EP3602324A1

EP3602324A1 - Method for mapping the concentration of an analyte in an environment

Info

Publication number: EP3602324A1
Application number: EP18722647.7A
Authority: EP
Inventors: Franck LASCAUX
Original assignee: Elichens
Current assignee: Elichens
Priority date: 2017-03-29
Filing date: 2018-03-27
Publication date: 2020-02-05
Also published as: US11467147B2; FR3064774B1; US20200025738A1; FR3064774A1; WO2018178561A1

Abstract

The invention relates to a method for mapping the concentration of an analyte in an environment, from sensors distributed in said environment, each sensor (10p) generating a measurement of the analyte concentration at different measuring intervals, the measurements made by each sensor at each measuring interval (t) forming an observation vector (0(f)), each term of which corresponds to a measurement derived from a sensor; the environment being the subject of spatial meshwork defining a plurality of meshes (20n), the concentration at the level of each mesh, at each measuring interval, forming a vector, called a state vector (M(t)), each term of which corresponds to an analyte concentration in a mesh; the method comprising: a correction, called global correction, of the state vector by a bias determined in positions occupied by measurement vectors, so as to obtain an unbiased vector; a correction, called local correction, of the state vector thus obtained, based on a correction vector.

Description

Method for establishing a mapping of the concentration of an analyte in an environment

Description

TECHNICAL AREA

The technical field of the invention is the mapping of analytes in the environment, and more particularly a mapping of pollutant molecules or particles harmful to the environment.

PRIOR ART

Obtaining maps describing the spatial distribution of concentrations of molecules or harmful particles is a need that meets the expectations of the population and the authorities, particularly in urban areas. Numerous models have been developed, making it possible to establish atmospheric pollution maps and predict their temporal evolutions. It is then possible to model urban air pollution in a routine situation, or in an accident situation, for example following a chemical or nuclear accident. Geographic coverage may be limited to a few km ² or even a country or continent scale in applications to model large scale transport of pollutants. Using data on the sources of pollutant emissions, and considering parameters related to topographic or meteorological conditions, the models make it possible to establish the spatial distribution of concentrations of molecules or particulate pollutants in the environment, the latter making the object of a spatial mesh.

The publication Berkowicz. "Modeling traffic pollution in streets", January 1997, issue of the Danish National Environmental Research Institute, describes for example a model of spatial dispersion of pollutants adapted to the specificities of urban environments. Indeed, in urban areas, the particular topography of streets separated by buildings justifies a specific approach, taking into account the formation of vortices of air circulation at the street level, these vortices playing a decisive role in the dispersion of the atmospheric pollution. Such models are referred to as "Street Canyon Model" or "Street Model". The aforementioned publication describes an urban pollution estimation model designated by the acronym OSPM, meaning "Operational Street Pollution Model", which can be translated by operational model of urban pollution. According to this model, from the emission of a pollutant in a street, depending on the number of vehicles and an average emission per vehicle, the model takes into account the recirculation vortex formed in the street, the aerological turbulence resulting from road traffic, ambient pollution from other streets, and the wind circulating at the level of the canopy, that is to say above the urban environment. The publication Berkowicz. "OSPM, a parameterised street pollution model", Environmental Monitoring and Assessment 65: 323-331, 2000, "also presents the assumptions on which the OSPM model is based, as well as an experimental validation of this model." Silver JD publication " Dynamic parameter estimation for a street canyon air quality model ", Envionmental Modeling & Software, Volume 47, 2013-06-25, describes a method, implementing a Kalman filter, to obtain the parameters of an OSPM type model. .

Some models may be biased. The publication Costa M., "Journal of Statistical Planning and Inference 176 (2016) 22-32, addresses this problem by implementing a Kalman filter. , each iteration includes an estimate of a bias. The issue of bias affecting a model is also discussed in CN105373673.

Pollution models may be confronted with measurements carried out locally, these measures allowing a registration; the confrontation between measured observations and a theoretical model is referred to as "data assimilation". A data assimilation technique is for example described in the publication Nguyen C. "Evaluation of Data assimilation Method at the Urban Scale With the Sirane Model". The publication describes an adjustment of a nitrogen dioxide dispersion model in urban areas by taking into account measurements made by 16 measurement stations distributed in a city. A similar technique is described in Tilloy A. "Blue-based N02 data assimilation at urban scale," Journal of Geophysical Research: Atmospheres, Vol 118, 2031-2040.

