WO2022049199A1

WO2022049199A1 - Method for calibrating a gas sensor

Info

Publication number: WO2022049199A1
Application number: PCT/EP2021/074276
Authority: WO
Inventors: Paolo Zanini; Pierre Jallon
Original assignee: Elichens
Priority date: 2020-09-06
Filing date: 2021-09-02
Publication date: 2022-03-10
Also published as: FR3113948A1

Abstract

A method for calibrating a gas sensor (3i), the gas sensor being intended to measure a quantity (R(t)) that is dependent on a concentration of an analyte in the air, the gas sensor being deployed to a position in a geographical area, the sensor being such that the concentration of the analyte is estimated, at each instant in time, by applying a response function to the quantity measured by the sensor at said instant in time, comprising, for at least one sensor, the following steps: • - a) determining quantities (R(t _c ), v(R(t _c )) coming from the sensor at various calibration times (t _c ); • - b) at each calibration time, determining a reference concentration (t _c ), each reference concentration (C _ref (t _c )) corresponding to an estimated concentration of the analyte at the position of the sensor; • - c) taking into account an analytical model of the response function, the model being parametrized by at least one parameter; • - d) based on the analytical model resulting from c), on the reference concentrations resulting from b) and on the quantities resulting from a), determining each parameter of the reference function. In step b), each reference concentration is: • - either a concentration, called background noise, obtained from a public database, at the calibration time; • - or a concentration established on the basis of concentrations of the analyte that are measured, at the calibration time, by a plurality of reference stations (5_k), which are different from the sensor, and are located in the geographical area.

Description

Title: Calibration process of a gas sensor

TECHNICAL AREA

The technical field of the invention is the calibration of a gas sensor intended to carry out gas measurements in the environment, and in particular in an urban or peri-urban environment.

PRIOR ART

Obtaining maps describing the spatial distribution of concentrations of molecules or harmful particles is a need that meets an expectation of the population and the authorities, in particular in sensitive geographical areas, such as urban areas or more generally in areas susceptible to to be affected by air pollution. Many models have been developed, making it possible to establish maps of atmospheric pollution and to predict their temporal evolution. These models are fed by sensors distributed in the geographical areas examined.

Using data relating to the sources of pollutant emissions, and by considering parameters linked to topographical or meteorological conditions, the models make it possible to establish the spatial distribution of concentrations of molecules or polluting particles in the environment, the latter making the object of a spatial mesh.

Regional or national agencies operate measurement stations spread over the territory, called reference stations, which make it possible to obtain regular measurements of the concentration of atmospheric pollutants. The latter are for example NO ₂ , O ₃ , CO, or even fine particles, for example particles with a diameter less than or equal to 10 μm (PM 10) or particles with a diameter less than or equal to 2.5 μm (PM 2.5) . The measurements carried out by certain agencies are open, ie easily accessible to the public. At European level, it is for example possible to obtain the concentrations of these pollutants on the website of the European Environment Agency. In France, regional agencies manage measurement stations, which make it possible to obtain maps of pollutants as well as forecasts. Measurement stations are reliable devices, but expensive and bulky. As a result, it is difficult to envisage their deployment according to a fine spatial mesh. Their number is limited to a few units per agglomeration, or even 10 to 20 for the largest agglomerations. However, to obtain a more precise cartography, and taking account of local particularities, for example locally congested traffic, it is preferable to deploy a large number of measurement sensors, the latter being spaced apart by only a few hundred meters. This makes it possible to obtain maps that are more reactive to the occurrence of local singularities, influencing the concentrations of pollutants. The document WO2018178561 describes for example a method for producing a cartography in the environment from sensors distributed according to a dense mesh. Given the number of sensors used, the latter have a simpler design and a lower cost than the measurement stations described above. On the other hand, care must be taken to ensure that the measured data is reliable, in order to obtain the most accurate maps possible.

One way to verify the accuracy of measurements delivered by sensors is to expose them to known concentrations of gas. But this type of calibration is difficult to perform in the field, and therefore requires that the sensors tested be moved to a laboratory, then exposed to a standard gas, before being deployed again in the field. It will be understood that this type of calibration cannot be envisaged when the number of sensors exceeds several tens, or several hundreds of units.

A solution, described in the publication “Field calibration of a cluster of low-cost available sensors for air quality monitoring. Part A: Ozone and nitrogen dioxide”, describes calibrations of gas sensors deployed in the field, using reference gas samples, whose composition is known. However, the exposure of sensors to reference samples is difficult to implement when the number of sensors to be calibrated is high.

The publication “Barcelo-Ordinas Jose M. et al “Calibrating low-cost air quality sensors using multiple arrays of sensors” describes a calibration of sensors deployed in the field, based on reference stations placed near said sensors. Such an approach assumes that reference stations are placed close to the sensors to be calibrated.

The document WO2020128311 describes the use of a reference station, or several reference stations, to calibrate gas sensors deployed in an urban environment.

