WO2007144013A1

WO2007144013A1 - Method and system for measuring the velocity of a moving object

Info

Publication number: WO2007144013A1
Application number: PCT/EP2006/005723
Authority: WO
Inventors: Riccardo Tebano; Carlo Battistella; Stefano Serra
Original assignee: Pirelli & C. S.P.A.
Priority date: 2006-06-14
Filing date: 2006-06-14
Publication date: 2007-12-21
Also published as: EP2027473A1

Abstract

The invention relates to a method and a system for measuring the velocity of a moving object. The method comprises: acquiring from a first sensor first data associated to the passage of the moving object in the sensitivity field of the first sensor and representative of a physical quantity variable with the object passage; calculating from the first data a time variation of the physical quantity; acquiring from a second sensor spaced from the first sensor by a known distance second data associated to the passage of the moving object in the sensitivity field of the second sensor and representative of the physical quantity; calculating from the first and second data a first and a second numerical quantity representative respectively of a time derivative and a spatial derivative of the physical quantity in a given time interval; and calculating the velocity of the moving object in the given time interval as a function of the first and second numerical quantity; wherein the method comprises the step of comparing the time variation of the physical quantity with a first threshold value and at least the step of calculating the velocity is conditional upon being the time variation of the physical quantity in the given time interval above the first threshold value. A system based on the above method is also disclosed.

Description

METHOD AND SYSTEM FOR MEASURING THE VELOCITY OF A MOVING

OBJECT

* * * * *

Field of the invention The present invention generally relates to methods and systems for measuring the velocity of moving objects, for example to the field of measuring the speed of vehicles on a road.

Background of the invention Traffic parameters like average speed, density, and flux have to be accurately known in order to perform traffic monitoring and management. The real time knowledge of the number and the speed of the vehicles passing by many key positions in a road network would allow a reliable computing of such traffic parameters and an effective dynamic traffic management. Throughout the present description, the term 'velocity' will refer to the velocity vector, while the term 'speed' will refer to the modulus of the velocity vector, i.e. the scalar velocity of a moving object.

Vehicle speed measuring devices are known which are based on a pair of magnetic sensors installed at a prescribed distance in a longitudinal direction. The two signals generated by the sensors when the vehicle passes are compared to obtain the time delay and the speed of the vehicle is computed from the time delay and the sensor distance.

The Applicant has found that the prior art devices have several drawbacks. In order to reach a suitable level of accuracy of speed evaluation using prior art devices based on the signal time delay, either the sampling rate of the sensor signals needs to be high (e.g., greater then or equal to several KHz) or the sensor spacing has to be large (e.g., greater then or equal to several tens of cm) or both. High sampling rate is detrimental in that it increases the power consumption of the speed measurement system, which is especially important in case the power supply relies solely on battery ('stand-alone devices'). It also requires large memory and/or computational resources in order to store and/or process the data, thus contributing to the high power consumption. Moreover, it increases the cost, the complexity and the reliability of the measuring system. On the other end, a large distance among the two sensors causes an increase in the size of the device comprising the sensors, which is particularly important when the device is to be buried, e.g. in the asphalt or concrete of a road pavement and, for example, linked with a data gathering structure by means of wireless transmission.

Another drawback of some prior art devices is that they need hard computational work, and thus large computational hardware, in order to perform the mathematics involved. This drawback is particularly important in case of stand-alone velocity measuring systems, in that it not only requires large power consumption, but also prevents from manufacturing miniaturized and low cost measuring systems. US patent n⁰ 5,331,276 entitled "Apparatus for passively measuring the velocity of a ferrous vehicle along a path of travel" discloses a passive velocity measuring system which includes first and second biaxial fluxgate magnetometers separated by a known distance and oriented precisely with respect to one another and with respect to the path of travel of a ferrous vehicle whose velocity is to be determined. An indication of the velocity of the vehicle is obtained from the ratio of the time derivative of the magnitude of the vehicle's magnetic induction to the negative of the spatial derivative of this same quantity.

The Applicant has found that there is a need for methods and systems for measuring the velocity of moving objects with reduced power consumption. Preferably, the above systems should be suitable to work long time in a stand-alone configuration (battery-only power supply). It is also desired that the velocity measuring systems be accurate, compact, fast, miniaturized, do not require large memory and/or computational resources and have low sampling rate. In addition, the velocity measuring systems should preferably be low-cost, reliable and apt to high volume and/or high yield manufacturability.

Summary of the invention

The Applicant has found a method and a system for measuring the velocity of moving objects which can solve one or more of the problems stated above. The solution of the present invention is simple, low cost and allows a high yield.

The Applicant has developed a method of measuring the velocity of an object as a function of at least a spatial derivative and at least a time derivative of a physical quantity, wherein the spatial derivative and the time derivative are approximately evaluated from at least two measurement signals acquired respectively by at least two sensors of the physical quantity spaced apart by a given distance. The Applicant believes that, in such a method, the fact that the velocity evaluation is conditional to a time variation of the physical quantity being above a certain threshold, wherein said time variation of the physical quantity is computed from the measurement signal from the first sensor, allows very low power consumption of the sensing device, while assuring an accurate velocity evaluation, at least on a statistical basis. In fact, the above method allows consuming power resources for velocity calculation solely when it is verified, with an acceptable degree of confidence, a condition suitable for an accurate velocity determination. »

In order to further reduce power consumption, the data from the second sensor used in the velocity calculation are preferably acquired solely when the above condition is verified. In this way, the use of the time variation as control parameter synergistically allows the monitoring of the condition suitable for velocity calculation by way of monitoring the physical quantity solely by the first sensor.

It is believed that the method and system of the present invention can be applied to the determination of the velocity of any traveling object provided that there exists a physical quantity which is subject to a change in correspondence to the passage of the object and which could be sensed by means of suitable sensors placed near the object trajectory. The term 'near' refers to the case wherein the object passes close enough to the sensor so that the latter can sense the presence of the object. In other words, the object is in the sensitivity field of the sensor, such sensitivity field depending, e.g., upon the nature and dimension of the object. For the invention to be implemented, at least two distinct sensors are needed. They are advantageously of the same kind, i.e., they are apt to measure the same physical quantity(ies). They are preferably fixed in the frame of reference with respect to which the object velocity has to be known.

An exemplary application of the present method is the speed measurement of magnetically permeable masses passing near a couple of magneto-resistive sensors, which are placed at a known distance with respect to one another and along the direction the object is expected to travel. The speed may be computed from the ratio of the difference between the data from the time series profiles of the first sensor and the second sensor at the same instant of time (which approximates the space derivative when divided by the known sensor distance), and the difference between two consecutive data in the time series profile of one of the two sensors (which approximates the time derivative when divided by the known time distance).

The Applicant has found that the system and method described above may be advantageously applied to a method and system for measuring the speed of a vehicle along a roadway. Among the advantages of the present invention is that the sensing device has small overall dimensions.

Several algorithms for velocity evaluation will be presented in the following as exemplary embodiments of the present invention. Remarkable reduction of the energy consumption and of the overall dimensions of the systems for sensing the velocity with respect to known systems is possible by implementation of such algorithms.

The Applicant has also found that the systems and methods described above may be advantageously used in a system for traffic monitoring.

According to a first aspect of the present invention, a method for measuring the velocity of a moving object as set forth in claim 1 is provided. The method comprises

- acquiring first data from a first sensor, said first data being associated to the passage of the moving object in the sensitivity field of the first sensor and being representative of a physical quantity variable with the object passage;

- calculating from said first data a time variation of said physical quantity; - acquiring second data from a second sensor spaced from the first sensor by a known distance, said second data being associated to the passage of the moving object in the sensitivity field of the second sensor and being representative of said physical quantity;

- calculating from said first and second data a first and a second numerical quantity representative respectively of a time derivative and a spatial derivative of said physical quantity in a given time interval; and

- calculating the velocity of the moving object in said given time interval as a function of said first and second numerical quantity; wherein the method comprises the step of comparing said time variation of said physical quantity with a first threshold value and at least the step of calculating the velocity is conditional upon being said time variation of said physical quantity in said given time interval above said first threshold value.