The invention aims to improve the methods described in the publications, so as to improve the confrontation between the models and measurements made by sensors distributed in the modeled environment.

SUMMARY OF THE INVENTION

An object of the invention is a method of estimating a mapping of the concentration of an analyte in an environment, from sensors distributed in said environment,

each sensor generating a measurement of the analyte concentration at different measurement times, the measurements made by each sensor at each measurement instant forming an observation vector, each term of which corresponds to a measurement resulting from a sensor; the spatially-meshed environment defining a plurality of cells, the concentration or quantity of the analyte at each cell, at each measurement instant, forming a vector, said state vector, of which each term corresponds to a concentration or an amount of analyte in a mesh;

the process comprising the following steps:

a) from the measurements made by each sensor, obtaining an observation vector, said measured, at a measurement instant;

b) obtaining a state vector at the measurement instant and, from the state vector, estimating an observation vector at said measurement instant;

c) comparing the estimation of the observation vector, obtained in step b) to the measured observation vector resulting from step a), and, from the comparison, determining an overall bias at time of measurement, the global bias being a scalar representative of the comparison between several terms respectively of the estimated observation vector and the measured observation vector;

d) correction of the state vector from step b) as a function of the overall bias obtained in step c), to obtain a state vector said debonded at the measurement instant;

e) from the debonded state vector obtained in step d), the bit rate estimate of the observation vector at said measurement instant;

f) comparing the streamed estimate of the observation vector resulting from step e) with the measured observation vector resulting from step a), and, from the comparison, determining a correction vector local ;

g) updating the state vector at the measurement instant, the latter being replaced by a sum of the debonded state vector resulting from step d) to the local correction vector resulting from step f), the updating of the state vector making it possible to estimate the mapping of the concentration of the analyte in different meshes of the environment.

The overall bias determined in step c) is preferably a scalar, the latter being subtracted from each term of the state vector in step d). Step d) is therefore a global correction step.

The analyte may be a molecule or particle dispersed in a gas. It is usually an analyte considered harmful to the environment or the population. The environment may be a geographical area, such as an urban area, whose air may be affected by pollution. The local correction vector is a vector whose terms may be different from each other, and are generally different from each other. At least two terms of the local correction vector are different from each other. Step g) is therefore a local correction step, the state vector being updated as a function of local variations of the analyte concentration. The method may include any of the following features, taken alone or in combination:

during step b), the observation vector is estimated by applying a matrix, said observation operator, to the state vector. This matrix makes it possible to interpolate the values of the state vector at each position respectively occupied by the different sensors. Each term of the state vector is associated with a mesh and a sensor, the term being even higher than said mesh is close to the sensor.

Step c) comprises the following sub-steps:

ci) making comparisons, for example in the form of a subtraction or a ratio, between different terms of the observation vector estimated during step b) and the observation vector measured during step a ); cii) calculation of a mean or median value of each comparison resulting from sub-step ci);

ciii) obtaining the overall bias from the mean or median value resulting from sub-step cii).

Step d) comprises subtracting the global bias at different terms, and preferably at each term, from the state vector.

During step e), the estimated output of the observation vector is obtained by applying a matrix, said observation operator, to the debated state vector.

In step f), the correction vector is determined according to the following substeps: fi) establishment of a comparison vector, resulting from a comparison, term by term, in the form of a subtraction or a ratio, between the observation vector resulting from step a) and the bit rate estimate of the observation vector resulting from step e);

fii) taking into account a gain matrix, each term of which is associated with a mesh and a sensor, the term being all the higher as the mesh is close to the sensor.

fiii) applying the gain matrix to the comparison vector so as to form a correction vector. Following step g), the method comprises a step h) of iterative updating of the state vector, at each iteration being associated an iteration row, step h) comprising the following substeps:

hi) taking into account a gain matrix corresponding to the rank of the iteration; hii) determining a comparison vector, associated with said rank of the iteration, by comparing the observation vector resulting from step a) with a vector resulting from the application of a matrix, said observation operator , the state vector resulting from step g), or resulting from a previous iteration;

hiii) application of the gain matrix taken into account in the sub-step hi) to the comparison vector determined during the sub-step hii), so as to obtain a local correction vector associated with the rank of the iteration; hiv) update of the state vector, the latter being replaced by a sum of the state vector resulting from step g), or a previous iteration, to the local correction vector resulting from the substep hiii );

hv) reiteration of substeps hi) to hiv) or stop of the iteration.

