WO2004008339A1 - Procede et dispositif d detection d'une similarite de la forme de signaux echantillonnes - Google Patents

Procede et dispositif d detection d'une similarite de la forme de signaux echantillonnes Download PDF

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Publication number
WO2004008339A1
WO2004008339A1 PCT/NL2003/000518 NL0300518W WO2004008339A1 WO 2004008339 A1 WO2004008339 A1 WO 2004008339A1 NL 0300518 W NL0300518 W NL 0300518W WO 2004008339 A1 WO2004008339 A1 WO 2004008339A1
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WIPO (PCT)
Prior art keywords
fragment
coefficients
function
sampled signal
polynomial
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Application number
PCT/NL2003/000518
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English (en)
Inventor
Antonius Johannes Robert Maria Coenen
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Technische Universiteit Delft
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Application filed by Technische Universiteit Delft filed Critical Technische Universiteit Delft
Priority to AU2003254967A priority Critical patent/AU2003254967A1/en
Publication of WO2004008339A1 publication Critical patent/WO2004008339A1/fr

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/21—Interference related issues ; Issues related to cross-correlation, spoofing or other methods of denial of service
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/22—Multipath-related issues
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations

Definitions

  • the present invention relates to a method for detecting a similarity in shape between a first and a second sampled signal fragment.
  • Many signals for example digital GSM signals, or the satellite signals used in GPS navigation systems
  • Many signals often have many repetitions of the same continuous signal (fragment) or at least a similarly shaped signal (fragment).
  • sampled signals are usually processed (with a specific sampling interval), it is not possible directly to define a correspondence between two temporally separated signal (fragments). The same amplitudes will hardly ever occur at the positions of the equidistant signal samples within the repeated identical signal (fragments) .
  • the sampled signals may be signals in the time domain, but also in the space domain (for example video signals), correlation domain, frequency domain, etc.
  • the object of the present invention is to produce a method for accurate and direct definition of domain parameters between two sampled identical or similarly shaped signals.
  • the correspondence is defined as a correspondence of the normalized derivative of the first fragment function and the normalized derivative of the second fragment function. It is thereby also possible to compare signals which have an identical shape, including identical amplitudes as a special case, with one another and to define the domain interval between corresponding signal fragments. In the case of multipath interference in GPS, two temporally consecutive correlation pulses, for example, will often have the same shape.
  • a domain interval for example the time interval, can be defined in a highly accurate manner as an integral number of sampling intervals st plus the displacement operator d, which is defined as the root of the equation
  • coefficients ao, a 1? au. and a ⁇ are polynomial coefficients of a second-order approximation of the first fragment function
  • coefficients ao v , a t v , au v and a R v are polynomial coefficients of a second-order approximation of the second fragment function
  • S sm is an operator equal to
  • the method can be further simplified in a further embodiment by defining a domain interval, for example the time interval, as an integral number of sampling intervals st, plus the displacement operator d as a sampling interval fraction which is equal to
  • coefficients ao and a. are polynomial coefficients of a first-order approximation of the first fragment function and the coefficients ao v , a ⁇ v are polynomial coefficients of a first-order approximation of the second fragment function.
  • These first-order polynomial coefficients can be implemented in a simpler, faster and more convenient manner. For specific classes of shape correspondences (for example in sinusoidal and sawtooth signals), a highly accurate definition of the domain interval is also made possible with this embodiment.
  • the correspondence is defined as a correspondence of the amplitude of the first and the second fragment functions.
  • the signal fragments must correspond exactly, not only in terms of shape, but also in terms of amplitude. This can often be applied in defining domain intervals between signal fragments in a signal originating from the same source.
  • a domain interval for example the time interval, is defined as an integral number of sampling intervals st, plus the displacement operator d, which is defined as the root of the equation
  • the root definition required here is arithmetically simpler to perform than the corresponding root definition in the embodiment in which shape correspondence is sought.
  • the coefficients ao and aj are polynomial coefficients of a first-order approximation of the first fragment function and the coefficients ao v , a ⁇ _ v are polynomial coefficients of a first-order approximation of the second fragment function.
  • specific types of signal fragments in particular for example sinusoidal and sawtooth signals
  • the root definition is performed with the aid of a series expansion.
  • a series expansion for defining roots of a quadratic equation is known per se to the person skilled in the art. In implementations of the method, a series expansion of this type can offer advantages in terms of complexity and speed.