The publication Hasenfratz D. "On the fly calibration of Low-Cost gas sensors" describes low cost (low cost) electrochemical sensors, deposited on public transport vehicles, subject to calibration. The calibration is carried out using measurements resulting a reference station with which each sensor is co-located, when the sensor is close to the reference station.

The publication Hagan D. “Calibration and assessment of electrochemical air quality sensors by co-location with regulatory-grade instruments” also describes low-cost sensors whose calibration is carried out using measurements resulting from a co-located reference station.

The Hasenfratz and Hagan publications describe the use of a reference station to carry out a calibration of a gas sensor, the gas sensor and the reference station being collocated, that is to say at a short distance from one of the other. However, in a geographic area, some gas sensors may not be placed at a sufficiently short distance from a reference station for co-location to be possible. This is particularly the case of stationary gas sensors positioned at a distance from reference stations.

The objective of the invention, described below, is to allow calibration of sensors deployed in the field, requiring neither movement of the sensors nor recourse to exposure of the sensors to reference gas mixtures, while freeing itself from a distance constraint between each sensor and the reference stations.

DISCLOSURE OF THE INVENTION

A first object of the invention is a method for calibrating a gas sensor, the gas sensor being intended to measure, at a time, a quantity depending on a concentration of an analyte in a gas, and in particular in the air, the gas sensor being deployed in a position in a geographical area, the sensor being such that the concentration of the analyte is estimated, at each instant, by applying a response function to the quantity measured by the sensor to said moment, the response function comprising a product of a gain of the sensor and the quantity measured, the method comprising:

a) determination of quantities from the sensor at different calibration instants, the calibration instants being distributed in the same calibration time interval;

- b) at each instant of calibration, determination of a reference concentration, each reference concentration corresponding to an estimated concentration of the analyte at the position of the sensor;

- c) taking into account an analytical model of the response function, the analytical model being parameterized by at least one parameter, variable between two different calibration time intervals, preferably comprising the gain of the sensor; - d) from the analytical model resulting from c), reference concentrations resulting from b) and quantities resulting from a), determination of the or each parameter of the response function; the process being such that during step b), each reference concentration is:

- or a concentration, called background noise, obtained in a public database, at the instant of calibration;

- either a concentration established from concentrations of the analyte, measured at the time of calibration, by several reference stations, different from the sensor, and located in the geographical area, each time of calibration being a time at which the concentrations measured by the different reference stations are considered to be homogeneous.

Thus, steps a) to d) can be performed without moving the sensor from the position in which it is deployed.

Step d) may in particular comprise an adjustment of the analytical model as a function of the reference concentrations and of the quantities resulting from a).

The gas sensor may be part of a group of sensors, each sensor of the group of sensors being deployed at a fixed position in the geographic area. The method can be implemented for one sensor or different sensors of the group of sensors.

According to one embodiment, the reference concentration is established from concentrations of the analyte measured by several reference stations, different from the sensor, and located in the geographical area. Step b) may include:

- b-i) taking into account concentrations measured by several reference stations at the same instant or at sufficiently close instants to be considered as merged;

- b-ii) determination of a dispersion indicator between the different concentrations measured during b-i);

- b-iii) taking into account a dispersion criterion;

- b-iv) comparison of the dispersion indicator with the dispersion criterion;

- bv) according to the comparison carried out during b-iv), in particular when the comparison carried out in b-iv) shows that the concentrations resulting from bi) are weakly dispersed, determination of a reference concentration from the concentrations measured by the various reference stations, the instant at which the concentrations are measured being a calibration instant. During sub-step bv), the reference concentration can be obtained from an average value or a median value of the concentrations measured by the various reference stations.

The duration of the calibration time interval is preferably greater than one day. At least two calibration instants, in the same calibration time interval, are preferably spaced apart by a duration greater than 1 hour, or even a day.

Steps a) to d) can be repeated regularly, respectively at different calibration time intervals, so as to update the response function of the sensor. Two successive calibration time intervals can be shifted by a period greater than one day.

According to one embodiment, the method comprises a determination of a correction function of the quantity measured by the sensor as a function of an environmental parameter, the environmental parameter being chosen from temperature or pressure or humidity. The process can then include:

- i-1) establishment of an analytical evolution model, representing an evolution of the quantity measured by the sensor as a function of the environmental parameter, the analytical model depending on coefficients;

- i-2) measurements, by the sensor, of different magnitudes at different times, at different levels of the environmental parameters;

- i-3) using the measurements resulting from i-2), determination of a function representing a variation of the quantity measured in the presence of the same concentration of analyte, as a function of the environmental parameter;

- i-4) calculation of the coefficients of the analytical evolution model from the function determined during i-3;

- i-5) determination of the correction function from the evolution model resulting from step i-4); the method comprising, following step i-5), at each instant of calibration:

- determination of a level of the environmental parameter at the position of the sensor;

- application of the correction function to the quantity measured by the sensor, taking into account the level of the environmental parameter determined at the moment of calibration, so as to obtain a corrected quantity; in such a way that the quantities determined during step a) are corrected quantities, the method being such that during step d), the determination of each parameter of the response function is carried out as a function of quantities corrected to each instant of calibration.

