FR2914126A1 - Low frequency signal demodulating method for estimating e.g. angular position of disc, involves calculating products of sample, where one of samples is proportional to result of multiplication of signal value by value of impulse response - Google Patents

Abstract

The method involves delivering a sample at each instant with the help of a synchronization signal. Products of two samples are calculated from the sample delivered at same instant, where one of the samples is proportional to result of multiplication of a signal value at an instant by a value of an impulse response of a finite impulse response filter. One of the products is added with another produce from the calculated products during observation period, resulting from an addition corresponding to a value estimated from a derivative. Independent claims are also included for the following: (1) an information recording medium comprising instructions to perform a synchronous demodulation method (2) a synchronous demodulator comprising a sample generator (3) a magnetic field sensor comprising a synchronous demodulator.

Description

SYNCHRONOUS DEMODULATION METHOD AND RECORDING MEDIUM FOR THIS

  The present invention relates to a synchronous demodulation method and a recording medium for this method, a synchronous demodulator and a sensor incorporating this demodulator. There are synchronous demodulation methods allowing the extraction of the derivative d-th ad (t) with respect to the time of a low frequency signal y (t) from a modulated high frequency signal following relation: e (t) ) = p (t) y (t) where.

  p (t) is a high frequency time carrier is known.

  d is a whole number greater than or equal to

  is equal to zero, the derivative yt) is defined as being equal to y (t).

  Here, a high frequency signal is referred to as a signal whose fundamental frequency est is strictly greater than the fundamental frequency f 2 of the low frequency signal. Typically, the frequency fi is at least ten times greater than the frequency f2.

  The response time of a synchronous demodulator is also defined as being the time necessary for the value of the dérivth derivative extracted by the demodulator to stabilize in a band of plus or minus 5% around the final value obtained in response. at a step of the 1 st derivative of the low frequency signal y (t). For example, this response time is equal to defined by the (1) e (t) whose evolution to zero. When the interval of time between the moment when the step is applied on the signal y (t) and the moment when the derivative dth extracted returns to stabilize in the band whose upper and lower limits are respectively equal at the final value plus 5% and the final value minus 5%. The start slope is also defined as being the derivative with respect to the time of the d-th derivative extracted by the synchronous demodulator at the moment when a step is applied to the 1 st derivative of the low frequency signal y (t ). For example, the existing methods comprise: the emission or the reception of a signal of

  synchronization for maintaining the demodulator in phase with the carrier p (t), - the analog-digital conversion of the signal e (t) with a sampling period Te and the delivery at each instant ti sampling of a sample el corresponding to the value of the signal e (t) at the instant ti, 20 - the generation of samples qi, each sample qi being proportional to a value r (ti) of a signal r (t) at the moment ti predetermined to be correlated to the carrier p (t), the signal r (t) being considered correlated to the carrier p (t) if the following equation is

  25 veri fi ed (p) (u) tcbs 0 - / pef refi where:. u is the integration variable,. Tobs is an observation period N times greater than a sampling period Te, where N is an integer greater than or equal to two,

  Tbr pef = f p2 (u) of the Tolu 0 '2 rei = 1 r (u) of, and lobs 0 - the delivery (82), at each instant ti, using the synchronization signal, the sample qi so that the temporal sequences of samples qi and ei delivered at the same times ti are both correlated to the same sequence of values p (ti), - the calculation (84) of the product eigi from samples el and qi delivered at the same time, - the addition (86) to each other of all eigi products calculated during the observation period Tobs, the result of the addition corresponding to the estimated value of the derivative ady (t) More precisely, in the existing processes, each sample qi is equal to the value p (t). The existing methods introduce a delay dd, which results in a so-called drag error as illustrated in FIG. 1. In FIG. 1, the curve y (t) represents the evolution over time of the signal y ( t) while the curve (t) represents the estimate of the time course of the signal y (t) obtained by one of the existing methods. The aim of the invention is to propose a synchronous demodulation method by which the error of dragging is greatly reduced. The subject of the invention is therefore a synchronous demodulation method in which each sample qi delivered is proportional to the result of the multiplication of the value r (ti) of the signal r (t) at time ti by the value hd (ti ) an impulse response hd (t) of a finite impulse response filter of order n greater than or equal to d, the impulse response hd (t) being a function of an impulse response h (t) of a n-order finite impulse response filter 3 of order n which is a solution of a system with n + 1 equations, where each of the n + 1 equations is defined by the following relation:

  Tobs J zmh (z) dz = a if m = d 0 = 0 d (m ≠ d and mn) where.

- n is the order of the filter,

  m is an integer ranging from 0 to n,

  - Tobs is the period of observation,

  - z is the integration variable, and - a is a constant different from zero.

  It has been found that by choosing the samples q, as indicated above, this makes it possible to eliminate or strongly reduce the delay Ad which is proportional to the observation period Tobs and thus to eliminate or greatly reduce the Misfeeding error Embodiments of this method may include one or more of the following features: • The signal r (t) satisfies the following inequality: TJ p (u) (u) of the peffreff

  the impulse response h (t) is a sequence of steps defined by the following relationships:

