EP2095133A1

EP2095133A1 - Method and system for determining the velocity of a moving object

Info

Publication number: EP2095133A1
Application number: EP06829803A
Authority: EP
Inventors: Riccardo Tebano; Stefano Serra
Original assignee: Pirelli and C SpA
Current assignee: Pirelli and C SpA
Priority date: 2006-12-21
Filing date: 2006-12-21
Publication date: 2009-09-02
Also published as: WO2008074351A1

Abstract

A method for determining the velocity of a moving object (200) such as a vehicle comprises: - acquiring from a first (10) and a second (20) sensor spaced apart by a given distance and lying along a direction substantially parallel to the direction of motion of the moving object (200) respectively a first and a second measurement signals, each of the two measurement signals being representative of a physical quantity P at a location of the respective sensor, the physical quantity P being subject to a change in correspondence to a passage of the moving object; - calculating from the first and the second measurement signals a difference between a first and a second value representing the physical quantity respectively measured by the first and the second sensor; - calculating from the second measurement signal a first and a second quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the second sensor; and - calculating the velocity of the moving object as a function of said difference and of said first and second quantity. A system implementing the above method is also disclosed.

Description

METHOD AND SYSTEM FOR DETERMINING 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.

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 digital 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.

US patent n° 5,331,276 titled "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. Summary of the invention

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, the sampling rate of the sensor signals needs to be high

(e.g., greater than or equal to several KHz) or the sensor spacing has to be large (e.g., greater than 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 devices rely on battery power supply ('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. under the asphalt or cement of a road.

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.

In addition, several prior art methods of velocity calculation typically give measurement results dependent on the choice, within the time interval corresponding to the vehicle passage, of the time instant when the speed is actually evaluated. Accordingly, a complex criterion for suitably choosing the exact time instant for evaluating the speed is often necessary, thus increasing the overall complexity of the system.

Moreover, several prior art methods of velocity calculation gives acceptable results only in a limited range of speeds.

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

Moreover it should also be preferable that the velocity measuring system does not rely on a criterion for selecting a sub-interval of the time interval corresponding to the passage of the object for speed calculation. Finally, the method should advantageously be accurate in a wide range of speeds.

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.

According to an aspect of the present invention, a method for determining the velocity of a moving object is provided. The method comprises acquiring from a first and a second sensor spaced apart by a given distance and lying along a direction substantially parallel to the velocity respectively a first and a second measurement signals, each of said two measurement signals being representative of a physical quantity P at a location of the respective sensor, the physical quantity P being subject to a change in correspondence to a passage of the moving object; calculating from the first and the second measurement signals a difference between a first and a second value representing the physical quantity respectively measured by the first and the second sensor; calculating from the second measurement signal a first and a second quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the second sensor; and calculating the velocity (or speed) of the moving object as a function of said first and second quantity and of said difference.

The passage of the moving object occurs near each respective sensor, i.e. sufficiently close to each sensor to determine a measurable change (e.g. with sufficient signal to noise ratio) of the physical quantity at the location of the sensor. Typically said difference is calculated between the values of the physical quantity sensed by the first sensor and the second sensor at the same instant of time.

The Applicant believes that the evaluation of the velocity of the object as a function of at least a spatial difference, at least a first time derivative and at least a second time derivative of the physical quantity, wherein the spatial difference, the time derivative, and the second time derivative are at least approximately evaluated from two measurement signals acquired respectively by two sensors spaced apart by a given distance solves the problem of measuring the velocity accurately and with low power consumption and small overall dimensions of the resulting device.

The feature that the two sensors lie along a direction substantially parallel to the velocity means that a possible tilt, in any direction, between the line which the two sensors lie along and the velocity vector is less than or equal to 30°, preferably less than or equal to 15°, even more preferably less than or equal to 5°. The given distance is preferably less than 50 cm, more preferably less than 25 cm, even more preferably less than or equal to 15 cm.

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 at least a physical quantity which is subject to a variation in correspondence to the passage of the object and that such variation could be sensed by means of suitable sensors placed sufficiently near the object trajectory.