Preferred embodiments of the method above are set forth in dependent claims 2 to 13. In a preferred embodiment, the method above further comprises the steps of calculating from said first and second data a further quantity representative of a space variation of said physical quantity, wherein at least the step of calculating the velocity is also conditional upon the value of this further quantity in said given time interval.

According to another aspect of the present invention, as set forth in the appended claim 14, it is provided a method for monitoring road traffic comprising a method for measuring the velocity of a vehicle according to the method above, wherein the moving object is the vehicle,.

According to another aspect of the present invention, the invention relates to a system for measuring the velocity of a moving object as set forth in claim 15. The system comprises a sensing device comprising at least a first and a second sensor spaced apart by a known distance, a processing unit and a connection operatively connecting said sensing device and said processing unit, wherein the processing unit is configured for operating the system according to the following steps:

- acquiring first data from the first sensor, said first data being representative of the physical quantity and being associated to the passage of the moving object in the sensitivity field of the first sensor;

- calculating from said first data a time variation of said physical quantity;

- comparing said time variation of said physical quantity with a first threshold value;

- acquiring second data from the second sensor, said second data being associated to the passage of the moving object in the sensitivity field of the second sensor and being representative of said physical quantity;

- calculating the velocity of the moving object in said given time interval as a function of said first and second numerical quantity; wherein at least the step of calculating the velocity is conditional upon being said time variation of said physical quantity in said given time interval above said first threshold value. Preferred embodiments of the system above are set forth in dependent claims 16 to 26. In one embodiment, in the system above the processing unit is configured for operating the system according to the further following step:

- calculating from said first and second data a space variation of said physical quantity; wherein at least the step of calculating the velocity is also conditional upon the calculated value of the space variation of the physical quantity in said given time interval.

According to another aspect of the present invention, a traffic monitoring system including the system above is provided, as set forth in the appended claim 27.

In a further aspect, as set forth in claim 28, the invention relates to a computer program product loadable into the memory of a computer, comprising software code portions for performing the steps of the method of the first aspect of the invention, the computer program product being adapted, when run on a computer, to calculate the velocity of the moving object.

Brief description of the drawings

Additional features and advantages of the present invention will be made clear by the following detailed description of embodiments thereof, provided merely by way of non- limitative examples, description that will refer to the annexed drawings, wherein:

Figure 1 is a schematic diagram showing in terms of functional blocks a traffic monitoring system including an exemplary system for sensing the velocity of a moving object according to the present invention; Figures 2, 3 and 4 schematically show in terms of functional blocks exemplary sensing devices according to the present invention;

Figures 5 and 6 show flowcharts of exemplary embodiments of the method of the present invention.

Figures 7a and b show simulations of responses of a magnetic sensor; and Figure 8 shows experimental results of an embodiment of the present invention.

Detailed description of the preferred embodiment(s) of the invention

Figure 1 shows, in terms of functional blocks, a system 1 for measuring the velocity v of a moving object 200 according to the present invention.

The system 1 includes a sensing device 100, a power supply 115 connected to the sensing device via a power connection 122, and a processing unit 110 operatively connected to the sensing device via a connection 120 and to the power supply via a connection 124. The sensing device 100 and/or the power supply 115 and/or the processing unit 110 device may or may not be physically separated.

A traffic monitoring system 150 based on the present invention may comprise the velocity measuring system 1, a base unit 130 and a communication link 140 between the velocity measuring system and the base unit. In an embodiment, the system 1 and the base unit 130 are located at a certain distance and the communication link 140 is a radio link apt to transmit the velocity measurement data from the velocity measuring system to the base unit for traffic analysis, monitoring and, possibly, management. The communication link 140 may be characterized by low power consumption transmission, such as, e.g., the ZigBee protocol or the like.

According to the present invention, as shown in the following Figures 2, 3 and 4, the sensing device 100 comprises at least a pair of sensors 10, 20 spaced apart by a known distance d, each sensor being sensitive to a physical quantity P , which may be a scalar or a vectorial field. In case of a vectorial field, a sensor which is sensitive to at least a component of a physical quantity will be referred to, for the purpose of the present invention, as 'sensitive to the physical quantity'. Each sensor 10, 20 is apt to provide at least a measurement signal representative of, or associated to, the sensed physical quantity. In case of a vectorial physical quantity P , each sensor may provide one measurement signal for each sensed component of the physical quantity. Typically, the measurement signals are affected by noise, of thermal, ambient and electronic nature, which causes the numerical quantities computed from the measurement signals being also affected by uncertainty. The lower is the signal to noise ratio, the higher is the uncertainty of the computed numerical quantities. Typically, each one output measurement signal is an analogical signal which is digitized, or sampled, by an analog-to- digital-converter (ADC - not shown).

With reference again to Figure 1 (not to scale), a moving object 200 is moving, with respect to an (x, y, z) frame of reference 160, at a point x in space and point t in time with a velocity v = (y_x,v_y,v_z). It is assumed that a physical quantity P = (/^ (xj, i^, (xjt P₂. [&)), e.g., a magnetic or electric field, at the same point x changes in time as a consequence of the passage of the moving object 200 in the point x . In the present description, any object, such as the moving object 200, able to modify the physical quantity P will be referred to as a 'source of variation' of the physical quantity P . The same terminology is used for actual sources of the field P .

The time derivative of such physical quantity at the instant t and point x is related to the spatial variation of such quantity at the instant t and point x and to the object velocity v according to the following general expression:

SP _ SP -

(Eq. 1), dt ^~ Sx wherein

is the 'spatial gradient' of the quantity P , i.e., the matrix of the spatial gradients of the

SP physical quantity components (each gradient defines a row) and — is the vector representing dt the complete time derivative of the quantity P .

Eq. 1 above holds in the typical case wherein the object speed is small in comparison with the speed of light (as is the case for vehicles traveling along a roadway).

The equations above assume a vectorial quantity P . In case the physical quantity to be measured by the sensors is scalar, e.g. a pressure field, φ = φ\x) , Eq. 1 takes the following dφ particular expression: — — = Vφ • v . dt

Eq. 1 can be explicitly written in the following form:

The Applicant has found that the velocity of the object can be obtained, in principle, by inversion of Eq. 1:

- SP dP ._ „ v = — •— (Eq. 3), dx dt

₌ _1 wherein — is the inverse matrix of the matrix — . The Applicant has found that dx dx the use of the equation above gives the advantage of very low computational resources requirements.

According to the present invention, the at least one time derivative and the at least one spatial derivative which need to be known in order to calculate the velocity in Eq. 3, are evaluated, at least approximately as described below, by using the two measurement signals provided respectively by the at least two sensors 10, 20.

Eq. 3 can be explicitly written (by solution of the system of Eq. 2) as:

4),

wherein det — is the determinant of the matrix — . dx dx

Eq.4 shows that if all the three spatial derivatives (i.e. the spatial gradient) and the time derivative of all the three components of the physical quantity P are known, it is possible to determine all the three components of the velocity of the object, irrespective of the trajectory of the said object.

Accordingly, in one possible embodiment of the present invention, as shown in Fig. 2, the sensor device 100 comprises at least four sensors 10, 20, 30 and 40, each one sensitive to all the three components of the physical quantity P (hereinafter referred to as 'tri-axial' sensors) and which are advantageously used to evaluate the three time derivatives and the nine spatial derivatives of Eq. 4, as exemplarily explained further below. For the purpose of the present invention, the expressions 'calculating a time or a spatial derivative' and equivalently 'evaluating a time or a spatial derivative' are used to indicate an evaluation of the derivative(s) subject to an approximation error, which is typically related to a finite incremental step (either spatial or temporal) used to evaluate the derivative(s) in discrete form. More details on this can be found further below, in correspondence to Eq. 9 and 10.

The at least four sensors 10, 20, 30 and 40 are preferably of the same kind, i.e. apt to measure the same physical quantities. Preferably, the sensors are identical.

They may be advantageously placed at known given distances with respect to one another. They are typically fixed in the frame of reference with respect to which the object velocity is measured. The at least four sensors 10, 20, 30 and 40 shall not lie in the same plane. They may be placed along a Cartesian set of three axes at a fixed reciprocal distance d as shυwn in Fig. 2. Pieferably, in order to reduce the noise, they may be placed at the four vertexes of a tetrahedron (not shown), the nine spatial derivatives and three time derivatives of Eq. 4 being in this case evaluated by suitable combination (weighted averaging) of the derivatives calculated from the signals of the sensors.