  h (t) = h, if te [b,; b; +1 [h (t) = O if t [0; Tobs Vb; Tobs> b, + 1> b; > 0

  or . i is an integer ranging from 0 to an integer Mh greater than or equal to n, the hi are predetermined predetermined values each selected from the group consisting of {-2i; 0; +23} where j is a positive integer or zero, and Tobs o> 0.5 - the bi are moments of transition between the values h ;, these bi being chosen so that h (t) is a solution of the system of n + 1 equations, • the signal r (t) is a sequence of steps defined by the following relation I (t) = rk If t [Ck; Ck + l [r (t) = 0 if t [O; Tobs ] `VC k; Tobs C k + 1> C k> 0 where: -k is an integer ranging from 0 to a positive integer Mr, 10 - the ri are predetermined values in advance, each of these values being selected from the group consisting of {-2 '; 0; + 2 '}, and - the ck are transition moments between the rk values chosen for the signal r (t) to be correlated to the carrier p (t) over the interval [0; T obs is zero; the impulse response hd (t) is defined by the following relation. n dt (i-d) hd (t) = Dfi (t) (i-d) id = 0si t E [O; Tobs J if t [0; TobS 20 where: - At is a predetermined time interval. These embodiments of the synchronous demodulation method furthermore have the following advantages: - choose a signal r (t) strongly correlated with the carrier p (t), that is to say, whose absolute value of the intercorrelation coefficient is greater than 0.9, makes it possible to increase the accuracy of the estimate of the dth derivative of y (t), the use of the smooth function (t) makes it possible to introduce additional degrees of freedom which allow to approximate the waveform of the impulse response h (t) of the predetermined template, choose the function smooth (t) so that h (0) is strictly greater than zero, increases the slope at startup, - choose the smooth function ( t) so that h (0) is on the contrary equal to zero, decreases the slope at startup and softens the response of the demodulator, - choose the function smooth (t) so that h (Tobs) is strictly different from zero increases the time of answer, - choose the function smooth (t) so that h (T obs) equal to zero makes it possible to decrease the response time, - choose an impulse response h (t) and a signal r (t) each formed of a series of values selected from the group consisting of {-23; 0; 2 '} makes it possible to simplify the execution of the multiplications because they can be realized by a simple shift, - to choose the values of the impulse response h (t) only in the group composed of {-1; 0; 1} or {--1; 1} further simplifies the execution of the multiplications, - choosing hd (t) as a function of At and fi (t) makes it possible to compensate, at least in part, for a delay of, for example, the computation time of the multiplications and additions involved in this process. The invention also relates to an information recording medium comprising instructions for executing the synchronous demodulation method above when these instructions are executed by an electronic computer. The invention also relates to a synchronous demodulator capable of implementing the synchronous demodulation method above. This synchronous demodulator comprises: at least one synchronization port able to transmit or receive a synchronization signal making it possible to keep the demodulator in phase with the carrier p (t),

  an analog-digital converter equipped with an input for receiving the signal e (t) to be sampled with a sampling period Te and an output delivering at each sampling instant ti a sample el corresponding to the value of the signal e (t) at time ti,

  a sample generator qi, each sample qi being proportional to a value r (ti) of a signal r (t) at time ti predetermined in advance to be correlated with the carrier p (t), the signal r (t) being considered as correlated with the carrier p (t) if the following equation is satisfied rl Ts p (u) r (u) of ≠ 0 7-lobs 0 1 / pef ref where

u is the integration variable,

  Tobs is an observation period N times greater than a sampling period Te, where N is an integer greater than or equal to two,

  Tb, 2 peff = 1 p (u) of Tobs 0 1 rff _ J r2 (u) of Tobs 0

  this generator being fit, using the signal of

  synchronization, to deliver at every moment ti

  The sample qi so that the time sequences of samples qi and el delivered at the same times ti are both correlated to the same sequence of values p (ti),

  a multiplier able to calculate the product eigi from samples ei and qi delivered at the same time

  30 by the analog-digital converter and the generator, - an accumulator able to add to each other all the eigi products calculated by the multiplier during the observation period Tubs, the result of these additions at the end of the corresponding to the estimated value of the generator is adapted for observation period the derivative 8dy (t) ad that each sample qi delivered is proportional to the result of the multiplication of the value r (t;) of the signal r (t) at time t by the value hd (ti) of an impulse response hd (t) of a finite impulse response filter of order n greater than or equal to d, the impulse response hd (t) being a function of an impulse response h (t) a finite impulse response filter of order n which is a solution or approximation of a solution of a system with n + 1 equations, where each of the n + 1 equations is defined by the following relation: where: - n is the order of the filter, - m is a integer ranging from 0 to n, Tobs is the observation period, - z is the integration variable, and - a is a non-zero constant. Finally, the invention also relates to a sensor 25 of a high frequency magnetic field obtained by amplitude modulating a high frequency carrier p (t) by a low frequency signal y (t), this sensor comprising: a clean transducer converting the high frequency magnetic field into an electrical signal e (t) proportional to the modulated high frequency magnetic field, = 0 V (m ≠ d and m _ <n) $ zmh (z) dz = a if m = d 0 and 9 - the synchronous demodulator above. The invention will be better understood on reading the description which follows, given solely by way of nonlimiting example and with reference to the drawings in which: FIG. 1 is a graph illustrating the error of dragging s, FIG. 2 is a schematic illustration of the architecture of a position sensor including a synchronous demodulator; FIG. 3 is a flowchart of a synchronous demodulation method implemented in the demodulator of FIG. 2; FIGS. 4 and 5 are graphs illustrating, respectively, polynomial impulse responses and the corresponding index responses; FIGS. 6 to 8, 9 to 11 and 12 to 14 are graphs representing smoothing functions and impulse responses and 5 and 16 are graphs, respectively, of a smoothing function and a corresponding impulse response. Fig. 17 is a schematic illustration of the architecture of a sensor of an angular position including synchronous demodulators; Figs. 18 and 19 are schematic illustrations showing in more detail the transducers used in the sensor of the FIG. 17; FIGS. 20 to 23 are graphs illustrating the curves whose definitions are recorded in a memory of the sensor of FIG. 17; FIG. 24 is a flowchart of a method of operation of the sensor of FIG. 17. and FIG. 25 is a graph illustrating the performance of the sensor of FIG. 17. FIG. 2 shows a sensor 2 of the vertical position y (t) and the speed 8340 of a moving part 4 in translation along the A vertical axis 6. The position y (t) is marked with respect to an origin O placed on the axis 6. Here, the end of the part 4 is equipped with a plate 8 of magnetic material. The sensor 2 comprises: - a generator 12 of a sinusoidal excitation magnetic field of frequency f1, - a transducer 14 capable of converting the amplitude-modulated excitation magnetic field as a function of the position y (t) into a signal modulated high-frequency electric motor e (t), a synchronous demodulator 16 capable of estimating the derivative d-th ad (t) with respect to the time of the position y (t) from the signal e (t), and - a clock 18 to generate a synchronization signal common to the generator 12 and the demodulator 16. The synchronization signal is here a clock signal formed by rising edges appearing at regular intervals. Typically, the frequency of occurrence of these rising edges in the synchronization signal is greater than ten times the frequency f1. The generator 12 is, for example, formed of a source of current suitable for supplying a coil 22. The source 20 generates a sinusoidal current of synchronized frequency, for example, on the rising edges of the clock 18. The coil 22 converts this sinusoidal current into a high frequency excitation magnetic field radiated near the magnetic plate 8. The transducer 14 is, for example, a coil also placed close to the plate 8 so as to be: sensitive to the amplitude modulated excitation magnetic field by the position y (t). The transducer 14 thus delivers a signal e (t) of the following form: e (t) = p (t) y (t) (1) where: p (t) is a sinusoidal carrier of frequency f1. The synchronous demodulator 16 comprises an analog-digital converter 26 equipped with inputs connected to the transducer 14 and an output connected to an electronic calculator 28. The converter 26 also comprises a synchronization port connected to the clock 18 for receiving the signal synchronization, which makes it possible to synchronize the converter 26 and the generator 12. The converter 26 is able to sample the signal e (t) with a sampling frequency fe. Here, the sampling frequency is an integer multiple of the frequency f1 and, preferably, at least ten times greater than the frequency f1. For example, the frequency f e is equal to the frequency of the clock signal generated by the clock 18.