During step h), during each iteration, each sensor can be assigned a neighborhood extending at a maximum distance, the terms of the gain matrix associated with said sensor being non-zero for the cells located at the within said neighborhood, the gain matrix terms associated with meshes outside the neighborhood being zero or less than the terms of the gain matrices associated with the meshes within the neighborhood.

Each term of the gain matrix is associated with a mesh and a sensor, the value of the term being all the higher as the mesh is close to the sensor.

Each term of the observation operator is associated with a mesh and a sensor, the value of the term being all the higher as the mesh is close to the sensor.

In step b), the state vector is formed using a model derived from data on environmental road traffic, environmental topography, and environmental meteorological data. the resulting model in an analyte concentration at each mesh. This is particularly an OSPM type model described in the publications cited in connection with the prior art.

According to one embodiment, the method comprises the following steps: taking into account a state vector, referred to below, at a time subsequent to the instant of measurement;

establishing a correction of the subsequent state vector as a function of the updated state vector at the measurement time in step g) or in step h).

The correction may consist of adding, to the subsequent state monitor, a difference between the updated state vector and the state vector at the measurement time.

Other advantages and features will emerge more clearly from the description which will suffice from particular embodiments of the invention, given by way of non-limiting examples, and represented in the figures listed below. FIGURES

Fig 1A is the plan of a studied urban area, in which measurement sensors are distributed.

FIG. 1B is a mapping of an analyte, in this case nitrogen dioxide, this mapping being obtained by application of an OSPM type model.

Figure 2 shows the main steps of a method according to the invention.

FIG. 3A represents the mapping of FIG. 1B after taking into account a global bias. Figure 3B shows a two-dimensional representation of the positive terms of a local correction vector.

Figure 3C shows a two-dimensional representation of the negative terms of a local correction vector.

DESCRIPTION OF PARTICULAR EMBODIMENTS

FIG. 1A shows a plan of an urban area in which a two-dimensional mapping of the concentration of an analyte is modeled according to a model known from the prior art, for example the OSPM model previously mentioned. In this example, the analyte is a nitrogen dioxide molecule. In general, the analyte is a chemical molecule or particle whose dispersion in the environment is desired to be known, that is, a spatial distribution of its concentration or amount. It can especially be an analyte from traffic. Figure 1B shows a map of nitrogen dioxide in the streets of the urban area shown in Figure 1A. In FIG. 1B, the gray levels correspond to a concentration of nitrogen dioxide expressed in ppb.

From the cartography modeled in FIG. 1B, it is possible to define a geographic grid of the urban area, and to form, on the basis of the model, a vector, called a state vector (t), of which each term M _m (t) corresponds to a concentration of nitrogen dioxide modeled at a mesh 20 _m at a time t, for example at each center of mesh. The index m is a strictly positive integer denoting a mesh. The size of the state vector (t) is (N _m , 1), where N _m represents the number of meshes considered. Each term of the state vector is obtained by applying a predictive model, such as the OSPM model described in connection with the prior art, taking into account data related to urban traffic, meteorological parameters, such as the temperature and / or the wind speed, as well as the three-dimensional topography of the environment, for example the geometry of the streets as well as the height of the buildings between each street. FIG. 1A shows, in the form of dots, simulated locations of sensors (10p), the index p being a strictly positive integer designating a sensor. In the example shown, each sensor is a nitrogen dioxide sensor, measuring a concentration p (t) in this analyte at each measurement time t. The measured concentrations c _p (t) form a vector C (t), said observation vector, at the measurement instant, each term of which is a concentration measured by a sensor at the instant of measurement. The dimension of the vector C (t) is (N _p , 1), where N _p represents the number of sensors considered. The sensors are connected to a processor, for example a microprocessor, the latter being programmed to execute instructions for implementing the method described in this application.