The method may be such that step i-3) comprises:

- i-3a) for different levels of the parameter, calculation of an average value or of a median or of another fractile of the magnitudes resulting from step i-2) respectively;

- i-3b) determination of the variation function from the calculated values, respectively for each level of the parameter, during i-3a).

Steps i-1) to i-5) can be implemented successively for different environmental parameters, chosen for example from temperature, pressure or humidity, so as to obtain, for each parameter, a correction function. The gas sensor can be an electrochemical sensor, comprising a detection material, the measured value corresponding to an intensity or a potential difference at the terminals of the detection material, or to a resistance of the detection material.

A second object of the invention is a method for determining a correction function of a gas sensor as a function of one or more environmental parameters, the sensor measuring a variable depending on a concentration of a gaseous analyte at different instants, the gas sensor being deployed in a position in a geographical area, the or each environmental parameter being chosen from temperature and/or pressure and/or humidity, the method comprising:

- i-2) measurement of different quantities by the sensor, at different times, at different levels of the environmental parameters;

- i-5) determination of the correction function from the evolution model resulting from step i-4).

The method may comprise the sub-steps i-3a) and i-3b) previously described. The gas sensor can in particular be an electrochemical sensor, comprising a detection material, the measured value corresponding to an intensity or a potential difference at the terminals of the detection material, or to a resistance of the detection material.

A third object of the invention is a gas sensor, arranged to deliver a physical quantity depending on the concentration of an analyte in a gas, in particular air, to which the sensor is exposed, the gas sensor being connected to a processing unit programmed to implement steps a) to d) of a method according to the first object of the invention, and/or steps i-1) to i-5) of a method according to the second object of the invention.

A fourth object of the invention is a method for measuring a concentration of an analyte in a gas, from a gas sensor according to the third object of the invention, the method comprising:

- measurement of a magnitude by the sensor, at a time, the magnitude depending on a concentration of an analyte in a gas to which the sensor is exposed at said time;

- application of a response function and/or a correction function to said quantity;

- estimation of the concentration of the analyte in the gas, at said instant, from the response function and the quantity measured by the sensor; the method being such that the response function is established by implementing steps a) to d) of a method according to the first object of the invention, and/or the correction function is established by implementing the steps i-1) to i-5) of a method according to the second object of the invention.

The invention will be better understood on reading the description of the embodiments presented, in the remainder of the description, in connection with the figures listed below.

FIGURES

FIG. 1 diagrams an installation of gas sensors forming a network of sensors covering a geographical area, in which there are also reference stations.

FIG. 2A shows changes in NO2 concentrations (axis of ordinates) as a function of time (axis of abscissas - dates), the concentrations being respectively measured by a sensor, calibrated according to the prior art, and a reference measurement station .

FIG. 2B illustrates the evolution of quantities, in this case of the voltages (ordinate axis) resulting from the sensor mentioned in connection with FIG. 2A, as a function of time. FIG. 3A schematizes the main steps of a method for determining a response function of a sensor.

FIG. 3B schematizes the main steps of a method for determining a correction function of a sensor, with respect to an environmental parameter such as temperature or pressure or humidity.

FIG. 4 illustrates quantities measured by a sensor (electrical voltages - ordinate axis) as a function of different temperature levels (abscissa axis), and for different concentrations of an analyte.

FIGS. 5A to 5D show measured concentrations (axis of ordinates) as a function of time (axis of abscissas) respectively according to the prior art, by implementing the invention, and by implementing a reference measuring station.

FIG. 6 is an example of the installation of sensors and reference stations in an urban geographic zone.

DESCRIPTION OF PARTICULAR EMBODIMENTS

There is represented, in FIG. 1, a geographical zone in which it is desired to determine a map of a concentration of an analyte forming an atmospheric pollutant. The analyte is for example a gaseous species, such as CO, NO, NO ₂ , O ₃ , SO ₂ , C ₆ H ₆ ... It can also be fine particles, for example particles in suspension of the PM10 type. or PM 2.5. The acronym PM, meaning Particulate Matter, or particulate matter, is known to those skilled in the art. In general, the geographical area considered comprises sources of emission of the analyte. These emission sources can be linked to vehicle traffic, to the presence of district heating installations, or to the presence of industrial installations likely to emit the analyte. The geographical area may include an urban or peri-urban area, or even an industrial or airport area. In the example represented in FIG. 1, the geographical area 1 is part of a town, comprising streets 2 symbolized by lines. Gas sensors 3i...3i...3i are distributed in the geographical zone 1, respectively in different fixed positions. I is a natural integer denoting the number of deployed gas sensors. I is generally greater than 10, or even greater than 100.