  The converter 26 delivers at each sampling instant ti a sample ei whose value is equal to e (ti). The times ti are synchronized with the carrier p (t) thanks to the synchronization signal received. The computer 28 is, for example, a programmable computer capable of executing instructions recorded on an information recording medium 30. For this purpose, the support 30 includes instructions for executing the method of FIG. Irstructions are executed by the computer 28. Typically, the computer 28 will be a DSP (Data Signal Processing) computer. In this particular embodiment, a block 32 for estimating the position y (t) and a block 34 for estimating the speed 33 4t) for moving the part 4 from the signal e (t) are implemented in the computer 28. The block 32 comprises a memory 40 containing samples qi correlated with the values p (ti) of the carrier p (t) at time ti multiplied by the value hd (ti) of an impulse response hd (t ) of a n-order finite impulse response hd filter. The samples qi will be described in more detail with reference to FIG. 3. The block 32 comprises a generator 42, incorporating the memory 40, capable of delivering at each instant t 1 the sample q 1 to a first input of a multiplier 44. generator 42 has a synchronization port connected to the clock 18 for receiving the synchronization signal. In this way, the generator 42 is able to deliver the samples qi synchronously with the converter 26 and the carrier p (t). A second input of the multiplier 44 receives the sample el. The multiplier 44 calculates the product eigi and delivers this product to a first input of an accumulator 46. The accumulator 46 is designed to add to each other the eigi products delivered by the multiplier 44 during the whole period of a period robs observation. The accumulator 46 has an output which delivers, at the end of the period Tobs, the result of the accumulation which corresponds to an estimate (t) of the current position y (t). The block 34 is designed to extract from the samples e1 an estimate Mt) of the speed of the movable gate 4. The block 34 is, for example, identical to the block 32 except that the memory 40 of the block 34 comprises samples q'i different from those recorded in the memory 40 of block 32.

  The operation of the sensor 2 will now be described in more detail with regard to the method of FIG. 3. The method starts with a phase 50 for determining and recording the samples q i, q i in the different memories 40 of the blocks 32 , 34. Samples qi can be determined to estimate any of the 1 st derivatives of the y (t) position. In the particular case of the sensor 2, the block 32 corresponds to the case where d == 0 and the block 34 corresponds to the case where d = 1. Here, phase 50 is described in the particular case where d = 0. However, the methodology described in this particular case is also applicable to determine the value of the samples qi making it possible to extract any one of the d-th derivatives from the position y (t). Initially, during a step 52, the value of the observation period Tobs is fixed. The period Tobs is chosen equal to N times the period Te of sampling. Here N is an integer strictly greater than two and preferably at least greater than ten. Here, N is chosen greater than 100 or 1000. Preferably, the period Tobs is chosen to be an integer multiple of 1 / f1. Then, in a step 54, the order n of a finite impulse response filter h is chosen. Finite impulse response filters are also known as FIR (Finite Impulse Response) filters. These filters have a finite impulse response over time. By impulse response, the response of the filter to a Dirac or Kronecker pulse shaped input is designated. By definition, these filters are non-recursive, that is, there is no loopback or feedback from the filter output to its input. These filters have the advantage of being unconditionally stable unlike recursive filters or Kalman filters. The order n of a filter is defined as being the capacity of this filter to follow without a trailing error a signal whose waveform is defined by a polynomial of order n. Therefore, here, to not have any error

  of drag on the estimate of the derivative d-th ady (t), n is not

  chosen to be an integer greater than or equal to d. For example, in the remainder of this description, n is chosen equal to two despite the fact that d is equal to zero for block 32 and to one for block 34. This makes it possible to eliminate the trailing error during the acceleration of the part 4. Once the order n is set, in a step 56, the waveform of the impulse response h (t) of the filter h is determined. A multitude of possible waveforms can be chosen. In a first step, during an operation 58, we choose an equation for the impulse response comprising n + 1 unknown coefficients. In a first example, during the operation 58, a filter of polynomial form is chosen, that is to say whose impulse response is defined by the following equation:

  n h (t) = Eh, t 'if te [0, Toes] i = o = 0 otherwise where hi are the unknown coefficients of the filter h. (2) Then, during an operation 60, we solve a system with n + 1 equations, in which each of the n + 1 equations is defined by the following relation:

  Where m = d (3) 0 = 0 d (m ≠ d and rn n) where.

  m is an integer ranging from 0 to n,

  z is an integration variable,

  h (z) is the impulse response of the filter h, and

  - a is a predetermined constant different from zero.

  Here, a is chosen equal to (-1) d.d!, Where the symbol

      represents the mathematical factorial operation.

  The system of n + 1 equations defined by relation (3) can be solved either analytically by solving the system of equations, or numerically using error minimization software. With this latter method, the system of n equations can be solved whatever the equation chosen to define the impulse response h (t).

  For example, in the case where n = 2 and d = 0, the following function is defined: g = errpos2 + errvit2 + erracc2 (4) where. N-1 errpos = Eh (ti) e ù (ù1) 0 0! (5) \ .i = o NU1 errvit = E ih (ti) Te2 i = o (6) (7) N 12 y ,, 25 erracc = Ei h (ti) e3 i = o We understand the criteria errpos, errvit and erracc are all criteria that must be null to solve the system of n + 1 equations. Thus, if all things being equal, d is taken equal to two, that is to say that we are trying to build a demodulator that extracts error-free acceleration, the criteria to be minimized should then be defined as follows: N-1 errpos = E h (ti) ii = o N1 errvit = ih (ti) 2 i = o erracc = Ei2h (ti) T3 - (- 1) 22! i = o

  To determine the hi coefficients that minimize the function g defined by the relation (4), various known methods can be used such as the Nelder-Mead technique or the Simplex technique.