  • the detection of the domain interval between two sampled signal fragments can be advantageously used in numerous applications, for example in positioning (GPS, LORAN-C and other positioning or navigation systems), multipath suppression (all kinds of applications in which radio waves are used), improvement of the signal-to- noise ratio in all kinds of signals, etc.
  • Other examples relate to synchronization applications, such as the automatic tuning of receivers to transmitted signals, extremely accurate phase comparators for sinusoidal signals, extremely accurate measurement of frequencies in a much shorter measuring time than in conventional frequency- measuring equipment, and the elimination of (time) digitization errors in transducers in which the measured variable (e.g. temperature) is converted into a pulse duration.
  • the present invention relates to a device for detecting a similarity in shape between a first and a second sampled signal fragment, whereby the device comprises an inverse interpolator for receiving a sampled signal fragment and for defining polynomial coefficients of a fragment function as the inverse interpolations of the sampled signal fragment, and a processing unit which is connected to the inverse interpolator and which is designed to carry out the present method.
  • the device may advantageously comprise delay elements, adder elements, inverter elements, multipliers and/or arithmic logic units which enable simple and efficient implementation of the method in the device.
  • Fig. 1 shows an illustration of a signal reconstructed from signal patterns in the time domain
  • Fig. 2 shows an embodiment of a digital filter for defining polynomial coefficients
  • Fig. 3 shows an illustration of two signal fragments with a corresponding shape
  • Fig. 4 shows an illustration of possible time relationships between the first and the second signal fragment, where d is negative
  • Fig. 5 shows an illustration of further possible time relationships between the first and the second signal fragment, where d is positive
  • Fig. 6 shows an embodiment of a possible implementation of a first-order polynomial approximation of a signal fragment
  • Fig. 7 shows an embodiment of a possible implementation of a second-order polynomial coefficient generator with eight inte ⁇ olation filter coefficients; and, Fig. 8 shows an illustration of the correlation between the time interval definition error and the oversampling factor.
  • the present invention is explained with reference to examples in which similarity in shape is detected in the time domain.
  • the present invention can also be applied to signals in other domains, such as the space domain (for example video signals), the frequency domain (for example speech analysis, narrowband interference suppression, synchronisation/tuning), the correlation domain (for example multipath suppression in GPS and CDMA receivers), etc.
  • time parameters must often be measured in relation to time-continuous signals. If the signals are (digital) sampled signals (therefore, in fact strings of numbers), it is often difficult or impossible to carry out time measurements with sufficiently high accuracy purely on the basis of oversampling. This is the case, for example, in positioning systems, in which time measurements are used to define distances.
  • the present invention is based on the principle that it is possible implicitly to reconstruct signal fragments from the string of digital numbers by applying inverse interpolation, and then performing time measurements relating to the interval between signal fragments with an identical shape.
  • many of the sampled signals often involve signals in which specific patterns or shapes of signal fragments occur repeatedly.
  • Fig. 1 shows an illustration of a reconstructed signal fragment (broken line) from a series of sampled values (the dots on the reconstructed signal).
  • Figure 2 shows a general design for a second-order polynomial coefficient generator.
  • a polynomial coefficient generator of this type is discussed, for example, in
  • the search for shape correspondence is geared toward a direct measurement of the time interval between related fragment functions of two similarly shaped signal fragments.
  • Fig. 3 shows two such fragment functions next to one another.
  • the polynomial coefficient vector A can be calculated in each case in the manner described above for the first signal fragment.
  • the polynomial coefficients Ai in relation to the first (non-delayed) signal fragment, must be compared with the polynomial coefficients Aiv of the second (to be delayed) signal fragment with a comparable shape. These polynomial coefficients Aiv are found by delaying the first values Ai by the aforementioned integral multiple of sampling intervals st within ti. [0029] Generally, for the ⁇ -th sample, the A factor in formula 2 is represented as:
  • two alternative embodiments exist for finding the shape correspondence between the first and second signal fragments.
  • One is based on a comparable shape, and the other on identical amplitudes.
  • Both alternative algorithms are based on the fault-compensating effect of two mirrored polynomial pairs. From two mirrored polynomial pairs, two roughly identical time measurements (ti) are implicitly calculated at time locations separated by a time fraction ⁇ *,-, which, through combination, thus compensate their reciprocal spectral amplitude deformation error for all possible values of t .
  • Fig. 4 and 5 show each of the two sampling interval pairs where the inverse interpolation will take place.
  • Two similarly shaped curves are deemed to be present within each sampling interval pair (not shown for the sake of clarity), with one curve in the interval on the left and one curve in the interval on the right.
  • the arrows in the intervals represent the interpolated sampling values where the similarity in shape occurs. The arrows are thus distinguished by a time period t,.
