RAM, a magnetic or optical storage element, registers or other memories volatile and / or non-volatile.

A program for implementing the method according to the invention may be resident or be recorded on a medium (for example: floppy disk or a CD ROM or a DVD ROM or a removable hard disk or a magnetic medium) likely to be read by a computer system or by the microcomputer.

According to one possibility, the algorithm BIMBO_inline and the noise generator can be implemented using an FPGA, the other elements in particularly the 1-bit ADC can be in the form of discrete components.

The identification method can be used in the context of BIST systems (BIST for "Built In Self Test") that is to say having the ability to self-test. This makes it possible to avoid, during the test, the use of an important apparatus. It is in this case to apply the BIMBO inline method presented to a system and to compare the desired impulse responses and realized to conclude a good operation of the system.

The identification method can be used to perform self-calibration of a system, in particular an electromechanical system. During its operation. Such a system can be considered to evolve over time. The method according to the invention then makes it possible to estimate these evolutions, by means of estimations of the impulse response of the system, and to adapt the control system according to these.

The impulse response estimate may be supplemented by a transfer function identification.

The method according to the invention was tested on a universal active filter UAF42 from Texas Instrument (UAF for "Universal Active Filter") and as shown in FIG. 28, with a sampling frequency, for example, of the order of 15 kHz, and resistance values RF1 = RF2 = 220 kΩ, RG = 22 kΩ, RQ = 10 kΩ. Such values correspond to a quality factor Q = 1.2, and an eigenfrequency fo of the order of 730 Hz.

FIGS. 28 and 29 give amplitude estimation curves C400 and gain C500 of the filter obtained with 100 impulse response coefficients after 4000 samples at the output of a device for example as described with reference to FIG. 13 , have been obtained.

For comparison, experimental curves of amplitude C402 and gain C502 are given.

In Figure 30 another example of device according to the invention is given. This device is provided with means 830, for example one of the structures 130, 230, 330 described above, for implementing the BIMBO inline method and making an estimate y _k of the output of a system 1000, which delivers a signal s _k . The means 830 also receive a noise signal u from the generator.

The presented BIMBO_inline algorithm receives the u and s signals coming respectively from the noise generator and the comparator (digital analog converter) and provides an estimate y _k of the signal y _k from the estimate of the impulse response. This estimate of the output of the observed system is used by a parametric adaptation algorithm.

The means 900 and 810 perform a parametric adaptation algorithm and use the output y _k of the system. We therefore consider that y _k = y _k . Block 810 contains the approximate model of the observed system. This approximate model is a model of the HR type (modeling in the form of a numerator / denominator transfer function with Infinite Impulse Response). This model is re-evaluated at each sampling period by the block 900 which includes the parametric adaptation algorithm itself, for example the least squares algorithm. At each sampling period, the approximate model provides an estimate y _k of y _k . The parametric adaptation algorithm will provide a new estimate of the approximate model whose output minimizes the error between y _k and y _k .

ANNEX

function [hhat] = verif_bimbo_inline (u, s, nh, nb_pts, a, b)

% initialization u_ligne_retard = zeros (nh, 1);

Csu = 0.5 * ones (nh, 1);

% processing loop for k = l: nb_pts u_backline = [u (k); u_ligne_retard (1: end-1)];

J = a / b * xor (s (k), u_ligne_retard) + J-a / b * J;

% estimate of h hhat = sqrt (2) * erfinv (-2 * D + 1). / sqrt (l + 2 * erfinv (- 2 * J + 1). ^Λ 2);

% estimate of y (cropping of u (0, 1) => (1, -1) yhat = (-2 * u_ligne_retard '+ l) * hhat; end;

Claims

An electronic or electromechanical system identification device (100), comprising:

means (110) for generating a noise signal (u _k ), for generating an input noise signal of said system (100),

an analog-to-digital converter (120) to which an output signal (y _k ) of the system (100) is to be applied,

means (130, 230, 330, 430, 530) for making an estimate (h) of the impulse response of said system (100) comprising:

first calculation means (25Oo,

25O ₁ , ..., 25O ₁ , ..., 250nh-1, 35O ₀ , 35O ₁ , ..., 35O ₁ , ..., 35O _nh -i): to perform an iterative calculation of a plurality of nh (with nh an integer) elements (Jo, ..., J ₁ ,, J _n hi) of a given criterion J, each element comprising at least one correlation term between said output signal of said converter and said noise signal.

The apparatus of claim 1, further comprising: means for performing an estimate (y _k ) of the output of said system (100) using said estimate of the impulse response of said system (100).