  It should be noted that the criteria to be minimized correspond each to one of the relations (3) respectively but expressed in numerical form and no longer using analytic functions.

  At the end of the operation 60, the coefficients hi have been determined so that it is possible to plot the index response and the impulse response of the filter

  r ... The graphs of FIGS. 4 and 5 represent, respectively, the impulse response and the index response obtained at the end of the operation 60 in the case of a filter h having the polynomial form defined by the relation (2). In FIGS. 4 and 5, the curves in solid lines, the dotted curves and the curves in broken lines respectively correspond to the case where the order n is equal to two, to one and to zero. In step 58, it is also possible to choose other forms of filters than the polynomial forms. For example, a polynomial form can be combined with any smooth smoothing function (t) (8) (9) (10). The impulse response of the filter is then defined by the following relation: h (t) = smooth (t) E ht `if te [0, robs = o = 0 sin on The function smooth (t) can be chosen to cancel the response impulse h (t) at the end of the period Tobs. This makes it possible to shorten the response time of the demodulator.

  Fig. 6 shows an example of smoothing functions that may be chosen to cancel the impulse response h (t) at time Tobs.

  FIGS. 7 and 8 show, respectively, the impulse and index responses obtained at the end of the operation 60 when the smoothing function chosen is that represented in FIG. 6.

  To achieve this result, smooth smoothing function (t) is chosen such that it is zero at time t = Tobs.

  Conversely, if we want to extend the response time of the demodulator, we will choose a function smooth (t)

  20 whose value at time t = Tobs is different from zero.

  One can also seek to cancel the impulse response at time t = 0, that is to say at the beginning of the observation period to cancel the slope at the start of the index response of the filter h. For this purpose,

  25 chooses a function smooth (t) which is zero at time t = 0. An example of such a function smooth (t) is shown in FIG. 9. FIGS. 10 and 11 represent, respectively, the impulse responses

  30 and indexes obtained at the end of the operation 60 when the smoothing function used is that represented in FIG. 9.

  A zero start slope corresponds to a synchronous demodulator that will react more smoothly to a sudden change in the signal y (t). Conversely, if it is desired to produce a synchronous demodulator which reacts abruptly at a step on the signal y (t), then a smoothing function is chosen whose value at time t = 0 is different from zero. One can also choose a smooth function (t) which makes it possible to obtain an index response having both a weak slope at startup (that is to say at time t = 0) and a short response time ( that is to say at the moment t = Tobs). For this purpose, a zero smoothing function is chosen for the instants t = 0 and t = Tobs. An example of such a smoothing function is shown in FIG. 12. The impulse and index responses obtained at the end of the operation 60 using the smoothing function of FIG. 12 are represented in FIGS. 13 and 14. respectively. It is also possible to choose a smoothing function that is not a continuous function of time. This makes it possible to introduce discontinuities in the impulse response h (t). Such a discontinuous smoothing function is shown in FIG. 15, while the impulse response obtained at the end of the operation 60 with this discontinuous smoothing function is shown in FIG. 16. In fact, the smoothing function is chosen. according to a predetermined template for the impulse or index response of the filter. In particular, it will be noted that it is not necessary for the smooth smoothing function (t) to be able to be put into the form of an equation. Indeed, the software that makes it possible to determine the hi coefficients makes it possible today to define the Smooth function (t) by a succession of points between the instants t = 0 and t == Tubs. Once the impulse response h (t) has been constructed, during step 56, a step 62 of constructing from the impulse response h (t) of an impulse response hd (t) making it possible to compensate for a predetermined delay At is realized. Here, the value of the delay Δt is chosen to correspond substantially to the time required for the multiplier 44 to calculate the product eigi and that the accumulator 46 performs an addition, as well as the duration of the transfer of the measurement to an external computer. The impulse response hd (t) is defined by the following relation: n dt (id) hd (t) = Efi (t) (d) id = 0si te [0; Tobs] if t [o; Tobs] (12) ) or . fi is the solution of the system of n + 1 equations defined by the relation (3) in the case where d = i, t is the time variable of the impulse responses.

  Once the impulse response hd (t) has been defined, in a step 64, the samples qi are calculated using the following relation: qi = hd (ti) (ti) (13) dù. hd (ti) corresponds to the value of the impulse response hd at the sampling instant ti, and r (ti) is the value of a predetermined signal r (t) at the sampling instant ti. The signal r (t) is chosen to be correlated with the carrier p (t) regardless of the observation period Tobs considered. We consider here that the signal r (t) is correlated with the carrier p (t) if the intercorrelation coefficient b defined by the following relation is different from zero:, p (u) r (u) of = b robs 0 JPeff reff where:

1 T '2 p, ff _ 1 p (u) d u robs 0

1 Tti, rej ~ _ 1 r2 (u) of the robs 0

  In order to improve the accuracy of the estimation of the dérivth derivative, the signal r (t) is chosen so that the absolute value of the intercorrelation coefficient b is strictly greater than 0.1 and preferably greater than 0. , 5 or 0.9.

  Typically, r (t) is a periodic signal of the same frequency as the carrier p (t).

  For example, here the signal r (t) is chosen equal to the carrier p (t) so as to obtain an intercorrelation coefficient b equal to 1.

  It is also understood that since the period Tobs is an integer multiple N of the period 1 / fl, then the number of samples qi stored in the memory 40 is reduced. In

  In this particular case, the value of the samples qi from one observation period to the next is the same, so that it is sufficient to record the samples that are necessary for a single observation period.

  Then, in a step 66, the samples qi calculated in step 64 are stored in the memory 40 of the block 32.

  Steps 52 to 66 are reiterated with the value d = 1 so as to determine the samples that must be recorded in the memory 40 of the block 34.