  • the DC term (ao) of the polynomial which represents the arrow amplitude in the middle of the interval is obtained by using this value in formula (1).
  • the required computing capacity can be drastically reduced by using a first-order polynomial approximation with two coefficients.
  • equation (12) is simplified to: given that all second-order terms are equal to zero in equation (12).
  • Fig. 6 shows an implementation of a first-order polynomial coefficient generator for obtaining the coefficients ao and aj.
  • a first-order polynomial coefficient generator can also be used in which a larger number of points of the sampled signal are included than in the implementation shown in Fig. 6, in which only two points are included. A time interval error accuracy is thereby achieved which is still lower by a factor of 4 than a second-order polynomial approximation with a comparable number of points N, but this is achieved without having to determine a root.
  • An alternative method is explained below, in which, as already indicated above, the similarity in amplitude between the two (reconstructed) signal fragments is used rather than the similarity in shape.
  • the polynomial representation as indicated in formula (1) can be directly used for this purpose.
  • two situations are distinguished, i.e. t ⁇ st and t ⁇ >st.
  • the final amplitude comparison function (shape correspondence) can be derived from the formulae (17), (20), and (21) (in matrix notation):
  • N indicates the number of points of the sampled signal, between which interpolation takes place, and thereby N similarly determines the number of interpolation filter coefficients.
  • Fig. 8 does not indicate the linear interpolator curves for more points (N>2), which will produce a higher-quality result.
  • the illustration shows that accuracy increases if the oversampling factor increases (to the right along the horizontal axis) and if the polynomial order increases.
  • N l, zeroth-order
  • 10 "2 N>1, first and second-order polynomial approximation
  • an accuracy can even be achieved which is higher by a factor of 10. Since, in periodic signal forms, the resulting time measurement errors also reveal a periodic pattern, a further improvement in accuracy is achieved if the time measurement values are averaged over the periodicity duration (and multiples thereof). The effect of intrinsically present noise is thereby also reduced.
  • Fig. 7 shows a possible implementation of a device for determining the time interval between two signal fragments with an identical shape.
  • the device uses a polynomial coefficient generator which is shown on the left-hand side.
  • the polynomial coefficient generator comprises delay elements, adder elements and multiplier elements.
  • the digital signal is fed in on the left-hand side and the polynomial coefficients relating to the sampling time concerned are delivered on the right-hand side.
  • These polynomial coefficients are then fed to a processing unit 10, such as a digital signal processor or a computing unit, which carries out the method described above and performs the displacement operator d as shown.
  • the processing unit 10 can of course also be set up to determine the integral number of sampling intervals st and to produce the time interval t ⁇ between two similarly shaped signal fragments.
  • the parameters CCi and C 2 ...C 4 which are used are derived from the following formulae in the case of a Lagrange approximation:
  • the quality of the definition of the polynomial coefficients may be negatively influenced by quantization noise, for example through the use of a finite word length in the sampled signal sequences. It may occur, for example that two consecutive samples are occasionally identical due to quantization effects. In this case, the first derivative will be zero instead of a more accurate value if no quantization error is present. This can be resolved by using more space between the quantization samples, by, for example, using delays of z "L instead of delays of z "1 , where L>1.
  • the quantization error will then decrease by a factor L.
  • the oversampling factor will simultaneously increase in proportion, and thereby the interpolation quality also. This option can therefore only be used if the oversampling factor is selected as being a factor L greater than is necessary for a desired final accuracy.
  • signals without bandwidth can preferably be used in order to achieve the highest possible accuracy in time measurement. In the case of transducers, in which the information on the measured variable is enclosed in the pulse duration of a time- continuous signal, the vertical edges must be converted into sloping lines with a fixed angle which is less than 90°.
  • the present invention can be applied to two consecutive signal fragments, which may or may not originate from the same signal source. However, the invention can also be applied to one signal fragment of a defined shape and a locally stored signal fragment, with which the exact moment of occurrence of the incoming signal fragment could then be defined (for example in GPS correlation peaks).
  • the highest possible measurement accuracy is achieved here if the incoming signal shape coincides within the resolution of one sampling period with the position of a stored reference signal shape.
  • a special feature here is that this sampling situation can already be predicted in immediately preceding sampling periods. Depending on the bandwidth limitation applied to the signals which are used, the measurement accuracy and therefore the prediction accuracy will decrease as the resolution in the coincidence differs two and more sampling periods.
  • the degree of similarity in shape In detecting multipath interference, it is thus possible to define the type of occurring multipath interference by determining the degree of correspondence.