Preferably, the step of calculating the velocity v of the moving object at a given instant of time / makes use of the following equation:

r_λ — r₂ + A₂ wherein δx is the given distance, P. and P, are said first and second value representing the physical quantity at the given instant of time t respectively measured by the first and the second sensor, and A₂ and B₂ are respectively said first and second quantity calculated at the given instant of time t. It is noted that P₁ -P₂ represents the above said spatial difference of the physical quantity P. It is to be understood that, for example, P₁ , P₂ , A₂ and/or B₂ may be taken at slightly different instants of time without departing from the teaching of this embodiment of the present invention, provided that the time difference between the values and/or quantities is low enough not to affect the accuracy of the result. For example, given a time increment τ as described below, a shift of the time instant less than one tenth (better one hundredth) of the time increment may be accepted. The Applicant has found that the use of the equation above gives the advantage of low computational resources requirements along with a wide range of validity of the results.

In one embodiment, the step of calculating the velocity of the moving object at the given instant of time t comprises an at least approximate inversion of the above equation with respect to the quantity to be known v.

Preferably said at least approximate inversion of the above equation takes the following form:

This allows further reducing the computational effort for calculating the velocity. Advantageously, the first quantity (e.g. Ai) represents a numerical approximation of the first time derivative of said physical quantity at the location of the second sensor and at the instant of time t. For example, it may be expressed as a ratio of a difference of a third and a fourth value representing the physical quantity measured by the second sensor at two instants of time separated by a time increment τ and the time

increment τ itself (e.g. wherein P, and P₄ are said third and fourth value). In this way, the first quantity may be expressed as a ratio of a difference of two consecutive measured values of the physical quantity, sampled at two consecutive instant of time at a relative time delay equal to the time increment τ and the time increment τ . Preferably, the third value is equal to the second value (e.g.

• Typically P, is preceding to P₁ .

Advantageously, the second quantity (e.g. Bi) represents a numerical approximation of the second time derivative of said physical quantity at the location of the second sensor and at the instant of time t. For example, it may be expressed as a ratio of a linear combination of a fifth, a sixth and a seventh value representing the physical quantity measured by the second sensor at three instants of time separated by the time increment τ , and the square of the time increment. For example said linear

P -2P +P combination may be expressed as ^ ₅ ^~ 2Z₆ + P₁ (e.g. B₂ = ₂ ) .

In this way, the second quantity may be expressed as the ratio of a linear combination of three successive values of the physical quantity measured at the second sensor, sampled at three successive instants of time at a relative time delay equal to τ , and the square of the time increment τ .

Preferably the same two values used for approximating the first time derivative are also used to approximate the second time derivative. Accordingly, the sixth value may be equal to the third one and the seventh value may be equal to the fourth one. In this way advantageously only one additional datum is necessary to calculate the second time derivative with respect to the first time derivative (e.g.

_P - _P , Λ -Λ & P₅ -2P_{3 +} P₄ (δx)² ]^{~ 2} τ v 2r² v ^K Still more preferably, the sixth value is equal to the third one and also equal to

the second value (e.g. ) . In this way, it is advantageously possible to calculate with accuracy the velocity by using only four data from the two sensors (one from the first sensor and three from the second one) . In another embodiment, the method above further comprises calculating from the first measurement signal a third and a fourth quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the first sensor; and, in the step of calculating the velocity of the moving object, calculating the velocity as a function also of said third and fourth quantity (in addition to the first and second ones and the spatial difference).

Preferably, in the step of calculating the velocity of the moving object, the velocity at the given instant of time t is calculated by an at least approximate inversion of the equation:

2P₁ , wherein A₁ and B₁ are respectively said third and fourth quantity calculated at the given instant of time t. The same discussion above for the substantial coincidence of the time instants holds also for the calculation of A₁ and B₁ . It is noted that in writing the above expression use has been made of the above equation:

P_x — _{as W1}n be also clear from what follows below. The at least approximate inversion of the said equation may take the following form:

This allows further reducing the computational effort for calculating the velocity.

Advantageously, the third quantity (e.g. A₁) represents a numerical approximation of the first time derivative of said physical quantity at the location of the first sensor and at the instant of time t. For example, it may be expressed as a ratio of a difference of a eighth and a ninth value representing the physical quantity measured by the first sensor at two instants of time separated by the time increment τ and the time increment r (e.g. A_x — _} wherein P₈ and P₉ are said eighth and ninth value).

In this way, the third quantity may be expressed as a ratio of a difference of two consecutive values of the physical quantity measured at the first sensor, sampled at two consecutive instant of time at a relative time delay equal to the time increment τ and the time increment τ .

Preferably, the eighth value is equal to the first value (e.g. A A P 1 = 1 - P 9 ) .