  Then, once all the samples q 'have been recorded in the memories 40, a phase 70 of use of the sensor 2 is used. Initially, during a step 72, the clock 18 emits the various signals synchronization required for the generator 12, the converter 26 and the computer 28. In a step 74, the generator 12 uses the synchronization signal to generate a sinusoidal magnetic field whose frequency is less than ten times the frequency of the clock 18. For example, the frequency of the excitation magnetic field is 1 MHz. The amplitude of this excitation magnetic field is modified as a function of the proximity of the magnetic plate 8 and therefore as a function of the position y (t). This corresponds to a modulation of the amplitude of the excitation magnetic field by the position y (t). It is of course assumed that the position y (t) is a low frequency signal with respect to the magnetic excitation signal. For example, the fundamental frequency f2 of the position y (t) never exceeds 100 kHz. During a step 76, the transducer 14 transforms the modulated excitation magnetic field into an electrical signal e (t) defined by the relation (1). In a step 78, the converter 26 samples at a frequency at least ten times higher than the signal frequency e (t). Then, during a step 80, at each sampling time ti, the converter 26 delivers the sample e, whose value is equal to e (ti).

  In parallel with the steps 74 to 80, during a step 82, the generator 42 delivers at each instant ti the sample q, corresponding. For this purpose, the generator 82 uses the synchronization signal transmitted by the clock 18 so that the samples qi and ei delivered at the same time - = i are both proportional to the same value p (ti). For example, the generator 42 reads from the memory 40, at the instant ti, the value of the sample qi to be delivered.

  The multiplier 44 calculates, during a step 84, the product eigi from the samples delivered at the same time by the converter 26 and the generator 42.

  Then, during a step 86, the accumulator 46 adds to each other the eigi products calculated during the same observation period.

  As long as the end of the observation period is not reached, steps 72 to 86 are repeated.

  When the end of the observation period is reached, during a step 88, the accumulated value in the accumulator 46 is delivered as corresponding to the estimate (t) of the position y (t) by the block 32. Block 34 functions identically to what has been described for block 32 and in parallel with the operation of block 32. At the end of each period

  observation, block 34 delivers an estimate y (t) of the

  4. If necessary, the estimate δ y (t) is multiplied by a calibration constant k to scale the estimate. For example, the constant k is determined by calibration or experimentally.

  FIG. 17 represents a sensor 100 of the angular position 0 (t) and of the angular velocity co (t) of an object 102 movable in rotation along a vertical axis Z perpendicular to the plane of the sheet. The position 0 (t) is marked with respect to an X axis perpendicular to the Z axis. A Y axis perpendicular to both the X and Z axes is defined to form an orthogonal coordinate system.

  The object 102 here has the shape of a disk whose center is located on the Z axis. The surface of this disk perpendicular to the Z axis is divided into two zones 104 and 106 made of materials, respectively, of conductivity C1 and C2. The conductivities Ci and C2 are different from each other. Preferably, the ratio between the conductivity C2 and C1 is greater than or equal to 1000. For example, here, the material forming the zone 104 is an electrical insulator whose conductivity C1 is less than 10 -10 S / m while the conductivity of the The material forming the zone 106 is an electrical conductor whose conductivity C2 is greater than 106 S / m. The juxtaposition of these two zones 104 and 106 therefore creates a conductivity breakage 108. Here, the zones 104 and 106 are arranged in such a way that the conductivity break 108 extends radially from the Z axis.

  For example, here the zones 104 and 106 are half-disks. The sensor 100 comprises: - a generator 110 of a sinusoidal excitation magnetic field of frequency f1r - two transducers 112 and 114 each adapted to convert the amplitude-modulated excitation magnetic field according to the position 0 (t) in a modulated high-frequency electric signal e (t), - two synchronous demodulators 116 and 118 able to estimate the position and the speed of the object 102 from the signal e (t), and a clean clock to generate a synchronization signal common to generator 110 and demodulators 116 and 118. To simplify FIG. 17, the clock has not been shown. Here, the transducers 112 and 114 are disposed substantially in the same plane perpendicular to the Z axis. The transducers 112 and 114 are arranged relative to each other so that when the signal measured by the transducer 112 is maximum, that measured by the transducer 114 is minimum and vice versa. For this purpose, in this embodiment, the transducers 112 and 114 are respectively disposed on the X and Y axes. Therefore, the transducer 112 measures the angle θ (t) between the X axis and the break 108 while the transducer 114 measures the angle O2 (t) between the Y axis and the break 108.

  The transducers 11.2 and 114 are respectively connected to the demodulators 116 and 118. The demodulator 116 is designed to extract an estimate O1 (t) from the position 6 (t) and an estimate w1 (t) of: a angular velocity. For this purpose, the demodulator 116 is, for example, structurally identical to the demodulator 16 except, if necessary, samples qi recorded in the memory of this demodulator. The demodulator 118 is able to extract an estimate a2 (t) from the angular position 8 (t) + 2 and an estimate cb2 (t) of the angular velocity. Finally, in this embodiment, the sensor 100 comprises a corrector 120 able to establish an estimate 0Wt) of the absolute position 0 (t) over an operating range of 0 to 360. The corrector 120 is also able to establish an estimate t) of the angular velocity of the object 102 and the direction of rotation of this object. For this purpose, the corrector is connected to a memory 122 containing the definition 124 of four curves 126, 128, 130 and 132 shown respectively in FIGS. 20 to 23. Curve 126 represents the evolution of the estimate OlW in function of the angle 0W.

  Curve 128 represents the evolution of the estimation α 2 (t) as a function of the angle θ (0. The curves 130 and 132 correspond, respectively, to the derivatives with respect to the angle θ of the curves 126 and The curves 130 and 132 make it possible to obtain for each value of the angle θ, respectively, the values of two correction coefficients pl and p 2. The curves 126 and 128 are, for example, measured experimentally. 132 are, for example, constructed by calculating the derivative with respect to the angle θ of the curves 126 and 128. Here, to simplify the illustration, it has been assumed that the transducers 112 and 114 are linear so that the evolution estimates 9, and e2 are linear as a function of the angle O. FIG. 18 shows in more detail an exemplary embodiment for the winding 22 of the generator 110. The winding 22 here comprises a single circular winding which is extends in a plane parallel to the X and Y. This winding is centered on the Z axis. The transducer 114 is here a differential transducer formed of two windings 114A and 114B wound in opposite directions and connected in series so that the absence of the object 102, the potential difference created between the ends of the two serially connected windings 114A and 114B is zero. The windings 114A and 1.14B extend only in a plane parallel to the X and Y axes. Here, the windings 114A and 114B are each disposed on either side of the Y axis. FIG. 19 shows in more detail an exemplary embodiment of the transducer 112. The transducer 112 is here a differential transducer formed of two windings 112A and 112B wound in opposite directions from each other and connected in series. Here, for example, the transducer 112 is derived from the transducer 114 by a rotation of 90 about the Z axis.