In one embodiment of the present invention, the velocity of the object to be measured may only have two components, i.e., it may lie substantially only on a fixed plane. The case of a vehicle traveling along a multi-lane road is an example of a velocity expected to lie in a plane.

For example, by suitable choice of the reference frame, it is assumed that the velocity has only the x and y components, i.e., v = (y_x, v_y,0). Eq. 2 then becomes:

Choosing for example the x and y components of the quantity P (similar expressions would result by choosing x and z components or y and z components of the quantity P ) the velocity may be calculated according to the following:

Eq. 6 and the discussion above show that if the object velocity is expected to lie in a fixed plane, it is possible to determine the two components of the velocity by knowing the spatial derivatives with respect to the two directions belonging to said plane and the time derivative of only two (which may be chosen) of the three components of the physical quantity P .

In this case, as shown in Figure 3, the sensing device 100 may comprise at least three sensors 10, 20 and 30, each one sensitive to at least two components of the physical quantity P (hereinafter referred to as 'bi-axial' sensors) and which are used to evaluate the three time derivatives and the six spatial derivatives of Eq. 6. The at least three sensors 10, 20 and 30 shall lie on a plane which is parallel to the plane comprising the velocity vector and shall not lie along the same line. They may be placed at fixed reciprocal distances at the vertexes of a rectangular triangle as shown in Fig. 3. They may preferably be placed at the vertexes of a non-rectangular triangle in order to reduce noise, the four spatial derivatives and two time derivatives of Eq. 6 being in this case evaluated by suitable combination (weighted averaging) of the derivatives calculated from the signals of the sensors.

It is possible to add redundancy to the measuring system 1 including the sensing device 100 of Figure 3 by choosing the at least three sensors 10, 20 and 30 tri-axial. In this case, it is possible to derive the two velocity components v_x and v_y using two different formulas: Eq. 6 and one of the two other similar expressions which result by choosing, respectively, x and z components and y and z components of the quantity P instead of the x and y components used in Eq. 6. The two results for each velocity component may then be averaged.

In one embodiment of the present invention, the velocity of the object to be measured may only have one component, i.e., it may lie substantially along a fixed direction. The case of a car traveling along a single lane road is a good example of a velocity expected to lie along the line of the lane.

Assuming for example the velocity having only the x component, i.e., v = (v_x ,0,6) Eq. 2 becomes:

Choosing for example the x component of the quantity P (similar expressions would result by choosing the y component or the z component of the quantity P ) the speed may be calculated by the following expression:

dx

Eq. 8 and the discussion above show that if the object velocity is expected to lie along a given direction, it is possible to determine the sole component of the velocity (i.e. the speed) by knowing the spatial derivative along the said direction and the time derivative of only one

(which may be chosen) of the three components of the physical quantity P .

In this case, as shown in Figure 4, the sensing device 100 may comprise at least a pair of sensors 10, 20, spaced apart by a known distance d, each one sensitive to at least one component of the physical quantity P (preferably each one sensitive to no more than one component, i.e. 'mono-axial sensor') and which are used to evaluate the time derivative and the spatial derivative of Eq. 8. The at least two sensors 10, 20 may be placed along the direction of the said one component of the velocity vector. A train running along the rail is another good example of an object whose velocity is expected to lie along a given fixed direction, while the velocity of a car running along a multi-lane road lies only approximately along the expected direction. In the latter case it's possible to estimate the error in the speed evaluation according to the present invention, in case the velocity forms an angle α with respect to the direction along with the sensors are placed. If the actual speed is v, for small angles the error in the speed evaluation is of the order of α²v, wherein α is expressed in radians.

It is possible to add redundancy to the measuring system 1 including the sensing device 100 of Figure 4 by using at least two sensors 10, 20 which are bi-axial or tri-axial. In this case, it is possible to derive the velocity component v_x using, respectively, two or three different formulas: Eq. 8 and, respectively, one or both of the other two similar expressions which result by choosing, respectively, the y component or the z component of the quantity P Instead of the x component. The two or three results for the speed may then be averaged, increasing the accuracy at the expenses, possibly, of a greater power consumption of the sensors with respect to the mono-axial case.

In general, the total number of sensors (and their number of axes) comprised within the sensing device 100 in order to measure the velocity of a moving object according to the present invention depends upon the number of the velocity components which the object velocity vector may have and, possibly, the degree of redundancy of the velocity measuring system 1.

Figure 5 diagrammatically shows the steps of operation of the velocity measuring system 1 in accordance to an embodiment of the present invention.

Typically, the entire procedure 500 illustrated in Fig 5 is performed cyclically every sampling time interval r' (the inverse of the sampling rate/'=l/r'). Preferably the sampling rate/' is between 50 Hz and 1000 HZ. In the following, it is assumed that at least one cycle of Fig. 5 has been performed before the current time instant / associated to the cycle of Fig. 5. It is to be understood that the time instant t is representative of a time interval comprising the time instant t and that the expression 'time instant' may refer to said time interval. For example, the time interval may consist in several time intervals τ\ e.g. 3 or 2. Typically, the time interval may consist in one time interval τ' or in a portion thereof, such as half thereof.

In step 510, the measuring system 1 is switched from an 'idle' mode to a 'measurement' mode. In the idle mode, the power consumption is kept at a minimum, for example by keeping the sensors powered off, as well as most of the electronics (such as the ADC, microcontroller in low power configuration, etc). In the idle mode, the system clock is always active and triggers the interrupt for wake the microcontroller 110 up.

In the measurement mode, the microcontroller 110 operates the power supply 115 so as to power on the sensors 100. Additionally, the following electronic components are typically powered on: ADC, amplifier, microcontroller and sensors. In step 520, at least a sample datum is acquired from a first sensor 10. Typically, this step is controlled by the microcontroller 110 which makes the ADC be powered on and digitally sample the (typically analog) signal output from the first sensor 10. The data so acquired are typically stored in a digital memory (not shown in Figure 1). This sample datum, which is typically a voltage value V_x{t), represents, or is associated to, the value P_x(f) of at least a sensed component of the physical quantity P at the instant of time t at which the datum is acquired. Preferably, no more than one sample datum is acquired at this step of the procedure, so as to minimize the power consumption. Preferably, this sample datum is associated to no more than one component of the physical quantity. However, in case the first sensor is bi-axial or tri-axial, it is possible to acquire additional sample data associated to additional component(s) of the physical quantity.

In step 530, a time variation AP₁ of the sensed physical quantity P (e.g. at least a component of the physical quantity) is evaluated by the microprocessor 110. Any numerical quantity representative of the above time variation may be suitable to the purpose of the present invention. For example, the numerical quantity may be a difference, in absolute value, between the current value acquired from the first sensor, F₁ (V), and a value acquired at a previous instant of time t from the first sensor, V_x [t - t ) . Preferably, t =nτ' where τ' is the sampling time step and n is an integer number (typically 1 or 2), so that

The choice of n may be done in real time by a raw estimation of the vehicle speed value. In case of a two-sensor system (Fig 4) a possible way to perform such raw estimation is to switch on the second sensor 20 the first time instant t, within a single object passage, at which the signal of the first sensor 10 V_x(t) departs by a fixed threshold amount from a baseline value Vi , typically associated to the physical quantity "background"(e.g. the earth magnetic field in the absence of vehicles, see below), i.e. V₁ ^)- V₁ > Threshold, and to count the number n ' of time steps τ' occurring between the said first time instant t and the occurrence of the same condition for the second sensor 20 ( V₂ (t + T)- V₂ > Threshold ). Depending on the number n ' of time steps (T=nV) it is possible to properly choose the parameter n above in the definition of the time variation of the physical quantity, n being higher (e.g. n=2 for speed above 30 km/h) in the case of low speed and lower in the case of high speed (e.g. «=1 for speed below 30 km/h).