Advantageously, the fourth quantity (e.g. Bi) represents a numerical approximation of the second time derivative of said physical quantity at the location of the first sensor and at the instant of time t. For example, it may be expressed as a ratio of a linear combination of a tenth, an eleventh and a twelfth value representing the physical quantity measured by the first sensor at three instants of time separated by the time increment τ , and the square of the time increment. For example said linear

P - IP + P combination may be expressed as o_λ — ^ ) .

In this way, the fourth quantity may be expressed as the ratio of a linear combination of three successive values of the physical quantity measured at the first sensor, sampled at three successive instants of time at a relative time delay equal to τ , and the square of the time increment τ .

Preferably the same two values used for approximating the first time derivative at the first sensor are also used to approximate the second time derivative at the first sensor. Accordingly, the eleventh value may be equal to the eighth one and the twelfth value may be equal to the ninth one. In this way advantageously only one additional datum is necessary to calculate the second time derivative with respect to the first time

deπvative (e.g. ) .

Still more preferably, the eighth value is also equal to the first value. In this way, it is advantageously possible to calculate with accuracy the velocity by using only six data from the two sensors (three from the first sensor and three from the second one) .

Advantageously in the step of calculating the velocity of the moving object use is done of a first and a second baseline value respectively of the first and second sensor. The baseline value of a sensor represents the value of the physical quantity in absence of the moving object (in absence of any moving objects). In other words, the method above preferably includes the step of evaluating a first and a second baseline value respectively from said first and second measurement signals.

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). Advantageously, the at least two sensors are identical sensors. They are preferably fixed in the frame of reference with respect to which the object velocity has to be known. Preferably, the at least two sensors are magnetic sensors and the physical quantity is at least a component of a magnetic field. Preferably, the at least one component of a magnetic field is the vertical component of the magnetic field with respect to the plane of movement of the object.

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 given distance with respect to one another and along the direction the object is expected to travel.

According to another aspect of the present invention, a system for measuring the velocity of a moving object comprises a sensing device comprising at least a first and a second sensor spaced apart by a given distance and each one sensitive to a physical quantity subject to a change in correspondence to a passage of the moving object, and a processing unit operatively connected to said sensing device, wherein the sensing device is configured for acquiring a first and a second measurement signal respectively from the first and second sensor, each of said two measurement signals being representative of the physical quantity at a location of the respective sensor; and the processing unit is configured for calculating from the first and the second measurement signals a difference between a first and a second value representing the physical quantity respectively measured by the first and the second sensor; calculating from the second measurement signal a first and a second quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the second sensor; and calculating the velocity of the moving object as a function of said difference and of said first and second quantity.

The preferred embodiments of the above system correspond to the above preferred embodiments of the method of the present invention.

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

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 shows a flowchart of an exemplary embodiment of a method for selecting a time instant for applying the method of the present invention;

Figure 3 shows experimental curves of the response of a magnetic sensor; and

Figures 4 shows calculated results of an embodiment of the present invention. Detailed description of the preferred embodiment(s) of the invention 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.

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.

As shown in Figure 1, the sensing device 100 comprises at least a pair of sensors 10, 20 spaced apart by a given distance Sc, each sensor being sensitive to a physical quantity P , which may be a scalar or a vectorial field. In case of a vectorial field, each sensor may be sensitive to at least one component of the physical quantity. Each sensor 10, 20 are 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, each one output measurement signal is an analogical signal which is digitized, or sampled, by an analog-to-digital-converter (ADC - not shown). In general, the total number of sensors comprised within the sensing device 100 of the present invention and the number of components of the physical quantity each sensor is able to sense (i.e. the number of 'axes') depend upon the degree of redundancy of the velocity measuring system 1. Preferably each sensor is sensitive to no more than one component, i.e. a 'mono-axial sensor', in order to save energy. However, the present invention equally holds in case of multiaxial sensor(s), for example applying the present method to more than one component separately or to a combination of the components (e.g. to the modulus of the vectorial physical quantity P) With reference to Figure 1 (not to scale), a moving object 200 is moving, with respect to an (x, y, z) frame of reference, with a velocity v = \v_x,v_y,v_z ). It is assumed

that the physical quantity P(x,t)= e.g., a magnetic or electric field, in a point x of a region around the moving object changes in time as a consequence of the passage of the moving object 200. 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 .

In one embodiment of the present invention, the at least two sensors 10, 20 may be placed along the direction of the velocity vector. This is particularly suitable when the velocity is expected to 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, while the velocity of a car running along a multi-lane road lies with good approximation along the expected direction. A train running along the rail is another example of an object whose velocity is expected to lie along a given fixed direction.