From the state vector (t) and the observation vector C (t), the method described below aims at updating the state vector, so as to increase the accuracy of the mapping of the zone. considered, taking into account the measurements made by each sensor. Indeed, some local features, not taken into account by the model, can have a local influence on the distribution of the analyte. It can especially be a traffic jam. The invention makes it possible to take them into account. The main steps of the process are shown in FIG.

Preferably, the distance between two adjacent sensors is less than 500 m, or even 200 m. Indeed, the method described below is all the more effective as the number of sensors is high. In terms of number of sensors per unit area, preferably, the number of sensors is greater than 2 or 3 per km ² . At the scale of a city, the use of a dozen or twenty sensors is not enough to perform a sufficiently effective update of the map.

Step 100: Data Acquisition This involves obtaining the state vector (t) from the modeled cartography and the observation vector C (t) from the sensors. FIG. 1B corresponds to a two-dimensional representation of the state vector (£), obtained by establishing a correspondence between each term of this vector and a two-dimensional spatial coordinate M _m (t) corresponding to a 20 _m mesh. In this example, the observation vector C (t) is obtained by simulation on the basis of established concentrations, at each sensor 10 _p , based on the model. A bias is added, as well as an error term, the latter following a Gaussian law.

Step 110: Estimation of the observation vector from the state vector.

It involves estimating an observation vector, denoted C (t), from the state vector (t). The estimation of the observation vector can be obtained by applying an H matrix, called the observation operator, to the state vector (t) in the form of a matrix product. The matrix H makes it possible to spatially interpolate the measured data forming the observation vector C (t) so as to obtain, from the state vector, estimates Cp (t) of the concentration of nitrogen dioxide at the level of of each sensor 10 _p . The matrix H is of dimension (N _p , N _m ). Each line and each column of the matrix H are respectively associated with a 10 _p sensor and a 20 _m mesh. The estimation of the observation vector C (t) is obtained according to the expression: C (t) = H x M (t), (1) where x denotes the matrix product.

The terms of the matrix H (p, m) depend on the relative position of a sensor 10 _p with respect to the different meshes 20 _m . When the sensor 10 _p coincides with the center of a mesh 20 _m , the line H (p,.) Of the matrix H corresponding to said sensor 10 _p has only 0, except at the column corresponding to said mesh. . In general, the matrix is such that on a line H (p,.) Corresponding to a sensor, the term of each column is even higher than the column is associated with a mesh located near the sensor. Preferably, the terms of the matrix H are between 0 and 1. Step 120: Comparison between the observation vector C (t) and its estimate C (t) and calculation of an overall bias.

During this step, each term of the observation vector C (t) is compared to the term, corresponding to the same sensor 10 _p , of the estimation of the observation vector C (t) resulting from step 110. comparison can take the form of a subtraction or a term-to-term ratio.

From the comparison, a global bias ε (ί) is calculated, the bias representing, at the time of measurement t, an overall comparison between the observation vector C (t) and its estimate C (t). Global bias is a scalar quantity. It can in particular be determined from an average or a median of a term-by-term comparison of the vectors C (t) and C (t). By

1 N

for example, e (t) = -Σ _p ^p _{= 1} (C _p (t) - C _p (t)) (2), where Cp (t) and Cp (t) are respectively a term of rank p of the vectors C (t) and C (t), corresponding to the same sensor 10 _p .

Step 130: Debugging of the state vector.

During this step, the state vector (t) is corrected for the global bias ε (ί), by subtracting the global bias at each term of the state vector. We then obtain a state vector said débiaisé and noted '(t). Thus, '(t) = (t) - E (t) (3) where E (t) is a vector of bias, of dimension (N _m , 1), each term of which is equal to the global bias ε (ί) · The term debinded means unbiased and corresponds to the term Anglosaxon "unbiased". The term debinding means removing bias.

This step forms a first correction of the state vector, based on an overall bias calculated on the basis of the observations obtained by the sensors 10 _p . Such a bias may be due to emissions affecting the entire urban area studied, for example, caused by district heating or diffuse pollution. The inventors have observed that the taking into account of such global bias allows a significant improvement in the accuracy of the state vector M {t).

FIG. 3A shows a two-dimensional representation of the debonded state vector M 't). In this example, the bias value is 9.2 μg / m ³ . At each point of this figure corresponds a mesh 20 _m and a term of the M ' _m (t) state vector débiaisé.