Preferably, the time variation of no more than one component of the physical quantity is computed. However, in case the first sensor is bi- or tri-axial and additional sample data associated to additional component(s) of the physical quantity have been acquired in the previous step, it is possible to compute the time variation of these additional components. Preferably, the time variation of the physical quantity is computed in step 530 from data acquired from no more than the first sensor 10 (e.g. no other sensors than the first sensor 10 are powered on for this purpose). However, e.g. in case of a device 100 comprising more than two sensors as shown in Fig. 2 and 3, the time variation of the physical quantity from more than one sensor or any combination thereof could be used for the purpose of selecting the instant of time when to compute the speed. In step 540, at least a sample datum is acquired from a second sensor 20. Typically, this step is controlled by the microcontroller 110 which makes the ADC be powered on and digitally sample the (typically analog) signal output from the second sensor 20. The data so acquired are typically stored in a digital memory (not shown in Figure 1). This sample datum, which is typically a voltage value V₂{t'), represents, or is associated to, the value of at least a sensed component of the physical quantity P at the instant of time t ' at which the datum is acquired. For the purpose of the present invention, this sample datum is acquired in order to be used in the step of velocity calculation (step 560). However, see e.g. the discussion above, data from the second sensor may also be used for other purposes. The instant t' may be coincident with the time instant t, but either for practical reasons (use of a single ADC) or for reasons of implementation of the evaluation algorithm (as explained below), it may be subsequent to the time instant t or precedent it. The component of the physical quantity P associated to F₂(^') is preferably the same component sensed in step 520 (e.g. associated to V₁ (t) ) , but the present invention also contemplates the case of different components. In the latter case, however, additional data need to be acquired from the first sensor associated to the same component sensed by the second sensor.

In step 550, the time variation AP₁ calculated in step 530, for example by use of a suitable numerical quantity, is compared to a first value. Conditional to a first result of this comparison, the step 560 of computing the velocity (or the speed) of the moving object is performed by the microcontroller 110. Preferably, conditional to a second result of the above comparison, the measuring system 1 is switched from the measurement mode to the idle mode

(as shown in step 570).

According to the present invention, the first result is associated to the condition that the above mentioned time variation is above the first value. For example ^Δ*H^F>(<)-^r>('-^?l^>v _™ -

The Applicant has heuristically found that the method of the present invention represents a good trade-off between low power consumption and high accuracy of velocity determination, at least on a statistical basis. The Applicant believes that the above condition on AP₁ is a good indicator that the velocity computed at the corresponding instant of time / via Eq. 3 (or variation thereof) has an acceptable accuracy, at least on a statistical basis. It is believed that a value of AP₁ above the predetermined threshold assures an acceptable signal to noise ratio associated to the quantities representative of the time derivative(s) of the physical quantity evaluated at the corresponding instant of time t for the purpose of computing the velocity. This in turn, at least on a statistical basis, implies that the velocity computed from these evaluated quantities has also an acceptable signal to noise ratio, and thus an acceptable accuracy. Preferably, the physical quantity's component of which the time derivative is computed for the purpose of velocity computing is the same component sensed by the first sensor in step 520. However, the Applicant has found that the component sampled in step 520 may be different from the ones actually entering the computation of the velocity. For example, with reference to Fig. 1, an x component of the physical quantity P may be sensed from the first sensor in order to evaluate AP_x , while an y component of the same physical quantity may be also sensed and acquired by at least two sensors, conditionally to the condition above, for the purpose of evaluating the velocity.

It is noted that, due to the fact that also at least one spatial gradient of the physical quantity enters the velocity computation in addition to a time derivative, the condition above does not assure, rigorously speaking, that at the same time instant t above also the spatial gradient has an acceptable error (low signal to noise ratio). However, the Applicant has found that, statistically, the condition above corresponds to an acceptable error also for the spatial gradient, by a suitable choice of the parameters of the algorithm of Fig. 5 and in the range of speed of interest. For the present description, the expressions 'on a statistical basis' or 'statistically', referred to a certain statement, mean that, given a large number of objects individually sensed with the present method and system, that statement is true for the major part of the objects. It is here pointed out that the present method and system find particularly suitable applications for traffic monitoring, which rely on 'statistical' information rather than on 'individual' information.

On the other hand, the Applicant has found that the fact that the velocity is computed conditionally to the condition above allows obtaining accurate velocity evaluation while reducing the power needed for computational work. It is pointed out that the computation of the velocity according to the present method requires the numerical computation of at least a ratio, which numerical operation consumes large computational resources (and power). The method and system of the present invention thus allows the computation of the velocity only at the point(s) in time wherein a good probability of having accurate results exists. The Applicant has moreover found that this solution gives better results than alternative solutions based on computing the velocity also in points in time having ΔfJ below the predetermined value and then averaging the computed velocities. Figure 6 diagrammatically shows a preferred embodiment of the general method of the present invention described with reference to Fig 5. From a logical point of view, the steps shown in Fig 6 are the same of Fig 5 (and the same reference numerals have been used), the main difference being that now also the step of data acquisition from at least the second sensor is conditional to the first result of the comparison step 550. Typically, said data from at least the second sensor are needed for velocity evaluation purpose (step 560), the velocity evaluation algorithm requiring storing at least three sampled values from at least two sensors: two values representative of a selected one component of the physical quantity P at two successive instants of time and output from the same one sensor (either the first or the second one) and one value representative of the same selected component of the physical quantity P at a point in time substantially close to the above two successive time instants and output from another sensor.

Preferably, the second sensor 20 is powered on conditionally to the result of step 550. Advantageously the method of Fig. 6 cyclically monitors the measurement signal from a restricted number of sensors (preferably no more than one) and determines, on the basis of this measurement signal, the appropriate time for switching on the other sensor(s) and for evaluating the velocity of the moving object. The appropriate time is typically associated to the signal to noise ratio of the measurement signal.

This solution has the advantage that the power consumption of the system may be greatly reduced with respect to known solutions. In fact, the number of sensors actually "active", i.e. the sensors providing regularly (e.g. at each sampling interval τ') data representative of, or associated to, the sensed physical quantity for monitoring purpose, may be less than the total number of sensors used for velocity evaluation purpose. The other ('non- active') sensor(s) may be powered on only for a limited time when the condition for velocity evaluation results acceptable, such condition being checked from the data provided by the 'active' sensor(s).

In an embodiment of the present invention, the procedure shown in Fig. 5 and 6 is cyclically iterated at successive instants of time (e.g. with a sampling period τ') during the whole passage of the vehicle near the sensors, keeping fixed the predetermined (threshold) value used for comparison of the time variation of the physical quantity (step 550). In a configuration, the step 560 of velocity evaluation is performed at any time instant wherein the condition at step 550 is verified. Once the vehicle has passed, it is possible to average the calculated velocities. In another configuration, advantageously saving power, the step 560 of velocity evaluation is performed at the first time instant, within the vehicle passage, wherein the condition at step 550 is verified and thereafter it is never performed again (by way, e.g., of a control flag within the procedure).

In still another preferred configuration, at each cycle 500 the current threshold value is kept equal to the value of the time variation of the physical quantity at the last previous cycle 500 wherein the condition at step 550 has been fulfilled. If this solution is repeated along the whole time interval associated to the vehicle passage, it allows finding the time instant wherein the time variation of the physical quantity is at a maximum. The Applicant has however found that, for power consumption reasons, it is preferable to define a maximum number M of times (M typically from 5 to 10) wherein the threshold value is updated to a new current value. In one configuration, when the condition 550 is verified, all the values (e.g. V, (t),

V₂{t), etc.) entering the computation of the velocity are stored in a memory (not shown). In this case, the velocity may be subsequently computed in correspondence to only a sub-selection (preferably a selected one) of the time instants verifying condition 550. In one embodiment, said selected one time instant is the last time instant verifying the threshold condition 550 (i.e. at the maximum of the time variation of the physical quantity), said last time instant being either when the predetermined maximum number M of iterations has been completed or when the object has completely passed the sensors. In another embodiment, said selected one time instant is chosen among the saved time instants on the basis of a further condition. In one configuration a quantity representative of a spatial variation of the physical quantity is evaluated from said saved values (e.g. the difference of two substantially contemporary outputs from the two sensors) and the further condition takes into account the value of the quantity representative of the spatial variation. For example, the selected one time instant is selected on the basis that the spatial variation is above a second threshold value or that the spatial variation is at a relative maximum among the saved time instants. Alternatively, for each of the saved time instants a figure of merit may be determined as a function of the respective time variation and the respective spatial variation (e.g. the sum of the respective absolute values), and the further condition is based on the value of this combined figure of merit, for example by seeking a relative maximum/minimum of said figure of merit among the saved time instants.