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Abstract

L'invention porte sur un procédé de détection d'une similarité en forme entre un premier et un second fragment de signal échantillonné. Le procédé consiste à : former une première fonction de fragment provenant du premier signal échantillonné par interpolation inverse, définir un intervalle de domaine, par exemple l'intervalle de temps, en recherchant le second fragment du signal échantillonné dont une seconde fonction de fragment à interpolation inverse correspond à la première fonction de fragment. Le procédé est utilisé, par exemple, dans le domaine temporel (définition des intervalles de temps, par exemple, de signaux GPS), le domaine spatial (par exemple, des signaux vidéo), le domaine de fréquence (par exemple, l'analyse vocale, la suppression des interférences en bande étroite, accord/accord), le domaine de corrélation (par exemple, la suppression multivoie dans les récepteurs GPS et les récepteurs AMDC), etc.
PCT/NL2003/000518 2002-07-16 2003-07-16 Procede et dispositif d detection d'une similarite de la forme de signaux echantillonnes WO2004008339A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU2003254967A AU2003254967A1 (en) 2002-07-16 2003-07-16 Method and device for detecting a similarity in the shape of sampled signals

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NL1021085 2002-07-16
NL1021085A NL1021085C2 (nl) 2002-07-16 2002-07-16 Werkwijze en inrichting voor gelijkvormigheidsdetectie in bemonsterde signalen.

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2005078657A1 (fr) * 2004-02-14 2005-08-25 Koninklijke Philips Electronics N.V. Detection de filigrane par analyse de forme par correlation
US7826561B2 (en) * 2006-12-20 2010-11-02 Icom America, Incorporated Single sideband voice signal tuning method
CN101893714A (zh) * 2010-07-09 2010-11-24 中国科学院测量与地球物理研究所 全球卫星导航系统广播电离层时延修正方法

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4809249A (en) * 1986-04-21 1989-02-28 North American Philips Corporation Apparatus for ultrasound flow mapping

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4809249A (en) * 1986-04-21 1989-02-28 North American Philips Corporation Apparatus for ultrasound flow mapping

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2005078657A1 (fr) * 2004-02-14 2005-08-25 Koninklijke Philips Electronics N.V. Detection de filigrane par analyse de forme par correlation
US7826561B2 (en) * 2006-12-20 2010-11-02 Icom America, Incorporated Single sideband voice signal tuning method
CN101893714A (zh) * 2010-07-09 2010-11-24 中国科学院测量与地球物理研究所 全球卫星导航系统广播电离层时延修正方法

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AU2003254967A1 (en) 2004-02-02

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