With reference again to Fig. 1, two sensors 10, 20 are placed at points xi and X₂ along the x-axis and spaced apart by a distance. 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). As far as the sensor distance δx is concerned, it is preferably shorter than the object size. Further, in order that the spatial variations are approximated sufficiently well, 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 (see e.g. Fig. 3). 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. As shown in Figure 3, 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 δx between the sensors is less than 50 cm, preferably less than 15 cm, more preferably less than 25 cm, still more preferably less than or equal to 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 δx is greater than or equal to 1 cm, preferably 2 cm. Assuming the velocity having only the x component, i.e., v = (v,O,θ) and 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 velocity v can be calculated by considering the fact that the same value of the physical quantity is measured at two different locations x, and X₂ separated by the distance δx with a

delay in time equal to — , and expanding the relevant expressions in a Taylor series v

comprising the power series of the time delay — truncated at the second order, as v follows :

(Eq.1) P(x₂,/) (Eq.2), wherein P(x,,t) is the physical quantity sensed by the first sensor at the location x, at the instant of time t, P(x₂ ,t) is the physical quantity sensed by the second sensor at the

, • _r • _{A/ \} dP(xi,t) , _H/ _λ d²P(xι,t) location X₂ at the instant of time t, P(x, ,/) := — *-^ and P(x, ,f):= ^^ are dt dt the first and second time derivative sensed at one of the two location x₍. , where i stands for 1 or 2.

Solving for v the Eq. 1 one gets: where the plus sign holds for P(x₂,/) > 0 , while the minus sign is appropriate when P(x₂,t) < 0 .

Considering now the subtraction of Eq. 1 and Eq. 2: and then solving (inverting) for v the resulting expression, one gets (Eq. 4bis): where the "plus" sign holds when p(x, ,t)+ p(x₂ ,/) > 0 , while the "minus" sign is appropriate when p(x, , /) + P(x₂ , t) < 0.

The Applicant has found that the use of the equations above gives the advantage of low computational resources requirements along with a wide range of validity of the velocity results. In order to further reduce the computational effort, it is possible to consider a power series (Taylor) expansion of the square roots in Eq. 3 and Eq. 4 truncated at the first order, resulting in simpler expressions which avoid square roots extraction:

From Eq. 3 one thus gets: From Eq. 4 one gets: ^'P(x_x,t)+P(x₂,t) , P(X₂₅Z)-P(X₁,/) v = δx + — (Eq.6)

P(x,,t)-P(^χ ₂,t) P(x,,0+P(^χ ₂,0_. In one embodiment of the present invention it is possible to advantageously numerically approximate the time derivatives and the second time derivatives in Eq.1 to 6 with the following relations: jfr ₎.ffr,.«*r)-2J(, /)₊ffr_l,/-r) ,_{=1,2 (Eq}.₇._2)>

being τ a time increment selectable in the interval from 400 μs to 8000 μs, preferably less than or equal to 4000 μs, more preferably in the interval from 1000 μs to 3000 μs.

Alternatively to Eq.7.1, it is possible to use the following equivalent numerical approximations: p, v P(x,,t + r)-P(x,,t-r) z=l, 2 (Eq.7.1").

Using Eqs.7 and introducing the following expressions:

it is then possible to express Eq.3 as: where the plus sign holds when P₂₁ - P₂₀ > 0 , while the minus sign holds when P₂₁ -P₂₀ <0. In the same way Eq. 4 may be rewritten as (Eq. 9):

Sx v= — x

4r

.. føi -^Q+^21 " AoWføi -P₁₀ +P_2i -Ao)² +4føi -PΛPn -2P₁₁ +P₁₀ -P₂₂ +2P₂₁ -P₂₀)

where the plus sign holds for P₁₁ -P₁₀ +P₂₁ -P₂₀ >0, while the minus sign holds forP_π - P₁₀ + P_2l - P₂₀ < 0.