The sensors are for example electrochemical, or optical, or NDIR (Non Dispersive Infra Red, meaning non-dispersive - infrared) sensors or with a solid substrate, for example made of metal oxide (MOX). In Figure 1, the gas sensors 3i are shown as black dots. These sensors define a mesh of the geographical zone 1 considered. The distance between two adjacent sensors is preferably less than 1 km, or even less than 500m. It is typically a few hundred meters. The density of the sensors is typically 10 sensors per km ² .

Each sensor 3i, l<i</ generates a physical quantity R, depending on the concentration of analyte in the gas (generally air) to which the sensor is exposed. The physical quantity is generally an electrical quantity, of the voltage or current intensity type, measured at the output of the sensor.

The quantities R(t) come from each sensor at a time t. The instants t can be distributed during the day and the night, generally according to regular time intervals, for example every lh or every 2h.

The sensors 3i are connected to a processing unit 4, which collects the quantities measured by each sensor at each instant, so as to establish a map of the analyte concentration over the geographical area considered, and possibly to carry out a forecast map. The processing unit can implement a response function u which allows a conversion of quantities 7? (t), from each sensor, in quantitative values of analyte concentrations C(t). The processing unit 4 can also implement a correction function v, taking into account a drift in the quantity measured by the sensor as a function of at least one environmental parameter, for example temperature or pressure or humidity . The establishment of the response function u and/or of the correction function v corresponds to a calibration of the sensor.

The geographical zone 1 can include at least one 5k measurement station, called a reference station. Unlike 3i sensors, which are compact and inexpensive sensors, each 5k reference station is a fixed station, making precise measurements day and night. The geographical zone can include several 5k reference stations, the index k being an integer between 1 and K, K corresponding to the number of reference stations in the geographical zone considered. Each 5k reference station is connected to a data collection network. In FIG. 1, three reference stations 5k=i, 5k=2 and 5k=3 have been represented, symbolized by a triangle. A 5k reference station can for example be operated by a public operator, aiming to make data relating to atmospheric pollution public. In the European Union, the data center on air pollution, operated by the European Environment Agency, ensures the availability of data, known as open data, measured by fixed measuring stations. As mentioned in connection with the prior art, such reference stations provide quality measurements, but their cost and their size limits their number. Such a station is in the form of a room, equipped with ambient air sampling devices, generally arranged at the top of the room. Inside the room there are analyzers specific to certain analytes, such as those previously listed.

In the example considered, in a non-limiting manner, the sensors considered are solid electrolyte electrochemical sensors. This type of sensor is usually used for the detection of analytes such as CO, O3 or NO _X . In general, an electrochemical sensor comprises a detection material, the resistance of which varies according to the concentration of a gaseous analyte. Thus, the quantity R(t) measured by an electrochemical sensor at a time t corresponds to a voltage value at the terminals of the detection material or to an intensity of a current between the terminals of the detection material.

As indicated in the publications cited in the prior art, from the quantity resulting from a gas sensor, at a given instant, the concentration C(t) of the analyte can be established according to a formula of the type:

C t)=gR(t)+b (1) where g is a gain and b is a bias (or offset), the gain and the offset being able to be determined by calibration.

FIG. 2A shows NO2 concentrations measured respectively: by a reference station (curve a), whose measurements are considered to be representative of reality; by an electrochemical sensor (curve c), positioned close to the reference station.

In FIG. 2A, the ordinate axis corresponds to a measured concentration (pg/m ³ ), while the abscissa axis corresponds to dates (year-month-day). The calibration of the sensor is carried out daily, according to the method described in WO2020128311, by updating the bias b of the sensor, the gain being kept fixed. The gain corresponds to a gain established before the deployment of the sensor. According to such a calibration, the value of the bias varies over time: it is updated during each calibration.

Despite regular calibration, a drift is observed between the measurements coming respectively from the sensor and from the reference station, and this drift tends to increase with time. FIG. 2B shows an evolution of the quantity R(t) measured by the sensor in as a function of time, on the same dates as those represented in FIG. 2A. Greatness follows oscillations, each oscillation corresponding to a day. A progressive drift in the amplitude of the daily oscillations of the quantity R(t) is observed. The inventors attribute such a drift to a temporal variation of the response function of the sensor, and in particular a temporal variation of the gain. Also, the gain of the sensor, and possibly the bias, must be considered as time-dependent, and must be regularly updated. Since the sensor is deployed in the geographical area, the update must be performed without moving the sensor relative to its position in the geographical area under examination, or without exposing the sensor to a reference gas mixture. Compared to WO2020128311, according to the invention, the method assumes that the gain is variable over time, as observed in connection with FIGS. 2A and 2B. This is a different approach from those described in the publications cited in the prior art.

More generally, the calibration aims to update a response function u, such that C(t)=u(R(t)). As previously indicated, by response function is meant a function establishing a relationship between the concentration C(t) of the analyte and the physical quantity R(t) output from the sensor. The response function can be of linear form, as explained in (1), or polynomial, or other, for example logarithmic.