Step 140: Estimated estimation of the observation vector.

During step 140, the debonded state vector M 't), resulting from step 130, is confronted with the measurements from the sensors 10 _p . For this purpose, a so-called streamed estimate of the observation vector, denoted C '(t), is calculated by applying the observation operator H according to the expression C' (t) = H x '(t) (4). ), similarly to step 110.

Step 150: Confrontation of the debated state vector M 't) to the measurements.

During step 150, a comparison is carried out, term by term, between the estimated bit rate of the observation vector C '(t), resulting from step 140, with the observation vector C (t). established in step 100. The comparison may take the form of a subtraction or a ratio. From this comparison is formed a local comparison vector comp (t). The vector local comparison comp (t) is of dimension (N _p , 1). Unlike the debinding step (steps 120 and 130), the comparison is a vector quantity. Thus, each term comp _p t) of the local comparison vector is such that comp _p (t) = C ' _p (t) - C _p (t) (5), the index p representing the rank of each term, p being between 1 and N _p . Unlike the bias vector E (t), the terms of the local comparison vector comp (t) may be different from each other, and are independent of one another.

Step 160: update the state vector.

After being debedged, during step 140, the state vector is subject to a second correction, called local correction, based on the local comparison vector comp (t) formed during step 150. A matrix, called gain matrix K, makes it possible to weight the correction to be made as a function of the distance of a mesh 20 _m from each sensor 10 _p . The gain matrix is of dimension (N _m , N _p ). Each line and each column of the gain matrix are respectively associated with a 20 _m mesh and a 10 _p sensor. The terms of a line K (m,.), Corresponding to a mesh 20 _m , are even higher than a sensor 10 _p , corresponding to a column, is close to the mesh. The terms K (m, p) of a gain matrix are preferably less than or equal to 1.

The updating of the state vector is carried out according to the following expression: * (t) = '(t) + KX comp (t) = M' (t) + KX (C (t) - C '( t)) (6)

= '(t) + KX (C (t) - HX' (t)) (6 ') * (t) corresponds to the updated state vector, making it possible to obtain a map of the pollutant that is closer to reality .

This operation is equivalent to applying a local correction vector corr (t) to the debated state vector '(t) to obtain a corrected (or updated) state vector M * (t). The local correction vector is of dimension (N _p , 1) and corresponds to the application of the gain matrix to the local comparison vector comp (t), according to the expression corr (t) = K x (C (t ) - C '(t)) = K x comp (t) = K x (C (t) - H x' (t)) (6 ")

Unlike the debinding step, the local correction vector is not uniform.

During this step, the correction of the state vector is not uniform, as during debinding, but differs from one term of the state vector to another. Figures 3B and 3C illustrate this aspect, and represent respectively the positive and negative terms of the vector of correction corr (t) to the different meshes of the cartography. It is observed that the correction is local, the correction being greater in some parts than in others. It can be negative in some parts, and positive in other parts.

The method allows, with a sufficiently high density of sensors, to obtain a map taking into account local traffic characteristics, for example the occurrence of a traffic jam. The combination between the taking into account of a global bias, followed by a local correction step, makes it possible to improve the spatial resolution of the cartography resulting from the updated state vector. It allows in particular the consideration of local evolutions, affecting only a few 20 _m meshes. The cartography obtained is thus more responsive to the occurrence of local particularities.

According to one embodiment, the subject of step 170 updating the state vector K is performed iteratively, by modifying the gain matrix at each iteration. Let n, the rank of each iteration, and K _n , the gain matrix associated with each iteration, step 170 comprises an update of the state vector resulting from step 160, or from a previous iteration n - 1 so that:

M _n ^* (t) =; _ _! (+ Κ _η X comp _n (t) (7)

With comp _n (t) = C (t) - HX ^* . ^) (8), where comp _n (t) is a comparison vector associated with the iteration of rank n;

Mn (t) is the state vector updated during the iteration of rank n;

C (t) is the previously measured measured observation vector;

H is the previously defined observation operator.