Similarly the simplified Eq. 5 and Eq. 6 may be respectively expressed as:

(Eq. 10) Eq. 1, 3, 5, 8 and 10 show that, according to the present invention, it is possible to compute the vehicle speed at a given instant of time t by measuring only one difference between the values of the physical quantity sensed by the first sensor and the second sensor at the same instant of time, and one first time derivative and one second time derivative of the physical quantity sensed by one of the two sensors. Indeed, as clear from Eq. 8 and 10, the present invention allows the evaluation of the speed by using only four measurement data from the two sensors 10, 20, of which three successive data are from one sensor and one datum is from the other sensor. This is particularly advantageous in comparison to prior art methods of measuring the speed based on correlation function, which need to process two whole time series of data. Preferably, in order to improve the accuracy of the algorithms of Eq. 1, 3, 5, 8 and 10 by reducing the effect of the noise which affects the sensors measurements, it is advantageous considering the subtraction of Eq. 1 and Eq. 2 and then solving for v the resulting expression, getting Eq. 4, 9 and 11. 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 (and thus the power consumption), in that Eq. 9 and 11 comprise only two additional measurement data (specifically P₁₀ and P₁₂ ) with respect to Eq. 8 and 10, which comprises four measurement data. It is noted that each datum represents the value of the sensed physical quantity at a certain instant of time at the location of the respective sensor. It has been verified that choosing a sensor distance of 4 cm, a time increment τ of the order of 2 ms and a sampling rate less than about 500 Hz (down to 100 Hz) all the algorithms above give satisfactory results.

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(t) = kP{t)+ V^0(T (Eq. 12), Wherein V(t) is the voltage response, P(t) is the generic physical quantity to be measured (e.g. one component of the quantity P ) and k and V^ are called the 'gain' and the 'voltage offset' (i.e. the zero-field response), respectively. The measured physical quantities P₁₀ = P(x,,/ -r) , P_n = P(x,,t) and P_n = P(x,,/ + r), /=1,2, will be related to the sensor voltage responses by the following relations (Eq. 13):

p — p _πt[ _γ f I - _\ _ . _ V₂2₁2 - V 2?_ k₂ k₂ hiserting Eqs. 13 into Eq. 8 one gets (Eq. 14):

Similarly, inserting Eq. 13 into Eq. 9 one gets (Eq. 15):

Similarly, inserting Eq. 13 into Eq. 10 one gets: + F- v = 20 (Eq. 16)

Similarly, inserting Eq. 13 into Eq. 11 one gets (Eq. 17):

In order to compute the speed v, the gains (kj and k£) and the offset voltages (V °^ff and Vf^ff) of the two sensors have to be known. Typically, two distinct sensors, even thought of identical type, have different gains k and voltage offsets V°^ff. Moreover the parameters k and V^ are subject to temperature drift and/or other changes due to environmental conditions. Usually, various procedures (called 'calibration') for acquiring the current values of the parameters k and V°^ff 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.

For example, magnetic field sensors of the kind of the commercially available magneto-resistive sensors HMClOOl/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 ΔP and evaluating the gain according to the formula:

F₁ - F₁ k = _ ' 2 (Eq. 18),

AP wherein V₂ is the sensor voltage reading when the field ΔP is applied and F_/ is the sensor reading without the field ΔP 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 V°^ff. 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^xl = kP + V^ojr and after the reset pulse the reading is F^reset = -kP + V^off , where P is the same magnetic field. Taking the sum or the difference between the two readings allows obtaining the following expressions: V^sel - V^κset = 2kP (Eq. 19)

V^xt + V^κsa = 2 V^ojr (Eq. 20)

The ratio κ_λ I K₂ in Eqs. 14 to 17 may be evaluated in one embodiment by measuring the gains (k_/ and ki) using the offset strap procedure (Eq. 18) for both the sensors. In another embodiment of the present invention, the ratio κ_] I K₂ in Eqs. 14 to

17 is given an approximate value of 1.

In still another embodiment, it is possible to advantageously use the set/reset approach (Eq. 19 and 20) 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 the same with good approximation. Using Eq. 19 it derives that:

^K2 V₁ V ) ^V2 V ) (Eq. 21).

These procedures may be performed every time that the ratio K₁ 1 K₂ in Eq. 14, Eq. 15 , Eq. 16 or Eq. 17 need to be updated. The offset voltages (V °^ff and V ₂ ⁰^) in Eqs. 14 to 17 may be evaluated by using the set/reset approach (Eq. 20) for both the sensors.