  The operation of the sensor 100 will now be described with reference to the method of FIG. 24. The method starts with a phase 150 for determining and recording the samples q i in each of the memories associated with the blocks 32 and 34 of the synchronous demodulators. For example, this step is performed as described with respect to step 50 of the method of FIG. 3 and will therefore not be described here in more detail. During the phase 150, the definition of the curves 126, 128, 130 and 132 is recorded in the memory 122.

  Then, a phase 154 of using the sensor 100 is used to estimate the angle θ (t) and the angular velocity. Initially, during steps 156 and 158, the estimates ê1 (t) and 22 (t) are extracted. amplitude modulated signals measured by the transducers 112 and 114. The steps 156 and 158 take place, for example, as described next to the phase 70. Then, the estimates 01 (t) and e2lt1 are transmitted to the corrector 120 which then proceeds to a step 160 of determining an estimate 0 (t) of the absolute angular position of the object 102 in the range [0; 360]. The accuracy of the estimate 0 (t) is typically less than 10. For this purpose, during an operation 162, the corrector 120 compares the absolute value of the estimate ê1 (t) with the absolute value of the estimate 02 (t). If the absolute value of the estimate λ 2 (t) is less than or equal to the absolute value of the estimate 0, (t), then, during an operation 27 164, the corrector 120 determines with the help of curve 128 what are the two values 0a and Ab possible for angle 0Wt). Then, during an operation 166, the corrector 120 selects from among the two possible values Oa and 0b, that corresponding to the estimate 6 (t) of the angle 0. For this purpose, during the operation 166, the corrector 120 uses the curve 126 and the value of the estimate 01 (t). More precisely, here only the sign of the estimate 01 (t) is used. Indeed, the values 0a and Ob correspond, necessarily to a negative value and a positive value of the estimate 0 ,. Thus, the sign of the estimate 01 (t) makes it possible to determine what is the value to retain for the estimation O. If, during the operation 62, the corrector 120 determines that it is the absolute value of the estimate 01 (t) which is strictly less than the absolute value of the estimate 02 (t), then it proceeds to a step 168 followed by a step 170, respectively identical to the steps 164 and 166 except that the estimates ê1 (t) and 02 (t) and curves 126 and 128 are used instead of estimates 02 (t) and ê1 (t) and curves 128 and 126. In other words, the roles of the values of estimates 01 (t) and 02 (t) and curves 126, 128 are reversed.

  In parallel with steps 156 and 158, in steps 172 e- = 174, the demodulators 116 and 118 construct, respectively, estimates GJ, (t) and 6) 21 of the angular velocity (t). For example, steps 172 and 174 are performed in a manner similar to what has been described in more detail with respect to step 70 of the method of FIG. 3 and will therefore not be described here in more detail.

  Then, the corrector determines, in a step 176, the estimation of the angular velocity t) using one of the following equations. ", t) = P2 (e (t)) 2 (t) 6) t) = P, (e (t)), (t) where: - pi (0 (t)) and p2 (a (t) ) are the values of the correcting coefficients, respectively pl and p2, corresponding to the estimate 0 (t) constructed at the same instant by the corrector 120. At the end of the step: 176, the corrector 120 delivers the estimate The sign of this estimate indicates the direction of rotation of the disk Figure 25 shows on the same graph the evolution as a function of time of the angular position 0 (t) (curve 200), of the estimate 6 (t) (curve 202) obtained using the method of FIG. 24 and estimation B '(t) (curve 204) obtained using a synchronous demodulator of the state of the art The curves were obtained by numerical simulation, respectively, of a model of the sensor 100 and a model of a conventional synchronous demodulator of the state of the art, more precisely the sensor 100 simulated here has been determined. using the following 25 numeric values antes: - Tobs = l ms, - Te = 100 ns, -n = 1, - p (t) is a sinusoid of frequency 1MHz, 30 d = 1, -h (t) = 4000-6000000t, hd (t) = h (t). (15) (16) As can be seen, the curve 202 is perfectly coincident with the curve 200 except after a sudden inflection of the curve 200. However, the error which appears between the curve 200 and 202 after this sudden inflection is caught up at the end of the Tobs period. Conversely, in the same situation, a conventional synchronous modulator has a trailing error that is not caught up. Many other embodiments are possible. For example, the clock 18 can be integrated inside the demodulator 16 or the generator 12. In the case where the clock 18 is integrated inside the demodulator 16, a synchronization port of the demodulator emits a signal of synchronization to the generator 12. In the case where the clock 18 is integrated inside the generator 12, a synchronization port of the demodulator receives the synchronization signal emitted by the generator 12. The clock can also be reconstructed or restored from the signal e (t) received by the synchronous demodulator. For example, a phase locked loop is used for this purpose. In this case, the synchronization port and the input port of s_Lgnal e (t) are merged. Here, the coefficients qi have been described as being stored inside the memory 40. As a variant, the coefficients q i are not stored beforehand in a memory but generated at time t i. For this purpose, for example, the different coefficients of the impulse response hd (t) are stored in the memory 40 and the generator 42 calculates at each instant ti the coefficient qi using the relation (13). Blocks 32 and 34 have been described as being realized by a software implementation. Alternatively, the blocks 32 and 34 are made by hardware blocks. These hardware blocks are, for example, made by an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). Here, the carrier has been described as a sinusoid. Alternatively, all functions known in advance and having a fundamental frequency strictly greater than the fundamental frequency of the position y (t) can be used. For example, the sinusoid can be replaced by a known pseudo-random sequence.