In the following, there are described exemplary implementations of the velocity computation step 560 based on Eq. 1 and 3, with reference to the case of a single component velocity (Eq. 7 and 8). However, nothing in the present description should be interpreted as a limitation or restriction of the scope of the present invention to the mono-dimensional case. Further, it is possible for the skilled person to implement correspondingly the other two cases (two and three velocity components) on the basis of the present description.

With reference again to Fig. 4, two sensors 10, 20 are placed at points X₁ and x₂ along the x-axis and spaced apart by a distance d which is preferably shorter than the typical object length. It is assumed that the object may move substantially solely along the x-direction. For example, the sensors 10, 20 may be two magnetic sensors buried in a roadway and oriented substantially along the direction of movement of the vehicles (i.e. parallel to the lanes).

In one embodiment of the present invention it is possible to advantageously approximate the spatial derivative in eq. 8 with the following relation: dP P_x(x + d)-P_x(x ) ^_{L ≡} ^_₁ 1 — Λ_J (Eq. 9), dx d wherein P_x[X₁ + d) is the physical quantity as measured at the time instant t by the second sensor at x = x + d and P_x [x ) is the same physical quantity as measured at the same time instant t by the first sensor at x . In practical implementations, however, P_x {x₂ ) and P_x [x J may be, and typically are, measured at slightly different time instants (if for example a single ADC converts signals from both sensors), as is well known by the skilled person and as will be clear from the description which follows.

Analogously, it is possible to approximate the time derivative of eq. 8 with the following expression: dP^ _≡ P_x(_Xι ,t ₊ r)-P_x(_Xι ,ή dt T wherein P_x (x ,t) is the physical quantity as measured by the sensor at, e.g., x at the instant of time t while P_x\x ,t + τ) is the same physical quantity as measured by the same sensor at x at a subsequent or precedent instant of time t + τ . Typically, the possible difference in the time instants at which P_x (x₂) and P_x [x ) of eq. 9 above are respectively measured (see discussion above) is much smaller than the time interval τ of eq. 10 (typically τ is in the ms range while the possible difference above is in the order of ns).

By combining Eq. 9 and Eq. 10 into Eq. 8 it is possible to derive a simple expression for the speed:

From a mathematical viewpoint, the time instant t on the left of eq. 11 is identical to the one on the right thereof. In practical implementations, however, there may be a difference between them, as is well known by the skilled person and as will be clear from the description which follows.

Eq. 11 shows that in step 560 of fig. 5 and 6 it is possible to compute the vehicle speed at a given instant of time t by measuring the time variation of one component of the physical quantity at a given sensor (either the first 10 or the second 20) and the spatial variation of the same component of the physical quantity between the two sensors at the instant of time t. Indeed, the present invention allows the evaluation of the speed by using only three measurement data from the two sensors 10, 20, of which two successive data are from one (e.g. the first) sensor and one datum is from the other. This is particularly advantageous in comparison to method of measuring the speed based on correlation function, which need to process two whole time series of data. Referring back to Fig 5 or 6, the three measurement data entering Eq 11 are acquired in step 540 of Fig 5 and 6 and either in step 520 (of the same cycle 500 or of a preceding or subsequent cycle) or, more preferably, in an additional (not shown) step of acquisition from the first sensor of measurement data for the purpose of computing the velocity, the additional step being substantially simultaneous to the step 540. For example, when using eq. 11 for velocity computation of step 560, the value

P_x(x₂,t) is acquired from the second sensor (step 540) substantially simultaneously with the acquisition from the first sensor of P_x (x_x ,t) (which may be acquired in step 520), while P_x(x_ut + τ) may be acquired in the corresponding step 520 of the preceding cycle 500 of Fig

5 or 6 (in this case τ = τ ' ) . The sign in eq 11 may be adjusted consequently. Preferably, in order to improve the accuracy of the algorithm of Eq. 11 with respect to the noise which affects the sensors measurements, it is advantageous to consider a spatial averaging of the time variation and a time averaging of the spatial variation, according to the following:

In general, 'a spatial averaging of a time variation' means that a time variation (i.e. a difference between two consecutive data from one sensor) is computed at various (e.g. two) points in space (i.e. they are measured for the various sensors 10, 20, and possibly 30 and 40), and then averaged.

Analogously, 'a time averaging of a spatial variation', means that the spatial variation . (i.e. a difference of two substantially contemporary data taken from two sensors) is measured for various (e.g. two) instants of time and then averaged. This solution allows a good improvement of the robustness of the algorithms of the present invention to the sensor noise(s) without substantially increasing the measurements requirements, in that Eq. 12 comprises only one additional measurement. P_x(x₂,t + τ) with respect to Eq. 11 which comprises three measurements.

Referring back to Fig 5 or 6, the four measurement data entering Eq 12 are acquired in step 540 of Fig 5 and 6 and either in step 520 (of the same cycle 500 or of a preceding or subsequent cycle) or, more preferably, in an additional (not shown) step of acquisition from the first sensor of measurement data for the purpose of computing the velocity, the additional step being substantially simultaneous to the step 540. In the example above, (in case τ =τ ' ) , P_x(x₂,t + τ) may be acquired in the corresponding step 540 of the preceding cycle 500 of Fig 5 or 6.

With reference to Fig 6, in a preferred embodiment (assuming that both the sensors measure the same component P_x in steps 520 and 540) when the condition in step 550 is verified (by using the sample datum P_x{x_λ,t) acquired in step 520), then the sample datum P_x(x₂,t) is taken at a time instant slightly subsequent to that of P_x(x_ut) (the time delay being as small as possible and being mainly due to the electronic delay due to the elaboration of step

550). After a suitable time delay t₀ , P_x{x_λ ,t + τ) and P_x{x₂,t + τ) of eq 12 are acquired, wherein (t + τ)=(t + t₀). A possible implementation is to keep the time difference between the two sampled signals, t₀ , less than the time associated with the sampling rate, τ'. This choice assures to complete the data acquisition for speed evaluation and the related algorithm within a single sampling time step τ' .

In order to further improve the signal to noise ratio an average over many samples could be considered instead of the single datum from the sensor. Therefore the values P_x(x_x ,t + τ), P_x(x₂ ,t + τ), P_x (x_x ,t) and P_x(x₂ ,t) may be the result of a "fast-average" of signal data from the two sensors over many time steps τ_fast . The time step r_fas, over with the average is performed is preferably much smaller than the other characteristic times τ\ τ and J₀. Typically r_fast ranges in the tens of microseconds (10-100 μs) while r' is in the millisecond range (1 - 10 ms) and t₀ could be taken as a fraction of r', for example t₀ = r'/2. An averaging over 8-10 time steps r_fast or less is suitable.

Typically, the sensor response is a voltage that is related to the value of the measured physical quantity. Typically, the sensor response is linear in character: v(ή = kP(t)₊ v_{0 (Eq l3)>} wherein V(t) is the voltage response, P{f) is the generic physical quantity to be measured

(e.g. one component of the quantity P) and k and Vo are called the 'gain' and the 'voltage offset' (i.e. the zero-field response), respectively. The measured physical quantities in Eq. 9, 10, 11 and 12 will be related to the sensor voltage responses by the following relations:

02

K

Inserting Eq. 14 into Eq. 12 one gets:

Similarly, inserting Eq. 14 into Eq. 11 one gets: v_£

In order to compute the speed v, the gains (k_/ and £_?) and the offset voltages (V oi and Voi) of the two sensors have to be known. Typically, two distinct sensors, even thought of identical type, have different gains k and voltage offsets VQ. Moreover the parameters k and Vo are subject to temperature drift and/or other changes due to environmental conditions. Usually, various procedures (called 'calibration' procedures) for acquiring the current values of the parameters k and Vo are embodied in many commercially available sensors. Once the current values of the gain and the voltage offset are determined, it is possible to estimate the value of the measured physical quantity. One of the drawbacks of any kind of calibration is that they are time and power consuming.