One of the objectives of the invention is to carry out a regular update of the gain of at least one sensor of the group of sensors, while the sensor is deployed in the geographical area examined. Thus, the calibration of each sensor is carried out without displacement of the sensors relative to the position in which it is deployed. Calibration does not require recourse to exposure of each sensor to a calibration gas, prepared in the laboratory, and whose composition is known.

FIG. 3A describes the main steps of a method allowing an update of the gain, and more generally of the response function u. The method described in connection with FIG. 3A can be implemented by a processing unit, for example the processing unit 4 previously described.

Step 100: taking into account a physical quantity R(t _c ) measured from the sensor at a calibration instant t _c .

This step corresponds to an acquisition of physical quantities measured by the sensor at different instants. Depending on the approach followed (cf. step 120), each instant of calibration t _c can be arbitrary, for example determined randomly, or be selected according to concentrations measured by reference stations present in the geographical area.

Step 110: correction of the quantity measured by the sensor. This step is optional, and is described below. This involves correcting the quantity measured by the sensor by applying a correction function v. The correction function v enables correction of the measurements from the sensor as a function of an environmental parameter, such as the temperature and/or the pressure and/or the humidity. The determination of the correction function is described later in connection with steps 80 to 84

In the steps 120 to 150 described below, the term quantity coming from the sensor corresponds either to a quantity R(t) measured by the sensor, or to a quantity v(R(t)) measured by the sensor and having made the object of a correction during step 110. Step 110 can be implemented for certain types of sensors, considered to be sensitive with regard to an environmental parameter. These are, for example, electrochemical sensors.

Step 120: Consideration of a reference concentration.

Calibration assumes that a reference concentration C _re f (t _c ) is taken into account. The reference concentration corresponds to an estimated concentration of the analyte at the position of the sensor, at the instant of calibration t _c .

According to a first approach, corresponding to steps 121 to 123, the reference concentration C _re f (t _c is established from several reference stations. According to this first approach, to determine the calibration instant t _c , one has concentration values Cfc=l( ■■■ ■ Ck=K (t) respectively measured by different reference stations 5k=i...5k=K distributed in the analyzed geographical area, and this at different times t.

During a step 121, a dispersion indicator cr _c (t) of the concentrations measured at each instant is determined. It can be a standard deviation or variance type indicator, or even a comparison max(C _fc=1 (t) ... . C _fc= (t)) — min(C _fc=1 ( t) .... C _fc= (t)), for example a difference, between the maximum and minimum values of the concentrations measured, at the same instant (or at sufficiently close instants to be considered as merged) by the reference stations . The dispersion indicator cr _c (t) is all the lower as the concentrations measured by the reference stations are weakly dispersed.

During a step 122, the dispersion indicator cr _c (t) is compared with a dispersion threshold o _th , for example previously established. When the dispersion indicator cr _c (t) is low, that is that is to say below the dispersion threshold, it is considered that the concentration of the analyte is homogeneous in the geographical area considered. Each instant during which the dispersion indicator cr _c (t) is less than the dispersion threshold o _th can then be selected as being a calibration instant t _c . The dispersion threshold o _th can for example be equal to 20 pg.m ⁻³ when the analyte is NO ₂ .

During a step 123, the reference concentration

is obtained from the different concentrations C _fc=1 (t _c ) ... . C _k=K t _c ) measured by the reference stations at the instant of calibration t _c . It can be a mean value or a median value of the concentrations C _fc=1 (t _c ) ... . C _fc= (t _c ).

It is understood from the foregoing that the use of reference concentrations from reference measurement stations allow determination of calibration instants t _c , each calibration instant corresponding to instants at which the concentrations measured by the measuring stations are considered as homogeneous, ie weakly dispersed. Reference concentrations

established at each calibration instant can be used to calibrate all the sensors present in the geographical area covered by the reference stations.

According to another approach, the calibration is carried out without using any reference stations located in the geographical area studied. During a step 125, the reference concentration, at the position of the sensor, is estimated using a so-called background noise concentration, coming from a public database 6. For example, the public database is the CAMS model (Copernicus Atmosphere Monitoring Service - Copernicus Service on the composition of the atmosphere), known to those skilled in the art. The calibration instants t _c are then arbitrary. They can therefore be determined randomly. They can also be chosen within a time range, established beforehand, during which it is considered that the concentration resulting from the public database forms a good descriptor of the concentration of the analyte at the level of the sensor considered. The advantage of this approach is that it does not require the presence of reference stations. According to such an approach, it is preferable that each calibration instant t _c corresponds to an instant at which it is considered that the concentration, at the position of the sensor, is comparable to a background noise concentration, which can be estimated by the model. To this end, the method can comprise a filtering of the quantities R(t _c ) measured at the different calibration instants t _c , so as to eliminate the highest quantities, for example the 30% or 20% of the highest quantities. Step 130: Reiteration of steps 100 to 120 so as to obtain, for different calibration instants t _c , a pair comprising: a quantity R(t _c ) output from the sensor, possibly corrected during step 110; a reference concentration

In order for the calibration to be of good quality, it is preferable to have calibration instants t _c distributed over a relatively long calibration time interval At _c : preferably greater than 1 day, and for example between 1 day and 2 weeks . A calibration time interval At _c of a duration of the order of 7 days, possibly ± 1 or 2 days, can be considered as optimal. Thus, the data used to perform the calibration (quantities from the sensor and reference concentrations) extend over a relatively long calibration time interval At _c . In the same calibration time interval At _c , two different calibration instants t _c can be separated by at least 1 hour.