In a preferred alternative embodiment, there can be followed an approach which avoids the need of performing a calibration procedure in order to evaluate the offset voltages, the approach being based on the consideration that the part of the physical quantity of interest is the one related to the movement of the moving object, i.e. the change of the physical quantity during the passage of the object with respect to the "background" value of the physical quantity when no moving object passes near the sensors. In other words, the "back-ground" of the physical quantity is not of interest. This approach suggests rewriting Eq. 12, as follows: V(t) = kP(t)+ V^σ = k(p(t)+ P_bg )+ V^off , where P'(t) is the (dynamic) part of the physical quantity related to the movement of the moving object (in the case the physical quantity is the magnetic field, it is the magnetic field increment or decrement related to the movement of the moving object), P_bg is the (static) part of the physical quantity related to the background (in the case the physical quantity is the magnetic field, it is the earth magnetic field, possibly including contributions from nearby static magnetic sources). There are defined the baselines voltages V₁ , J- 1,2, as follows:

According to Eq. 22 and Eq. 13, it is possible to rewrite Eq. 8, Eq. 9, Eq. 10 and Eq.

11, respectively as follows:

(Eq. 23);

(Eq. 24);

(Eq. 26).

The equations 23 to 26, based on the baselines values, are advantageous in that the baselines values V₁ and V₂ are simply evaluated by sampling the signal from the sensors when no moving objects are present (i.e. no moving object in the nearby of the sensors), without the need of specifically determining the value of the offset voltage V°^ff. Typically the baseline is continuously updated. The processing unit 110 is suitably configured to recognize if a certain value coming from a sensor is a 'baseline' value (and thus apt to be used to update the baseline value).

For example an algorithm may be implemented in the processing unit 110 in order to decide if the current reading of the sensor is a 'baseline' value or a value in presence of a moving object.

In general, and for the reason above, it is advantageous to combine the method of velocity calculation according to the present invention with a method for detecting the presence of a moving object passing nearby the sensors. In one embodiment of the present invention, the method for detecting the object's presence is based upon periodically and repeatedly sampling at least one (advantageously no more than one) sensor measurement signal at a sampling rate /(and corresponding sampling period Mf). Typically the sampling period Iff is in the interval from about 0.1 ms to 20 ms, preferably greater than or equal to 1 ms, more preferably greater than or equal to 4 ms. Among the advantages of the present invention is that the sampling frequency/may be kept low in comparison with comparative methods.

Preferably, in order to further reduce power consumption, the at least one sensor used for detecting moving objects is periodically switched off and turned on repetitively. The sensors stay switched on just for the time necessary for the signal to be sampled by at least one ADC-analog to digital converter. The most of the electronics necessary to perform the tasks described above stay also turned on just for the time strictly necessary to complete the process.

For example, the presence of a moving object is triggered when the measured value departs from the value measured in the absence of moving objects (i.e. the baseline value) by a predetermined (threshold) amount. hi addition, it is preferable to combine the method of velocity calculation according to the present invention with a criterion suitable to select the specific time instant for applying the present speed evaluation method within the time interval corresponding to the passage of the object close to the system 1.

Such a criterion should be suitable to reduce as much as possible the effect of any noise or error which can affect the measurements. This can be reached by selecting an instant of time when the signal to noise ratio is high, e.g. by selecting an instant of time when the time variation of at least one signal from a sensor are large. The criterion for selecting the instant of time when to evaluate the speed during the object passage can be also repeated several times during the passage of the vehicle, in order to improve the performances of the system 1.

Such criterion may exemplarily be applied to the above values of the sampled signal from the at least one sensor when in presence of the moving object (i.e. when the above method of detecting the presence of a moving object has actually detected the presence). In this case also the rate at which the above criterion is cyclically performed is the above sampling rate/

Fig. 2 diagrammatically shows the steps of operation of a method for selecting the time instant for applying the velocity measuring system in one embodiment of the present invention. The entire method of figure 2 is preferably run only in presence of a moving object, i.e. it may be triggered by the above method of detecting the presence of a moving object. In step 210 the system 1 (at least one sensor and related electronics) is switched from a low power consumption mode to a normal mode. A datum (e.g. a voltage) representative of the physical quantity is then acquired from the switched on sensor in step 220. In step 230 a difference (absolute value) of such datum with respect to a time preceding datum (e.g. at a time difference of Vf) from the same sensor is calculated and then (step 240) compared with a predetermined threshold. If the calculated time difference, which represents a time variation of the physical quantity, is below the threshold, then the system is put back to a low power mode (step 270). If the calculated time difference is above the threshold, then also the other sensor is switched on (step 250) and the speed calculation method according to an embodiment of the present invention is performed (step 260). Then the system is 'switched-off (step 270). The method of velocity calculation according to the various embodiments of the present invention may be implemented as a microcontroller firmware or a computer software program. The actual operations performed by the method, implemented in suitable software code portions of a computer program or of a microcontroller firmware, may be carried out by any well-known general purpose computer/microcontroller 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/microcontroller firmware 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. diskette, a CD or DVD-ROM., or a USB Key), or an external disk readable through a LAN (Loca Area Network). For the purpose of the present invention, the term "software program", "computer program" also comprises 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. diskette, a CD or DVD-ROM., or a USB Key), or an external disk readable through a LAN (Loca Area Network). Furthermore, for the purpose of the present invention, the term "software program", "computer program" also comprises 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 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. diskette, a CD or DVD-ROM., or a USB Key), or it can be available for the 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 results of an exemplary implementation of the present invention are described.