3. Device according to claim 2, the means (130) for making said estimate (y _k ) of the output of the system (100), further comprising: second calculation means (26Oo, 26O ₁ , ..., 26O ₁ , ..., 26O _n h- i,): to apply to the elements (Jo, ..., Ji,, J _n hi) calculated of said given criterion J, a predetermined passage function f as a function of the noise signal (u _k ) transmitted at the input of said system, and such that: with hi an impulse response element h of said system and hi an element of said impulse response estimate h of said system.

4. Device according to one of claims 3, wherein said input signal (uk) of the system is a binary white noise signal, said function f of passage according to the relation:

5. Device according to one of claims 1 to 4, wherein the means (130,230,330,430,530) comprises: a chain of blocks (240i, ..., 240 _n hi) respectively forming a delay function of order 1 or having z ¹ as a z-transfer function, said chain being adapted to receive said input signal (u _k ), and to output values (Uk, ... Uk-i, Uk-nh-i) of the noise signal delayed respectively output of said blocks (240i, ..., 240 _n hi) •

6. Device according to one of claims 1 to 5, wherein said first calculation means comprise: means (302,352) forming an exclusive OR logic gate, for performing an exclusive OR logic operation between said output signal (sk) of said comparator taken at a time k and said noise signal (u _k -i, with 0 <i <nh) delayed by i with respect to said given instant.

adder means (304, 354) for adding the result of said logical operation to a term dependent on an element of said given criterion calculated previously.

7. Device according to one of claims 1 to 6, wherein the acquisition of the signal (sk) output of said converter, is performed for a given number (N) of samples, the calculation of the criterion given J by the first computing means, being dependent on at least one predetermined coefficient λ, with λ substantially equal to said given number (N) of samples.

The apparatus of claim 7, further comprising: means (680) for modifying the values of said coefficient λ during said estimate (") of said impulse response.

9. Device according to claim 7 or 8, the first calculation means comprising means for applying said coefficient λ in the form of at least one shift register and / or means for applying a ratio l / (l + λ) in the form of at least one shift register.

10. Device according to claim 9, the first calculation means comprising means for applying a ratio 1 / λ in the form of at least one shift register.

11. Device according to one of claims 8 to 10, wherein said modification of the coefficient λ is performed according to the evaluation of a second criterion Jt, the device further comprising:

means for evaluating said second criterion Jt comprising at least one exclusive OR logic gate (XOR) to perform an exclusive OR (XOR) logic operation between said output signal (sk) of said converter and an estimate ( ^s k) of this signal , adding means (686), for adding the result of said logic operation between said output signal (sk) of said converter and an estimate ( ^s k) of this signal, to a term dependent on an element of said second criterion calculated previously .

12. Device according to claim 11, the modification of the coefficient λ, being performed according to the evaluation of said second criterion Jt, according to the following relationship: λ = α * Jt + β (with α> 0 and β> 0).

13. Device according to one of claims 1 to 12, the means (130, 230, 330, 430,

530) for performing said estimation (' ^k ) comprising convolution computing means, provided for performing the calculation of a convolution between the estimated impulse response (") and the noise input signal (u).

14. Device according to one of claims 1 to 13, said analog-digital converter being a 1-bit ADC.

15. Device according to one of claims 1 to 14, said system being an electronic filter or MEMS.

An electronic or electromechanical system identification method (100, 1000) comprising the steps of:

applying at least one noise signal (u) at the input of said system,

applying an output signal (y _k ) of said system to a one-bit analog-to-digital converter (120),

performing an estimate (y _k ) of the output of said system (100) using means for making an estimate (h) of the impulse response of said system (100), the estimate (h) of said impulse response comprising : the iterative computation of a plurality of nh (nh being an integer) elements (Jo, ..., Ji,, J _n hi) of a given criterion J, each element comprising at least one correlation term between said output signal of said converter and said noise signal.

The method of claim 16, further comprising: estimating (y _k ) the output of said system (100) using said estimate of the impulse response of said system (100).

18. The method of claim 16 or

17, the estimate (h) of the impulse response further comprising: applying to said calculated elements (Ji) the criterion (J) of a function (f) of passage, said function (f) of passage being predetermined according to said noise signal applied at the input of said system, and such that: nh-l

/ (J) = ^ h ₁ H ₁ with h _± a response element

impulse h of said system and Zz ₁ an element of said impulse response estimate h of said system out of a plurality of impulse response elements (ho, ..., h _{± 1} , Âh-i).

19. The method according to one of claims 16 to 18, wherein said input signal (uk) of the system is a binary white noise signal, said function f of passage according to the relation:

V1 + 2 (CT / - (1-2./))