For example, magnetic field sensors of the kind of the commercially available magneto-resistive sensors HMC 1001/1002 or HMC 1021/1022 made by Honeywell are provided with built-in functionalities apt to determine the gain and the offset For example, the Offset strap' calibration procedure provides a way to check the current value of the gain k, by applying to the sensor a known (even thought subject to an error) magnetic field AP and evaluating the gain according to the formula:

V — V k = ^-—^ (Eq. 16), AP wherein V ₂ is the sensor voltage reading when the field AP is applied and Vi is the sensor reading without the field AP being applied (this calibration needs to be performed under steady state condition of the background magnetic field).

Another calibration procedure present in the Honeywell sensors above and which may possibly be useful for the implementation of the present invention is the 'set/reset' procedure, which is apt to determine the voltage offset Vo- It is based on a pair of current pulses, the set and the reset pulse, which are apt to set the gain of the sensor at the same value but with opposite sign. After the set pulse, the sensor reading is V^sa = kP + V₀ and after the reset pulse the reading is p^"reset = -kP + V₀ , where P is the same magnetic field. Taking the sum or the difference between the two readings allows obtaining the following expressions: V^set - V'^eM = IkP (Eq. 17) τ_/-set preset _ η y ^{v + y ~ λ V}° (Eq. 18)

Accordingly, the speed in Eq. 15 above may be evaluated by measuring the gains (ki and ki) using Eq. 16 and the offset voltages (V0₁ and V₀₂) by using Eq. 18 for both the sensors. In the particular case wherein the at least two sensors 10, 20 are provided with a calibration procedure of the kind of the set/reset procedure of the Honeywell sensor above described, it is possible to use, in order to implement the present invention, the following method: during the passage of the moving object 200 (or at any time before it) a "set" pulse is done in both sensors; after a small time interval much lower than r' during which the transient is substantially finished, the measures V^ (t) and F₂ ^{sel l}(t) are taken at the time t; after a small time interval much lower than τ (needed for acquiring the two measures above) a "reset" pulse is done in both sensors; after a small time interval much lower than τ during which the transient is substantially finished, the measures Fi"^*" (f) and V₂ ^nset(t) are taken at the time t incremented by a small time interval ε much lower than τ; at the time t + τ a "set" pulse is done in both sensors after a small time interval much lower than τ during which the transient is substantially finished, the measures Vf* (t + τ) and F₂ ^set (t + τ) are taken at the time t+r, after a small time interval much lower than τ (needed for acquiring the latter two measures above) a "reset" pulse is done in both sensors;

- after a small time interval much lower than τ during which the transient is substantially finished, the measures F₁ ¹""^ + r)and V₂ ^κset(t + τ) are taken at the time t+τ incremented by a small time interval ε' much lower than τ. Using Eq. 17, Eq. 12 becomes:

v =

(Eq. 19), wherein the Vi₎₂ in the numerator could be either all set or all reset measurements and it is understood that the reset measurements are taken at a point in time incremented by a small time interval ε or ε' with respect to the corresponding set measurement.

In one embodiment of the present invention, the ratio K_x I K₁ in Eq. 15 and 19 is given an approximate value of 1.

In another embodiment, an estimation of the actual current value of the ratio κ_x I K₂ is done, for example by performing the offset strap procedure (Eq. 16) for both the sensors. Alternatively, it is possible to advantageously use the set/reset approach for both the sensors at a same instant of time t ' wherein the magnetic field seen by the two sensors is the same. A possible implementation is to choose t' when no object is passing close to the sensors so that the measured field at the two sensors is probably the same. Using Eq. 17 it derives that:

This set/reset procedure is performed every time that the ratio K₁ 1 κ₂ in Eq. 15 or 19 and/or the off set voltages Voi and V₀₂ in Eq. 15 need to be updated.

An alternative embodiment of the present invention allows avoiding any calibration procedure. This is possible by a suitable combination of a set of measurements performed at different instants, closely spaced in time (with respect to the typical ratio between the speed of the object and the spacing between the two sensors).

Using Eq. 11 at three different instants of time, t_x , t₂ , t₃ , with t_x < t₂ < t₃ and t₂ - t_x ≡ t₃ - t₂ « d I v , it is possible to write three independent expressions for the velocity: _v ^ d P_x(x_xJ_{3 +}τ)-P_x(x_xJ_i) T P_x{^χ _λ,h)-P_x{^χ ₂,h)

_{v ~} d P_xJx₁J_{x +} τ)-P_x(x_xJ_x) τ P_x(X_x J_x )- P_x (X₂J_x ) It is possible to show that the previous equations, expressed in terms of voltage outputs and offset and gain via Eq. 14, are a system of three equations in three unknown

1 k ( — v , — -v and v). It can be shown that the system (non-linear) is solvable for v, and the

solution for the velocity, if one chooses equally spaced instant of time, t_x = t , t₂ = t_x + τ and t₃ = t₂ + τ = t_x + 2τ , may be expressed only in terms of measured quantities: _v

wherein:

F₁, = V_x (t + I T) and / e {0,1,2,3} F₂, = K₂ (. + i τ) and / e {0,1,2}

It is thus possible to measure the velocity in terms only of the voltage outputs read by the at least two magnetic sensors at three different instants of time. The Applicant has found that in case other sources of variation or sources of the physical quantity P are present besides the object under measurement 200, they may affect the calculations performed according to the equations given above.

In case additional contributions to the quantity P are present, Eq. 13 (the response of a sensor) may be rewritten in a more general form as:

V(f) = kP(t)+ V₀ = k(P'(t)+ P_BASE + P_sp)+ V₀ (Eq. 13'), wherein P'(t) is the (time-variable) contribution to the physical quantity P(t) given solely by the passage of the moving object 200, PB_ASE is the background or 'baseline' physical quantity, i.e. the contribution given by sources of variations of P or sources of P which are far enough from the sensing device 100 so that each sensor 10, 20 (and possibly 30 and 40) measures substantially an identical contribution P_BASE, and P_sp is the 'spurious' contribution, i.e. that contribution which varies on a spatial scale comparable to the distance between a pair of sensors. This is the case, for example, of sources which are close enough to a pair of sensors so that each sensor of the pair will measure a different value of the physical quantity involved. This phenomenon results in spurious spatial variations while, in the typical case of steady spurious terms, the time variations will not be affected by it.

In absence of the spurious term (P_sp=0) or when it is negligible, the equations given above (such as for example Eq. 9, 11, 12, 15, 19, 21 and so on) equally holds in case the physical quantity entering therein is regarded as solely the contribution P'(t) and in case it is regarded as the contribution P'(t) plus the baseline contribution P_BASE- In fact, the above equations are based on a difference between two contemporary or substantially contemporary measures of two distinct sensors and the term P_BAS_E cancels being identical for the two sensors. This is the case of, for example, the earth background magnetic field when the measured physical quantity P is the magnetic field. The earth magnetic field sensed by the sensors could be considered the same all over the sensing device 100 because the sensor spacing is smaller than the typical length over with the earth magnetic field changes. The same is true also for time varying sources of variation, provided that they are sufficiently far.

On the other hand, the Applicant has discovered, during the experiments associated to the present invention, that if the sensing device 100 was placed near a source of variation of the sensed quantity, the results were inaccurate. For example, this happened in case the sensing device 100 including magnetic sensors 10, 20 was placed nearby a large iron body, such as a pipe.

This effect is believed to be due to the spurious contribution by the nearby source and it may be advantageously taken into account in the invention implementation in order to reduce errors in the object speed evaluation. Accordingly Eq. 12 (similarly for Eq. 11) is advantageously modified as follows:

wherein P_x is the total quantity as measured by the sensors and AP_sp is the spurious variation of the physical quantity due to the unwanted sources: AP_sp = P₃₉(X₂)- ^, (^₁) and it has been assumed that the spurious contribution is time-independent. Now the denominator comprises only the terms P' due solely to the passage of the moving body 200 (see the discussion above for the baseline contribution). Analogously, Eq. 15 may be corrected as follows:

In the same way, starting from Eq. 19 it is possible to derive an expression similar to Eq. 19 itself and including at the denominator the correction term -2k_\ΔP_sp.

In order to evaluate the above expressions including the spurious term, a procedure for spurious variation evaluation is necessary, for example by measuring a baseline signal V of the sensors defined by:

- _{r ]} (Eq. 24),

V2 = k₂ [P_BASE + P_sp2 \+ V_O2 which may be evaluated from the reading of the sensors when no objects under measurement are present near the sensors (baseline condition). In order to evaluate the spurious variation, it is necessary to evaluate the sensors' parameters in Eq. 24 according to known technique (see, e.g., Eqs. 16-18).