  In a simplified embodiment, the impulse response hd (t) is chosen to be equal to the impulse response h (t). Samples qi can also be obtained using the following relation: qi = khd (ti) p (ti) (15) where k is a calibration constant, for example, determined experimentally. This makes it possible to integrate the scaling operation in the blocks 32 and 34. The corrector 120 of FIG. 17 has been described in the particular case where the transducers 112 and 114 are linear. However, it is not necessary for the transducers to be linear. Under these conditions, the curves 126 and 128 are not linear and make it possible to compensate for these nonlinearities introduced by the transducers. The corrector 120 has been described in the particular case where it is used to correct the estimates of the angle 0 (t) and the angular velocity cw (t). However, what has been taught with respect to FIG. 17 can be generalized to the correction of any 1 st derivative of the 0W position. In the case where a d-th derivative has to be corrected, the definition of the d-th derivatives of the curves 126 and 128 is then stored in the memory 122 and used, for example, in place of the curves 130 and 132 when a correction step similar to step 176. The corrector 120 may also be used to correct the estimates of the th-derivatives produced by any synchronous demodulator, including a conventional synchronous demodulator. The sampling frequency f e may also be chosen as being a sub-multiple of the excitation frequency f 1. This allows sub-sampling, which can reduce the cost of analog-to-digital converters. It is also possible to choose a sampling frequency that is a non-integer multiple of the frequency f1. In this case, the samples that will have to be calculated as the samples are received. It is not necessary that the constant a of relation (3) be predetermined before solving the system of n + 1 equations. For example, the n equations of the following system are first solved to determine the impulse response h (t). Then, we verify that the impulse response h (t) found using the system of n equations above satisfies the following condition: 'robs f zmh (f) z) dz = a ≠ 0 / if m = d 0 In this case, the constant a is fixed after the system resolution. Thus, the impulse response h (t) sought must have only at least n unknowns.

It is also possible to choose an impulse response h (t) which has no polynomial coefficients such as hi above. For example, it is imposed that the impulse response h (t) is a temporal sequence of at least n + 1 values each selected from the group consisting of {-2 '; 0; 2 ') over the interval [0; Tobs], where j is a positive integer or zero. For example, here we choose j equal to zero and the values of h (t) are all different from 0 over the interval [0; Tobs]. Outside the interval [0; Tobs], the impulse response h (t) is equal to zero. The impulse response h (t) is thus formed of a succession of Mh + l steps in the interval [0; Tobs] • This impulse response is, for example, defined by the following relation: h (t) = h; if te [b ;; b; +1 [h (t) = 0 if te [O; TobS] b'b>; TobS> _b1 + l> b; > 0 cents - i is an integer ranging from 0 to Mh, where Mh is an integer greater than or equal to n, - the hi are predetermined predetermined values each selected from the group consisting of {-1; +1}, and - the bi are transition moments between the hi values. This impulse response therefore has Mh transitions from one hi value to another over the interval [0; Tobs]. The bi moments at which the transitions occur are determined so that this impulse response h (t) is a solution of the system of n + 1 equations defined by relation (3). For example, if Mh is equal to n + 1, these moments are determined to minimize the relation (4). The choice of such an impulse response h (t) is particularly advantageous when the signal r (t) is also composed only of values included in the same set as that used for the hi values. For example, the signal r (t) is also a sequence of steps defined by the following relation: r (t) = rk If tE [Ck; Ck + 1 [40 = 0 if te [0, Tobs] `lek; Tobs> Ck + l> Ck> 0 where: - k is an integer ranging from 0 to Mr, where Mr is a strictly positive integer, - the rk are predetermined values selected from the group consisting of 1-2 '; 0; +2 '}, and - the ck are transition moments between the values rk chosen for the signal r (t) to be correlated with the carrier p (t) over the interval [0; Tobs]. Under these conditions, by choosing hd (t) equal to h (t), the value of each sample qi is included in the set composed of {-2 '; 0; +2}. For example, if the values hi and rk are selected from the group consisting of {-1; +1}, then the value of each sample qi is also included in this set, which simplifies the manufacture of the multiplier for calculating products eigi.

Here, the relation (3) and other relations have been denoted in analog form. However, they can also be expressed in digital form. The transition from an analog to a digital form and vice versa is considered obvious to those skilled in the art.

It will also be noted that the resolution of the system of equations defined by relation (3) can involve the realization of approximations. When we say that the impulse response h (t) is a solution of the system of n + 1 equations defined by the relation (3), we mean that the impulse response h (t) constitutes either an exact solution of this system of equations, an approximation under constraints of this exact solution. The constraints may be imposed by the developer and may also be imposed by the computer in which the demodulation method is to be implemented. For example, one of the constraints may be the number of maximum bits available to encode one of the coefficients hi or one of the instants bi. Here, we consider that an impulse response h (t) is an approximation of an exact solution hs (t) of the system of equations defined by relation (3) if the intercorrelation coefficient d defined by the following relation is at least greater than or equal to 0.5: T (hs (u) h (u) J = d Tubs p, where sff h aeff where: - h (t) is the approximation of the exact solution, - hs ( t) is the exact solution of the system of equations obtained using one of the methods of resolution described previously, - hseff is defined by the following relation: 1 Tobs hseff = f hs (u) of the Tubs p - haeff is defined by the following relation: Tom hieff = T1 f h2 (u) of the ubs p Preferably, the intercorrelation coefficient d is greater than or equal to 0.9, or even greater than or equal to 0, 99.

Claims (11)