Step 170 is repeated until an iteration criterion is reached. Such a criterion can be a predetermined number N _n of iterations, or a sufficiently small difference between two successive updates of the state vector j ^ (t), Wn + i (- each gain matrix K _n can be determined during each iteration n, as a function of a weight w ^ _p assigned to each iteration, the indices m and p respectively representing a row and a column of the gain matrix K _n The weight is defined according to the following expression : Rn _iP is a maximum influence radius associated with each 10 _p sensor; for example, the radius of influence of a sensor disposed in the middle of a place may be greater than the radius of influence of a sensor disposed in a narrow street.

r _mp is a distance between a 10 _p sensor and a 20 _m mesh. The value of each term K _n (m, p) is then such that:

- K _n (m, p) = 0 if r _{m> p} > R _np (10)

w ⁿ

- K _n (m, p) = ₂ _ ™ Ίη _Λ ^{if r} m, p R Rn, p (H), where a is a term representing an error between the observations and the model, a is a predefined scalar can be for example, be equal to 0.1. Thus, each sensor 10 _p is associated with a neighborhood V _{n> v} , the extent of which depends on the maximum influence radius ff _np associated with the sensor 10 _p . It is considered that the concentrations of the analyte in the 20 _m cells located in this vicinity are impacted by the measurement resulting from the 10 _p sensor. The higher the rank of iteration, the more the maximum radius of influence R _np corresponding to one or more sensors 10 _p decreases. For example, it is assumed that the maximum radius of influence is identical to each sensor R _np = R _n . During the first iteration (n = 1), R _{n = 1} is set at 500 meters. During the second and third iterations R _{n = 2} and R _{n = 3} are respectively fixed at 300 m and 100 m.

According to one variant, the neighborhood V _{n> v} associated with a sensor 10 _p , that is to say the cells 20 _m at which the concentration can be influenced by a measurement made by the sensor, is not circular, but has a predetermined shape, taking into account the topography, and in particular the presence of buildings around the sensor and / or the dimensions of a street in which the sensor is placed. The vicinity of a sensor located in a street may for example extend significantly in a direction parallel to the axis of the street and lower in a direction perpendicular to the axis of the street. According to one embodiment, on the basis of an updated state vector, whether it is the state vector * (t) updated during step 160 or a vector d iteratively updated state (t) in step 170, the method may include a step 200 of predicting the state vector at a time t + dt subsequent to the measurement time t. For this, we have a state vector M (t + dt) provided by the model, in this case the OSPM model. The time interval dt can to be of the order of one hour. The state vector M (t + dt) can then be corrected by using the state vector updated at the measurement instant t, according to the following expression:

M * (t + dt) = ((t + dt) - (t)) + * (t) (12), or

M * (t + dt) = ((t + dt) - (t)) + * (t) (12 ') Thus, the local correction made to the model M (t + dt) depends on a variation between the vectors of states at the respective measurement instants t and t + dt, and of the state vector updated at the measurement instant t, whether it be ^ (t) or M * (t). It is observed that the correction of the subsequent state vector does not require new measurements, and is performed with respect to the state vector updated at the measurement instant. Although described in connection with nitrogen dioxide, the invention may be implemented with other analytes, and in particular pollutant molecules or particles. Moreover, in the above example, the state vector is established is OSPM type, but other models known to those skilled in the art can be applied to form the state vectors at each measurement instant.

Claims

A method for estimating a map of the concentration of an analyte in an environment, from sensors distributed in said environment,

each sensor (10 _p ) generating a measurement of the analyte concentration at different measurement times, the measurements made by each sensor at each measurement instant (t) forming an observation vector (C (t)), each term of which corresponds to a measurement from a sensor;

the spatially-meshed environment defining a plurality of cells (20 _m ), the analyte concentration at each cell, at each measurement instant, forming a vector, called a state vector ( (t)), each term of which corresponds to an analyte concentration in a mesh;

the method comprising the following steps, implemented by a processor:

a) from the measurements made by each sensor, obtaining an observation vector (C (t)), said measured, at a measurement instant (t);

b) obtaining a state vector ((t)) at the measurement instant (t) and, from the state vector, estimating an observation vector (C (t)) at said instant measuring;

c) comparing the estimate of the observation vector (C (t)) obtained in step b) with the observation vector (C (t)) measured resulting from step a), and from of the comparison, determining a global bias (ε (ί)) at the measurement instant, the global bias being a scalar representative of the comparison between several terms respectively of the estimated observation vector (C (t)) and the observed observation vector (C (t));