An alternative approach according to the present invention may eliminate the need for evaluating the spurious variations. It is based on the baselines of the sensor signals V\ and

Vi . By subtracting the baseline signals from the whole sensor signals, it is possible to get the contribution to the measured field P due to the moving object (see Eq. 13'):

Accordingly, Eq. 23, using Eq. 13', may be rewritten as follows:

In order to evaluate the expression of Eq. 25, it is enough to evaluate the baseline signals and the ratio K_X I K₁ .

In one embodiment of the present invention, the ratio K_x I K₁ in Eq. 25 is given an approximate value of 1.

In another embodiment, an estimation of the actual current value of the ratio K_x I K₁ is done, for example by performing the offset strap procedure (Eq. 16) for both the sensors.

The Applicant has noted that in case the spurious variations affect the velocity measurement, it is preferred to use the implementation of the present invention according to Eq. 25.

It is noted that the method above (Eq. 24 and 25) may also be advantageously used in absence or in negligible presence of any spurious terms and in this case the evaluation of the baseline signal (which represents the offset voltage plus the voltage due to the background field) takes advantageously the place of the evaluation of the offset voltage. The method of velocity calculation according to the various embodiments of the present invention may be implemented as a computer program, such as software or firmware. The actual operations performed by the method, implemented in suitable software code portions of a computer program, may be carried out by any well-known general purpose computer having appropriate processing abilities, as it will be clear to those skilled in the art. In the present description, descriptions of steps and/or objects are presented that will enable those skilled in the art to realize computer program code portions appropriate to particular contexts and facilities, such as particular machines, computer languages, operating systems and the like. The computer program implementing the method of the present invention can be for example embodied in one or more executable files, resident on a suitable support accessible from the memory of the computer, such as a hard disk, a removable disk or memory (e.g. a diskette, a CD- or DVD-ROM, or a USB key), or an external disk readable through a LAN (Local Area Network). For the purposes of the present invention, the terms "software program" or "computer program" also comprise files needed for the execution of the executable file or files, such as libraries, initialization files and so on, that can be resident on a suitable support accessible from the memory of the computer, such as a hard disk, a removable disk or memory (e.g. a diskette, a CD- or DVD-ROM, or a USB key), or an external disk readable through a LAN. Furthermore, for the purposes of the present invention the terms "software program" or "computer program" also comprise files possibly different from the executable file or files and/or from the files needed for the execution of the same, embodied in an installable software, adapted, when run on the computer, to install the executable file or files and the files needed for the execution of the same. The installable software can be resident on a suitable support, such as a removable disk or memory (e.g. a diskette, a CD- or DVD-ROM, or a USB key) or it can be available for download from a network resource, such as a server comprised in a LAN, or reachable through an external network, for example the Internet. In the following, simulated and experimental results of an exemplary implementation of the present invention are described.

First, a static magnetic signature of a particular car model (Citroen Xantia™) has been acquired from a mono-axial Honeywell magnetic sensor model HMClOOl placed at the road level below the car and having a suitable orientation for sensing the vertical or z-component (oriented along the car height) of the magnetic field. By spline-interpolating this vertical component magnetic curve, the Applicant has derived the expected time responses of two sensors having two different values of gains and two different values of offset voltages, in correspondence to the passage of the above car moving with two different speeds.

Fig. 7a and 7b show the simulated responses of the first sensor in correspondence to a speed of respectively 10 and 100 krn/h. The horizontal axis represents the number of samples taken from an arbitrary starting point (sample number 1) so that the whole car passage is comprised within the curve shown in Figs. 7. The vertical axis represents the respective readings (Voltage) of the sensor, which senses the Earth magnetic field distortion by the car. In Figs. 7 the baseline signal 710' and 730' is also shown, which may be interpreted with a good approximation as the Earth baseline magnetic field. The baseline value has been computed as the average over many points of the curves 710 and 730 in correspondence to the absence of the object.

Figure 7a and Figure 7b each shows the superposition of a set of ten simulated responses (curve 710 and 730) of the first sensor taking into account the noise effect in order to better evaluate the actual behavior. Three kind of noise have been added to the ideal (no- noise) sensor responses: i) Ambient noise, i.e. the environmental noise due to the 50 Hz electro-magnetic pollution. It has the form: V_A (t) = V_0A sin(2π501 + φ) where φ is a pseudo-random generated phase between 0 and 2π and VQA has been set equal to 1 mV; ii) Thermal noise, V_τ(t) , i.e. a pseudo-random generated voltage value with a normal Gaussian distribution centered at zero voltage and having a V₀₇. amplitude equal to 1 mV; iii) Digitization noise, i.e., the finite resolution error introduced by the digitization of the signal in the electronics (i.e. in the ADC), assuming a 15 bit ADC converter with 3.6 V amplitude, the maximum error being in this case 3.6V/2¹⁵.

The method shown in Fig 6 has been applied to the obtained sensor responses, with the step 560 based on the speed evaluation algorithm of Eq. 25 (with the ratio K₁ 1 K₂ equal to the exact value) in the case the two sensors (positioned along the direction of movement of the car) are spaced apart by a distance of 4 cm and the sampling rate is equal to 250 Hz (τ'=4 ms). It has been assumed that no spurious contribution was present.

Figure 7 a shows the ten instants of time (720) selected by the algorithm of Fig. 6 for computing the speed, when the car is assumed to pass at the speed of 10 km/h. The parameter n entering the calculation of the time variation of the magnetic field |F, (t ) - V₁ (t - n τ)j was set n=2 for 10 KnVh and n=\ for 100 km/h. At the beginning of the car passage, the threshold value V₇₁₁₁ for determining the condition of velocity calculation {γ_x (t)- V_x (t - nτj > V₁₁₁₁ ) was set equal to 0,005V. The threshold value was dynamically updated each time the time variation of the magnetic field reached the current threshold value. The maximum number of times the threshold value could be updated within a single car passage was set equal to 8. Within each simulation, the algorithm has always updated the threshold value 8 times and the corresponding last time instant is the one shown in Fig. 7a. The average (ten simulations) calculated speed was 10.13 km/h with a standard deviation of 0.17 km/h.

Figure 8a shows the ten instants of time (740) selected by the algorithm of Fig. 6 for computing the speed, when the car is assumed to pass at the speed of 100 km/h. The same setting described above has been used. Within each simulation, the algorithm has always updated the threshold value 2 times. It is noted that all the simulations select the same time instant for speed calculation. The average (ten simulations) calculated speed was 99.99 km/h with a standard deviation of 0.50 km/h.

Fig 8 shows experimental results of field trials of the method of the present invention for the same vehicle shown in Figs. 7. Horizontal axis represents the speed as reported by the in-car speedometer and vertical axis represents the speed as calculated by the system and method of the present invention in the embodiment described with reference to Figs. 7. All the parameters set for the field trials are identical to the parameter values set in the simulation described above. Curve 810 represents the exact correlation curve (no error). Open circles represent the average of the experimental results. Y-error bars are the standard deviations of the averages. X-error bars represent an estimated 5% error due to the speedometer reading.

In the method and system for measuring the velocity of a moving object according to the present invention, an important role is played by the value of the sensor distance(s) d and of the sampling time step(s) τ'.

For the sake of clarity, the following discussion will be referred to the particular embodiment of the present invention wherein a speed measurement system for road vehicles uses a pair of magnetic sensors installed along the direction of the vehicle velocity. The choice of the sensor distance d and of the sampling time step τ' may be done according to the following considerations.

As far as the sensor distance d is concerned, it is preferably shorter than the object size. Further, in order that Eq. 9 approximates sufficiently well the space derivative, it is advantageous that the distance between sensors is smaller than the spatial length over which the measured physical quantity changes significantly in static conditions, so that the sensor responses belong to the same nearly linear portion of the static signal of the physical quantity. For example, the signal variations related to the high magnetic permeability parts (e.g. the engine block) of a car is in the tens of centimeters range or less. For distances between the object under measurement and the sensing device 100 sufficiently short, (typically from about 20 cm to about 1 m), the static signature measured by a sensor shows variations in correspondence to spatial scales of the same order of the magnetic permeability masses. Accordingly, it is preferred that the distance d between the sensors is less than 15 cm, preferably less than 10 cm. On the other hand, in order not to degrade the signal to noise ratio of the signals measured, it is preferable that a minimum distance between the sensors is kept which depends upon the sensitivity of the sensors. Typically, it is preferred that the distance d is greater than or equal to 1 cm, preferably greater than or equal to 2 cm.