  1. Synchronous demodulation method enabling the extraction of the derivative d-th adYt ~ with respect to the time ad of a low-frequency signal y (t) from a modulated high-frequency signal e (t) defined by the relation following: e (t) = p (t) y (t) where: p (t) is a high frequency carrier whose time evolution is known and d is an integer greater than or equal to zero and when d is equal to zero, the derivative ay (t) _a is defined as being equal to y (t), ~ 0 this method comprising: - the transmission (72) or the reception of a synchronization signal making it possible to keep the demodulator in phase with the carrier p (t), - the analog-to-digital conversion (78) of the signal and) with a sampling period Te and the delivery at each sampling instant ti of a sample ei corresponding to the value of the signal e (t) at time ti, - the generation of samples qi, each sample qi being proportional to a value r ( ti) of a signal r (t) at time ti predetermined in advance to be correlated with the carrier p (t), the signal r (t) being considered as correlated with the carrier p (t) if the following equation is satisfied p (u) r (u) of ≠ 0 Tail 0 V Peff reff O L.. . u is the integration variable ,. Tobs is a period of observation that a sampling period Te, integer greater than or equal to two, 1 Th2 2 ~, peff = J p (u) of Tobs 0 reg- -T1 J r (u) of, and obs 0 - the delivery (82), at each instant ti, with the help of the synchronization signal, the sample qi so that the temporal sequences of samples qi and ei delivered at the same times ti are both correlated in the same sequence of values p (ti), - the calculation (84) of the product eigi from the samples ei and qi delivered at the same time, - the addition (86) to each other of all eigi products calculated during the observation period Tobs, the result of the addition corresponding to the estimated value of the derivative adY (t) ', characterized in that each sample qi delivered is proportional to the result of the multiplication of the value r ti) of the signal r (t) at time ti by the value hd (ti) of an impulse response hd (t) of an impulse response filter finite onal of order n greater than or equal to d, the impulse response hd (t) being a function of an impulse response h (t) of a n-order finite impulse response filter which is a solution or approximation 25 of a solution of a system with n + 1 equations, where each of the n + 1 equations is defined by the following relation: Tub, f zmh (z) dz = a if m = d 0 = 0 V (m ≠ d and mn) where. n is the order of the filter, N times greater where N is a number m is an integer ranging from 0 to n, Tubs is the observation period, z is the integration variable, and - a is a constant different from zero.   2. Method according to claim 1, wherein the signal r (t) satisfies the following inequality: p (u) r (u) of> - 0.5 o Peff reff   The method of claim 1 or 2, wherein the impulse response h (t) is defined by the following relationship. n h (t) = smooth (t) • h; t 'if t e [0, Tobs = o = 0 otherwise where. - hi are constant coefficients, - n is the order of the filter, - smooth (t) is a non-polynomial function chosen to approximate the waveform of the impulse response h (t) of a predetermined template.   4. The method of any of the preceding claims, wherein the impulse response hd (t) is equal to the impulse response h (t).   The method of any of the preceding claims, wherein the impulse response h (t) is a sequence of steps defined by the following relationships: h (t) = h; if te [b ;; b1 + 1 [h (t) = O if t e [0; Tobs dbi; Tobs> b, 1> b; > 0 25 where. - i is an integer ranging from 0 to an integer Mh greater than or equal to n, robs- hi are predefined values in advance each selected from the group consisting of {-2 '; 0; +23} where j is a positive integer or zero, and - the bi are moments of transition between the values 5 h_, these bi being chosen so that h (t) is a solution of the system of n + 1 equations, • the signal r (t) is a series of steps defined by the following relation r (t) = rk if tE [Ck; Ck + 1 [0 = 0 if to [O; Tubs] VCk; Tobs ~ Ck + l> Ck> 0 10 where: - k is an integer varying from 0 to a positive integer Mr, - the ri are predetermined values in advance, each of these values being selected from the group consisting of {-15 2 '; 0; + 2'1, and - the ck are moments of transition between the values rk chosen so that the signal r (t) is correlated to the carrier p (t) over the interval [0; tobs]   6. The method of claim 5, wherein j is zero.   7. A method according to any one of claims 1 to 6, wherein the impulse response hd (t) is defined by the following relation: n dt (i-d) hd (t) ù ~ fi (t) (1d)! if tE [O; Tobs] d = 0 if t e [O; Tobs] 25 where. -At is a predetermined time interval, - fi (t) is the solution of the system of n + 1 equations in the case where d is equal to i.   8. Method according to any one of the preceding claims, wherein the order of the filter n is greater than or equal to 1 and preferably greater than or equal to 2 or 3.   An information recording medium (30), characterized in that it includes instructions for executing a synchronous demodulation method according to any one of the preceding claims, when said instructions are executed by a electronic calculator.   Synchronous demodulator capable of extracting the derivative d-th adyt) with respect to the time of a low frequency signal y (t) from a modulated high frequency signal e (t) defined by the following relation: t) = p (t) y (t) where. p (t) is a high frequency carrier whose time evolution is known and d is an integer greater than or equal to zero and when d is equal to zero, the derivative aoY (t) is defined as equal to ay (t) - ao this demodulator comprising: - at least one synchronization port adapted to transmit cu receive a synchronization signal for maintaining the demodulator in phase with the carrier p (t), -an analog-digital converter (26) equipped with an input for receiving the signal e (t) to be sampled with a sampling period Te and an output delivering at each sampling instant ti a corresponding sample ei. to the value of the signal e (t) at the instant ti, a generator (42) of samples each sample qi being proportional to a value r (ti) of a signal r (t) at the instant ti predetermined at the advance to be correlated to the carrier p (t), the signal r (t) being considered as correlated with the carrier p (t) if the following equation is satisfied 1 Tl, p (u) r (u) 1 of ≠ 0 Tobs 0 Jpeff reff where. u is the integration variable, • Tobs that a sampling period Te, where N is an integer greater than or equal to two, 1 ln, 2 p, ff = fp (u) of Tobs o 1 "- 2 Since this generator is adapted, by means of the synchronization signal, to deliver at each instant t i the sample q i so that the time sequences 15 of samples q i and e i delivered to the the same instants ti are both correlated to the same sequence of values p (ti), - a multiplier (44) able to calculate the product eigi from the samples ei and qi delivered at the same time by the analog-digital converter and the Generator, - an accumulator (46) able to add to each other all the eigi products calculated by the multiplier during the observation period Tobs, the result of these additions at the end of the observation period corresponding to the estimated value of the at) derived ad "'ad characterized in that the generator is adapted so that the sample crack qi delivered is proportional to the result of the multiplication of the value r (ti) of the signal r (t) at time t i by the value hd (t i) of a response is a period of observation n times greater10 impulsive hd (t) of a pulse response filter Finite of order n greater than or equal to d, the impulse response hd (t) being a function of an impulse response = h (t) of a filter finite impulse response of order n which is a solution or approximation of a solution of a system with n + 1 equations, where each of the n + 1 equations is defined by the following relation: rbz f zmh (z) dz = a if m = d 0 = 0 d (m ≠ d and m <_n) where. - n is the order of the filter, - m is an integer varying from 0 to n, - Tobs is the observation period, - z is the integration variable, and - a is a constant different from zero.   11. A sensor of a magnetic field obtained by amplitude modulating a high frequency carrier p (t) by a low frequency signal y (t), this sensor comprising: a transducer (14) capable of converting the high frequency magnetic field into an electrical signal e (t) proportional to the modulated high frequency magnetic field, and - a synchronous demodulator (16) capable of extracting the derivative d-th a ~ t ~ with respect to the time of the signal y (t) from the signal e (t), characterized in that the synchronous demodulator is according to claim 10.