Fig. 3 shows the static magnetic 'signatures' of a particular car model (Citroen Xantia). A mono-axial Honeywell magnetic sensor model HMC 1002 placed at the road level below the car has been used with a suitable respective orientation for each of the three curves of Fig. 3. In case the sensor is buried below the asphalt of a road, no or negligible modification of the curves shown in Fig. 3 occurs. The horizontal axis represents the spatial distance from one end of the car. The vertical axis represents the respective readings (Voltage) of the sensor, which senses the Earth magnetic field distortion by the car. Curve 310 is the sensor reading associated to the x-component (oriented along the car length) of the magnetic field, curve 320 is the reading associated to the y-component (oriented along the car width) and curve 330 is associated to the z- component (oriented along the car height). In Fig. 3, the respective baseline signals 310', 320' and 330' are also shown, which may be interpreted with a good approximation as the Earth baseline magnetic field.

By spline-interpolating the vertical component magnetic curve obtained from the experimental curve 330 in Fig. 3, 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 associated car moving with various different speeds. The method shown in Fig 2 has been applied to the obtained sensor response, with the step 260 of speed evaluation based on the speed evaluation algorithm of Eq. 15. The two sensors are oriented along the direction of movement of the car and they monitor the vertical component of the magnetic field. The algorithm parameters used in the simulation are the following: δx (the distance between the two sensors) = 4 cm τ (the time increment for calculating the numerical derivative) = 2 ms /(the sampling rate at witch the whole algorithm scheme of fig. 2 is cyclically repeated) = 128 Hz (which corresponds to a sampling period of about 7.8 ms).

Fig 4 shows calculated results (light gray squares) of the above embodiment of the present invention. Horizontal axis represents the actual speed and the vertical axis the calculated speed. Curve 400 represents the exact correlation curve. For the purpose of comparison, there are also plotted the numerical results (dark circles) resulting from a comparative method of calculation according to the inversion of the following equation:

1&

2[P[X₁ J)- P(X₂J)I- [P(X₁ J)₊ P(x₂,t)]- = 0 v wherein the mathematical symbols have the same meaning of above. It is noted that the comparative example represents the difference of Eq. 1 and Eq. 2, without the terms of the second order (i.e. it represents a first order expansion of the relation

_/>(_{X; t}) = A x, _{t +} — ) ) • The improvement of the present method is clearly visible.

Noise effect is also taken into account in order to simulate the actual behavior. Each symbol shown in Fig. 4 is the results of 18 different simulations with random noise added as described below. The vertical error bars represent the standard deviation resulting from the 18 different simulations.

Three kind of noise are added to the ideal 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_{0 Λ} sin(2;r501 + φ) where φ is a pseudo-random generated phase between 0 and 2π and V_OA has been set equal to 1 mV; ii) Thermal noise, V_τ (/) , i.e. a pseudo-random generated voltage value with a normal Gaussian distribution centered at zero voltage and having a V₀₁. amplitude equal to 1.0 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 3.6V amplitude, the maximum error being in this case 3.6V/2¹⁵.

Although the present invention has been disclosed and described by way of some embodiments, it is apparent to those skilled in the art that several modifications to the described embodiments, as well as other embodiments of the present invention are possible without departing from the spirit or essential features thereof/the scope thereof as defined in the appended claims.

Claims

1. A method for determining the velocity of a moving object, the method comprising:

- acquiring from a first and a second sensor spaced apart by a given distance and lying along a direction substantially parallel to a direction of motion of the moving object respectively a first and a second measurement signals, each of said two measurement signals being representative of a physical quantity P at a location of the respective sensor, the physical quantity P being subject to a change in correspondence to a passage of the moving object;

- calculating from the first and the second measurement signals a difference between a first and a second value representing the physical quantity respectively measured by the first and the second sensor;

- calculating from the second measurement signal a first and a second quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the second sensor; and - calculating the velocity of the moving object as a function of said difference and of said first and second quantity.