Step 140: Taking into account an analytical model of response function u of the sensor.

During this step, an analytical model of response function u of the sensor is taken into account. For example, the model is linear, as described in connection with expression (1), the model parameters being g and b. According to other possibilities the model can be polynomial. Preferably, the gain is a parameter considered to be variable as a function of time, and in particular between two successive calibration time intervals. It is considered fixed in the same calibration time interval. One objective of the calibration is to determine the value of the gain g in each calibration time interval.

Step 150: calibration: determination or updating of the response function.

During this step, the model is confronted with the pairs (R(t _c )

_c )) obtained at each calibration instant t _c . This makes it possible to update the parameters of the response function, in particular the gain g and the bias b. This step can be performed by adjusting the model with respect to the different torques obtained during the calibration time interval. The adjustment can be carried out by an optimization algorithm, for example a linear regression.

According to one possibility, the bias b is considered to be fixed, or zero.

Steps 100 to 150 can be implemented in different calibration time intervals At _c . This allows regular updating of the response function u of the sensor. In particular, a regular update of the gain g makes it possible to avoid a drift of concentrations measured by the sensor as seen in Figure 2A. Two successive calibration time intervals At _c can be shifted by a duration greater than or equal to a day.

Following each calibration, the response function u is used to convert the quantities R(t) measured by the sensor, in particular during or after the calibration time interval, into concentrations of analyte C(t).

The approach described in connection with sub-steps 121 to 123 can help to obtain reference concentrations

distributed according to a wide range of values: the calibration is then carried out on the basis of reference concentrations covering both low and high values, which improves the precision of the update of the response function u, during step 150. Indeed, the more the reference concentrations C _re f (t _c ) are distributed according to a high dynamic, the better the precision of the determination of the response function u.

Another aspect of the invention relates to the sensitivity of certain sensors, for example electrochemical sensors, to environmental parameters, for example temperature, humidity or pressure. Such sensitivity leads to a variation of the physical quantity R(t) measured by each sensor. In order to improve the precision of the concentrations measured by each sensor, it is preferable that the physical quantity R(t) measured by the sensors undergoing such a variation be corrected. This is the subject of step 110 mentioned in connection with FIG. 3A. This step includes a sub-step 111, of measuring (or estimating) at least one environmental parameter P(t) at the position of the sensor considered. It can be a measurement made with a dedicated measuring instrument (for example a thermometer, barometer or hygrometer). It can also be an estimate of the parameter, for example on the basis of a meteorological model.

During a step 112, a correction function v is applied to the measured physical quantity 7? (t), so as to obtain a corrected quantity v(R(t)).

Steps 120 to 150 are then performed on the basis of corrected quantities v(R(t)). Thus, to update the response function u of the sensor, we use pairs: v(R(t _c )),

The correction function v of a sensor, or of each sensor, is established as described in connection with FIG. 3B. Step 80: measurement of quantities R(t) measured by the sensor at different instants t, and determination of the level of a parameter P(t) at the position of the sensor, at each instant. As previously described, the parameter P(t) can be the temperature, the pressure or the humidity. Parameter level means a value taken by the parameter. In this example, the parameter P(t) is considered to be the temperature T(t). The measurements are preferably carried out during an acquisition time period of one day, or even of several days, for example one week.

FIG. 4 represents different quantities measured by an electrochemical NO2 sensor (axis of ordinates), as a function of temperature (axis of abscissas). The measurements were made during each hour, during a time period of 7 days. In the example shown in Figure 4, the R value is positive, and is a decreasing function of analyte concentration. The lower the R value, the higher the analyte concentration.

Step 81: taking into account an analytical model of the evolution of the quantity measured as a function of the temperature.

During this step, a model of the dependence of the quantity measured with respect to temperature is taken into account.

For example, the model is linear, of type

R = xT + y (2) where x and y are model coefficients.

According to other approaches, the model can be polynomial or otherwise.

Step 82: Selecting a concentration value

During this step, a concentration value is selected, on the basis of which it is desired to determine the coefficients %, y of the model. It may for example be a maximum value, or average, or median, or other or during the time period of acquisition. The selected concentration value can be estimated on the basis of assumptions or measurements of reference stations or public database. In this example, the minimum value is selected, the latter being considered as zero.