d) correction of the state vector ((t)) resulting from step b) as a function of the overall bias (ε (ί)) obtained during step c), in order to obtain a state vector said to have been debed ( '(t)) at the moment of measurement;

e) from the debonded state vector (M '(t)) obtained during step d), estimate debaiaisée the observation vector (C' (t)) at said measurement instant (t);

f) comparing the estimate of the observation vector (C '(t)) resulting from step e) with the observed observation vector (C (t)) resulting from step a), and from the comparison, determination of a local correction vector (corr (t)); g) updating the state vector ((t)) at the measurement instant ()), the latter being replaced by a sum of the debed state vector ('(t)) resulting from the step d ) to the local correction vector (corr (t)) resulting from step f), updating the state vector for estimating the mapping of the concentration of the analyte in different meshes of the environment.

2. Method according to claim 1, wherein during step b), the observation vector (C (t)) is estimated by applying a matrix (H), said observation operator, to the state vector. ((t)).

3. Method according to any one of the preceding claims wherein step c) comprises the following sub-steps:

ci) making comparisons between different terms of the observation vector (C (t)) estimated in step b) and the observation vector (C (t)) measured in step a); cii) calculation of a mean or median value of each comparison resulting from sub-step ci);

ciii) obtaining the global bias (ε (ί)) from the mean or median value resulting from the sub-step cii).

4. The method as claimed in claim 1, in which step d) includes a subtraction of the global bias (ε (ί)) at each term of the state vector ((t)).

5. Method according to any one of the preceding claims, wherein during step e), the estimate debaiaisée of the observation vector (C '(t)) is obtained by applying a matrix (H), said operator observation, at the state vector debed ('(t)).

6. Method according to any one of the preceding claims, wherein during step f), the correction vector (corr (t)) is determined according to the following substeps:

fi) establishment of a comparison vector (comp (t)), resulting from a comparison, term by term, between the observation vector (C (t)) resulting from step a) and the debut estimation the observation vector (C '(t)) resulting from step e);

fii) taking into account a gain matrix (K);

fiii) applying the gain matrix (K) to the comparison vector (comp (t)) so as to form a correction vector (corr (t)).

7. Method according to any one of the preceding claims, wherein following step g), the method comprises a step of iterative update of the state vector ((t)), with each iteration being associated an iteration rank (n), the method comprising the following steps: hi) taking into account a gain matrix (K _n ) corresponding to the rank of the iteration (n); hii) determining a comparison vector (comp _n (t)), associated with said rank of the iteration, by comparing the observation vector (C (t)) resulting from step a) with a vector obtained the application of a matrix (H), said observation operator, to the state vector obtained following step g), or resulting from a previous iteration; hiii) applying the gain matrix (K _n) taken into account when hi sub-step) to the comparison vector determined during eta pe hii), so as to obtain a local correction vector (corr _n ( t)) associated with the rank of the iteration;

hiv) update of the state monitor ( _n (t)), the latter being replaced by a sum of the state vector resulting from step g), or from a previous iteration (n-1), to local correction vector (corr _n (t)) resulting from sub-step hiii);

hv) reiteration of substeps hi) to hiv) or stop of the iteration.

8. Method according to any one of claims 6 or 7, wherein each term of the gain matrix (K (m, p)) is associated with a mesh and a sensor, the value of the term being all the more high that the mesh is close to the sensor.

9. Method according to any one of claims 2, 5 or 7, wherein each term of the observation operator (H) is associated with a mesh and a sensor, the value of the term is all the more high that the mesh is close to the sensor.

A method according to any one of the preceding claims wherein in step b) the state vector is formed using a model derived from data relating to road traffic in the environment, topography. environment as well as environmental meteorological data, resulting in a concentration of the analyte at the level of each mesh (20 _m ).

11. The method as claimed in any one of the preceding claims, comprising the following steps:

taking into account a state vector (t + dt), referred to later, at a time (t + dt) subsequent to the measurement instant (t);

establishing a correction of the subsequent state vector as a function of the updated state vector at the measurement instant in step g).

The method of claim 7, comprising the steps of:

taking into account a state vector (t + dt), referred to later, at a time (t + dt) subsequent to the measurement instant (t); establishing a correction of the subsequent state vector according to the updated vector, at the measurement time, in step h).