2. The method of claim 1 wherein the step of calculating the velocity v of the moving object at a given instant of time t makes use of the equation:

is said given distance, P, and P₇ are said first and second value representing the physical quantity at the given instant of time t, and A₂ and B₂ are respectively said first and second quantity calculated at the given instant of time t.

3. The method of claim 2 wherein the velocity v at said given instant of time / is calculated by an at least approximate inversion of the said equation.

4. The method of claim 3 wherein said at least approximate inversion of the said

A, B, equation takes the following form: v = δx '2

P - P IA

5. The method of any of claims 1 to 4 wherein said first quantity is expressed as a ratio of a difference of a third and a fourth value representing the physical quantity measured by the second sensor at two instants of time separated by a time increment τ and the time increment τ .

6. The method of the claim above wherein the third value is equal to the second value.

7. The method of any of the above claims wherein said second quantity is expressed as a ratio of a linear combination of a fifth, a sixth and a seventh value representing the physical quantity measured by the second sensor at three instants of time separated by the time increment τ , and the square of the time increment τ .

8. The method of the claim above and one among claim 5 and 6 wherein the sixth value is equal to the third value and the seventh value is equal to the fourth value .

9. The method of any of claims 1 to 8 further comprising:

- calculating from the first measurement signal a third and a fourth quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the first sensor; and

- calculating the velocity of the moving object as a function also of said third and fourth quantity.

10. The method of the claim above wherein in the step of calculating the velocity of the moving object, the velocity at the given instant of time t is calculated by an at least approximate inversion of the equation:

IP_x — 2P₂ + {A₂ + A_x) Ai and Bi are respectively said third and fourth quantity calculated at the given instant of time t.

11. The method of the claim above wherein said at least approximate inversion of the

A_x + A₂ B₂ - B_x said equation takes the following form: v = δx

P_x - P₂ A_{x +}A₂

12. The method of any of the preceding claims wherein in the step of calculating the velocity use is done of a first and a second baseline value derived respectively from said first and second measurement signals.

13. The method of any of the preceding claims wherein the two sensors are magnetic sensors and the physical quantity is at least a component of a magnetic field.

14. The method of the preceding claim wherein the at least one component of the magnetic field is the vertical component of the magnetic field with respect to the plane of movement of the object.

15. 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.

16. 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 given distance and each one sensitive to a physical quantity subject to a change in correspondence to a passage of the moving object, and a processing unit (110) operatively connected to said sensing device, wherein:

- the sensing device (100) is configured for acquiring a first and a second measurement signal respectively from the first and second sensor (10, 20), each of said two measurement signals being representative of the physical quantity at a location of the respective sensor; and

- the processing unit (110) is configured for:

- calculating from the first and the second measurement signals a difference between a first and a second value representing the physical quantity respectively measured by the first and the second sensor; - calculating from the second measurement signal a first and a second quantity representing respectively at least an approximation of a first and a second time derivative of said physical quantity at the location of the second sensor; and

- calculating the velocity of the moving object as a function of said difference and of said first and second quantity.

17. The system of claim 16 wherein the processing unit (110) is configured for calculating the velocity v of the moving object at a given instant of time t by making use

of the equation r_χ δx is said given distance, P, and P₂ are said first and second value representing the physical quantity at the given instant of time t, and A2 and B₂ are respectively said first and second quantity calculated at the given instant of time t.

18. The system of claim 17 wherein the processing unit (110) is configured for calculating the velocity v at said given instant of time t by an at least approximate inversion of the said equation.

19. The system of claim 18 wherein said at least approximate inversion of the said

A, B, equation takes the following form: v = δx '2

P - P, 2 A.

20. The system of any of claims 16 to 19 wherein the processing unit (110) is further configured for:

21. The system of claim 20 wherein the velocity at the given instant of time t is calculated by an at least approximate inversion of the equation:

2/| wherein A₁ and B₁ are respectively said third and fourth quantity calculated at the given instant of time t.

22. The system of claim 21 wherein said at least approximate inversion of the said

equation takes the following form: v =

23. The system of any claims 16 to 22 wherein the at least two sensors are identical sensors.

24. The system of any claims 16 to 23 wherein the at least two sensors are magnetic sensors and the physical quantity is at least a component of a magnetic field.

25. A traffic monitoring system including the system according to any of claims 16 to 24.