Step 83: determining the parameters of the model

During this step, the model is compared with the quantities R(t) measured during step 81, so as to determine the coefficients of an average model, representing an average evolution of all the values measured as a function of the temperature. According to the example, a linear regression is carried out in order to determine the coefficients of the model Medium. This corresponds to curve (a) in Figure 4. In this example, the average model is of type:

R = x T + ÿ (3) where the operator is the mean value.

On the basis of the average model, a variation function is determined, corresponding to a variation of the quantity measured as a function of the temperature, for the concentration selected during step 82. In this example, the concentration selected is the minimum concentration in the time interval considered, the minimum concentration being assumed to be zero. From (3), we take into account a confidence interval, for example of 2<J, around the average model, which makes it possible to obtain the curve (b):

R=xT+y=xT+ÿ+2<J (4) where G is the standard deviation of the magnitudes R measured during step 81.

Curve (b), whose equation corresponds to (4), is a function representing the variation of the measured quantity R as a function of temperature, for the same concentration, in this case a zero concentration, as a function of the temperature. The coefficients x,y sought are established from the function represented on the curve (b).

When during step 82, the selected concentration value is the average value, the desired coefficients are established from the curve (a): these are x and ÿ. It can also be the median or other fractile.

Step 84: determination of the correction function

Following step 83, the correction function v is determined such that: v(R(t, T) = R(t) — xP — y (5)

Steps 81 to 84 can be implemented considering different parameters respectively. An evolution model is thus obtained for each parameter P. The resulting correction function is then a composition of the evolution models respectively established for each parameter. For example, if evolution models have been established respectively for temperature or humidity, the resulting correction function takes into account the evolution models determined for each parameter.

After the correction function v has been established, during step 110, the quantity R(t) measured by the sensor is corrected according to expression (5). For this, step 110 includes a determination of the level of one or more parameters at the position occupied by the sensor (step 111), then a correction of the measured value using the correction function v (step 112 ).

When step 110 is combined with steps 100 to 150, taking into account linear correction and response functions, a correction function of the type is obtained:

Given (1), we get:

The expansion of expression (7) leads to:

C(t) = Yo + 71^( + Yi T (8)

Yo' Yi < Y2 are scalars.

Note that step 110 can be implemented without necessarily implementing steps 120 to 150. In this case, the method makes it possible to perform a correction of the quantities measured by the sensor. The response function u of the sensor can then be determined according to methods of the prior art.

Experimental results.

The inventors have implemented the process described above. The implementation parameters are as follows. The calibration (step 150) was carried out each day, on the basis of measurements (steps 100 to 130) carried out during the last 7 days.

A correction function v has also been established taking into account the sensitivity of the sensor to temperature (steps 80 to 84). For this, we used measurements taken every hour, for 7 days.

FIGS. 5A and 5B represent respectively, for a sensor placed in the same location: reference concentrations of NO2 (FIG. 5A) and O3 (FIG. 5B) (curve a), measured by a reference station considered as representative of the sensor; concentrations of NO ₂ (FIG. 5A) and O ₃ (FIG. 5B) measured by a sensor calibrated respectively by implementing the invention (curve b) and by implementing a calibration of the prior art (curve c). To perform the calibration, concentrations from reference stations were used, as described in connection with steps 121 to 123. FIGS. 5C and 5D represent respectively, for a sensor placed in the same location: reference concentrations of NO2 (FIG. 5C) and O3 (FIG. 5D) (curve a); concentrations of NO ₂ (FIG. 5C) and O ₃ (FIG. 5D) estimated by a sensor calibrated respectively by implementing the invention (curve b) and without implementing the invention (curve c). To perform the calibration, concentrations from a public database were used, as described in connection with step 125.

Table 1 represents, in connection with the measurements represented in FIGS. 5A to 5D, the correlation coefficient R ² as well as the mean absolute error (MAE: Mean Absolute Error) by implementing the invention (column b) and without implementing the invention (column c).

Table 1

The MAE and R ² indicators are clearly more favorable by implementing the invention than by carrying out a calibration according to the prior art, and this regardless of the approach adopted during step 120: concentrations resulting from stations of reference or taken from a public database.

Thus, the implementation of the invention allows a significant and lasting improvement in the precision of the measurements.

FIG. 6 is a real example of the installation of 3i sensors in an urban geographic area, in and around the city of Grenoble (France). Each sensor is identified by a mark comprising the letter e. Also shown are 5k reference stations, symbolized by dark polygons. The reference stations are used to carry out a calibration of the sensors not by considering the closest station, but at a time at which the concentrations resulting from the reference stations are homogeneous.