As far as the sampling time step τ' is concerned, in order to 'see' the magnetic masses according to the discussion above, it is preferably chosen to be comparable to the ratio of the spatial scale of static magnetic variation and the speed of the car which may be assumed to vary between about 10 and 150 km/h. Assuming a distance between the two sensors in a range from about 1 centimeter to about 15 centimeters, the above implies a time step τ' of the order of 0.2 ms to 4 ms, corresponding to a sampling rate ranging from about 20 Hz to about 4 kHz. Preferably, the sensors distance ranges from about 2 centimeter to about 10 centimeters, the time increment from about 0.5 millisecond to about 40 milliseconds, and the corresponding sampling rate from about 30 Hz to about 2 kHz.

For all the algorithms, choosing a sensor distance of 5 cm, a sampling rate less than about 1 kHz, and preferably less than or equal to about 500 Hz (down to 200 Hz) has been verified to give satisfactory results. The sampling time step τ' and distance d enter the equations above always in the form of a ratio. The Applicant has found that the preferred range for this ratio spans over the range of speeds one expects to measure. For example, if the application is in roadway vehicle speed measurement, the preferred range could be between about 1 and 150 Km/h. In fact, the other ratio entering Eq. 11 and the corresponding ratios in the equations above would otherwise be largely different from unity, and this would turn into largely different numerator and denominator. This in turn would require a higher resolution and higher dynamic in the measurement.

Claims

1. A method for measuring the velocity of a moving object, the method comprising: - acquiring first data from a first sensor, said first data being associated to the passage of the moving object in the sensitivity field of the first sensor and being representative of a physical quantity variable with the object passage;

- calculating from said first data a time variation of said physical quantity;

- acquiring second data from a second sensor spaced from the first sensor by a known distance, said second data being associated to the passage of the moving object in the sensitivity field of the second sensor and being representative of said physical quantity;

- calculating from said first and second data a first and a second numerical quantity representative respectively of a time derivative and a spatial derivative of said physical quantity in a given time interval; and - calculating the velocity of the moving object in said given time interval as a function of said first and second numerical quantity; wherein the method comprises the step of comparing said time variation of said physical quantity with a first threshold value and wherein at least the step of calculating the velocity is conditional upon being said time variation of said physical quantity in said given time interval above said first threshold value.

2. The method of claim 1 wherein also the step of acquiring the second data from the second sensor is conditional to being said time variation of said physical quantity in said given time interval above said first threshold value.

3. The method of claim 1 or 2 wherein in the step of acquiring the first data from the first sensor, a subset of the first data is acquired conditionally to being said time variation of said physical quantity in said given time interval above said first threshold value, said subset being used in the step of calculating the first and the second numerical quantity.

4. The method of any of the above claims wherein said first data from the first sensor comprises a time series of data representative of the physical quantity in equally-spaced successive time slots.

5. The method of the preceding claim wherein said time variation of the physical quantity is calculated from said time series of data in each of said time slots.

6. The method of any of the above claims wherein said first threshold value is set to a predetermined value in correspondence to the start of the passage of the moving object.

7. The method of claim 6 when depending on claim 5 wherein said first threshold value is varied in time slots successive to the start of the passage of the moving object, wherein at each of said time slots after the start of the passage the respective first threshold value is related to the value of the time variation of the physical quantity at the last preceding time slot in which the respective time variation was above the first threshold value at said preceding time slot.

8. The method of the preceding claim wherein said given time interval corresponds to the time slot wherein the time variation of the physical quantity is maximum within the passage of the moving object.

9. The method of any of the above claims wherein, in the step of calculating the velocity dP SP - of the moving object, the velocity is calculated by inversion of the equation — = v , dt dx

wherein P is the physical quantity, — includes said time derivative, — is the spatial dt dx gradient of the physical quantity P, including said spatial derivative and v is a vector representing the velocity.

10. The method of any of the above claims wherein the first and the second sensor (10, 20) lie along a direction substantially parallel to the velocity.

11. The method of claim 10 wherein the time derivative is the time derivative of one component of the physical quantity and the spatial derivative is the spatial derivative along said direction of said one component of the physical quantity and the velocity is obtained as the ratio of said time derivative and said spatial derivative.

12. The method of claim 13 wherein, in the step of calculating the time derivative and the spatial derivative;

- the time derivative is approximated by the ratio of the difference between two data from one of the two sensors and a corresponding time increment; and - the spatial derivative is approximated by the ratio of the difference of two substantially contemporary data taken from the two two sensors and the known distance.

13. The method of any of the preceding claims wherein the calculation of the spatial derivative uses baseline values of the first and second sensor measured in absence of the moving object.

14. A method for monitoring road traffic comprising a method for measuring the velocity of a vehicle according to any of the preceding claims, wherein the moving object is the vehicle.

15. A system (1) for measuring the velocity of a moving object (200), said system comprising a sensing device (100) comprising at least a first and a second sensor (10, 20) spaced apart by a known distance, a processing unit (110) and a connection (120) operatively connecting said sensing device and said processing unit, wherein the processing unit (110) is configured for operating the system (1) according to the following steps:

- acquiring first data from the first sensor, said first data being representative of the physical quantity and being associated to the passage of the moving object in the sensitivity field of the first sensor; - calculating from said first data a time variation of said physical quantity;

- acquiring second data from the second sensor, said second data being associated to the passage of the moving object in the sensitivity field of the second sensor and being representative of said physical quantity; - calculating from said first and second data a first and a second numerical quantity representative respectively of a time derivative and a spatial derivative of said physical quantity in a given time interval; and

- calculating the velocity of the moving object in said given time interval as a function of said first and second numerical quantity; wherein at least the step of calculating the velocity is conditional upon being said time variation of said physical quantity in said given time interval above said first threshold value.

16. The system of claim 15 wherein also the step of acquiring the second data from the second sensor is conditional to being said time variation of said physical quantity in said given time interval above said first threshold value.

17. The system of claim 15 or 16 wherein in the step of acquiring the first data from the first sensor, a subset of the first data is acquired conditionally to being said time variation of said physical quantity in said given time interval above said first threshold value, said subset being used in the step of calculating the first and the second numerical quantity.

18. The system of any of claims 15 to 17 wherein said first data from the first sensor comprises a time series of data representative of the physical quantity in equally-spaced successive time slots.

19. The system of the preceding claim wherein said time variation of the physical quantity is calculated from said time series of data in each of said time slots.

20. The system of any of claims 15 to 19 wherein said first threshold value is set to a predetermined value in correspondence to the start of the passage of the moving object.

21. The system of claim 20 when depending on claim 19 wherein said first threshold value is varied in time slots successive to the start of the passage of the moving object, wherein at each of said time slots after the start of the passage the respective first threshold value is related to the value of the time variation of the physical quantity at the last preceding time slot in which the respective time variation was above the first threshold value at said preceding time slot.

22. The system of any of claims 15 to 21 wherein the processing unit (110) is configured

for calculating the velocity by inversion of the equation — = v , wherein P is the dt dx

physical quantity, — includes said time derivative, — is the spatial gradient of the physical dt dx quantity P , including said spatial derivative and v is a vector representing the velocity.

23. The system of claim 22 wherein the first and second sensor (10, 20) lie along a direction substantially parallel to the velocity.

24. The system of claim 23 wherein the time derivative is the time derivative of one component of the physical quantity and the spatial derivative is the spatial derivative of said one component of the physical quantity along said direction and the velocity is obtained as the ratio of said time derivative and said spatial derivative.

25. The system of any claims 15 to 24 wherein the first and second sensor are magnetic sensors and the physical quantity is at least a component of a magnetic field.

26. A traffic monitoring system including the system according to any of claims 15 to 25.

27. A computer program product loadable into the memory of a computer, comprising software code portions for performing the steps of the method of any of claims 1 to 14, the computer program product being adapted, when run on a computer, to calculate the velocity of the moving object.