Claims

CLAIMS Method for calibrating a gas sensor (3i), the gas sensor being intended to measure, at a time (t), a quantity (R(t)) depending on a concentration of an analyte in the air, the gas sensor being deployed in a position in a geographical area, the sensor being such that the concentration of the analyte is estimated, at each instant, by applying a response function to the quantity measured by the sensor at said instant, the response function (u) comprising a product of a gain of the sensor (g) times the quantity measured, the method comprising:

- a) determination of quantities (R(t _c ), v(R(t _c )) from the sensor at different calibration instants (t _c ), the calibration instants being distributed in the same calibration time interval (At _c );

- c) taking into account an analytical model of the response function, the analytical model being parameterized by at least one parameter, variable between two different calibration time intervals, including the gain of the sensor;

- d) from the analytical model resulting from c), reference concentrations resulting from b) and quantities resulting from a), determination of the or each parameter of the response function; the method being characterized in that during step b), each reference concentration is a concentration established from concentrations of the analyte, measured at the instant of calibration, by several reference stations (5k), different of the sensor, and located in the geographical area, each instant of calibration being an instant at which the concentrations (C _fc=1 (t _c ) ... . C _k=K t _c )) measured by the various reference stations are considered as homogeneous, the process being such that step b) comprises:

- bi) taking into account concentrations (C _fc=1 (t) .... C _k=K (t)) measured by several reference stations at the same instant or at sufficiently close instants to be considered as merged;

- b-ii) determination of a dispersion indicator (cr _c (t)) between the different concentrations measured during i); - b-iii) taking into account a dispersion criterion

;

- b-iv) comparison of the dispersion indicator with the dispersion criterion;

- bv) when the comparison made in b-iv) shows that the concentrations resulting from bi) are weakly dispersed, determination of a reference concentration from the concentrations measured by the various reference stations, the instant at which the concentrations are measured being a calibration instant (t _c ).

2. Method according to claim 1, in which step d) comprises an adjustment of the analytical model according to the reference concentrations

and quantities resulting from a).

3. Method according to any one of the preceding claims, in which steps a) to d) are carried out without moving the sensor from the position in which it is deployed.

4. Method according to any one of the preceding claims, in which during sub-step bv), the reference concentration is obtained from an average value or a median value of the concentrations measured by the various monitoring stations. reference.

5. Method according to any one of the preceding claims, in which the duration of the calibration time interval (At _c ) is greater than one day.

6. Method according to any one of the preceding claims, in which at least two calibration instants (t _c ), in the same calibration time interval (At _c ), are spaced apart by a duration greater than 1 hour.

7. Method according to any one of the preceding claims, in which steps a) to d) are repeated regularly, respectively at different calibration time intervals (At _c ), so as to update the response function (u) of the sensor.

8. Method according to claim 7, in which two successive calibration time intervals are offset by a period greater than one day.

9. Method according to any one of the preceding claims, comprising a determination of a correction function (v) of the quantity measured (R) by the sensor as a function of an environmental parameter (P), the environmental parameter being chosen from temperature or pressure or humidity, the method comprising:

- i-1) establishment of an analytical evolution model, representing an evolution of the quantity measured by the sensor as a function of the environmental parameter, the analytical model depending on coefficients (x,y);

- i-2) measurements, by the sensor, of different quantities (R(t)) at different instants, at different levels (P(t)) of the environmental parameters;

- i-3) using the measurements resulting from i-2), determination of a variation function, representing a variation of the measured quantity (R(t)) as a function of the environmental parameter, in the presence of a same analyte concentration;

- i-5) determination of the correction function from the evolution model resulting from step i-4); such that following step i-5), the method comprises at each calibration instant (t _c ):

- determination of a level of the environmental parameter (P(t _c )) at the position of the sensor;

- application of the correction function (v) to the quantity measured by the sensor (R(t _c )), taking into account the level of the environmental parameter (P(t _c )) determined at the moment of calibration, so as to obtain a corrected quantity (v(R(t _c )); such that the quantities determined during step a) are corrected quantities, the method being such that during step d), the determination of each parameter of the response function (u) is performed as a function of corrected quantities ((v(R(t _c )) at each calibration instant.

10. Method according to claim 9, in which step i-3) comprises:

- i-3a) for different levels of the parameter, calculation of an average value or of a median of the quantities resulting from step i-2) respectively;

11. Method according to any one of claims 9 or 10, in which steps i-1) to i-5) are implemented successively for different environmental parameters, chosen from temperature, pressure or humidity, so as to obtain, for each parameter, a correction function. Method according to any one of Claims 9 to 11, in which the gas sensor is an electrochemical sensor, comprising a detection material, the measured value corresponding to an intensity or a potential difference at the terminals of the detection material, or to a resistance of the sensing material. Gas sensor, arranged to deliver a physical quantity depending on the concentration of an analyte in a gas to which the sensor is exposed, the gas sensor being connected to a processing unit programmed to implement steps a) to d) of a method according to any preceding claim. A method of measuring a concentration of an analyte in a gas, from a gas sensor according to claim 13, the method comprising:

- measurement of a magnitude (R(t)) by the sensor, at a time, the magnitude depending on a concentration of an analyte in a gas to which the sensor is exposed at said time;

- application of a response function (u) to said quantity;

- estimation of the concentration of the analyte in the gas (C(t)), at said instant, from the response function and the quantity measured by the sensor; the method being such that the response function is established by implementing steps a) to d) of a method according to any one of claims 1 to 12.