FR3060795A1 - METHOD FOR CONSTRUCTING THREE-DIMENSIONAL REPRESENTATION OF ATMOSPHERE, DEVICE AND PROGRAM THEREOF - Google Patents

Abstract

The invention relates to a method for constructing a three-dimensional representation of an atmosphere (REP1 ... REPN) operating within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of subdomains, referred to as boxes, which comprise a plurality of particles representing the atmosphere in this subdomain. According to the invention, such a method comprises at least one iteration of an update phase (20) of a current representation (REPT) of particles evolving within the atmospheric volume, this update phase (20). comprising, for a current time step T: a prediction step (21), from the current representation (REPT), of speeds and positions of the particles of each box of the atmospheric volume at a time step following T + 1, delivering an intermediate representation (REPiT + 1) at the time step T + 1; - A step of modifying (22) the distribution of particles in each box of the intermediate representation (REPiT + 1) delivering a set of treated boxes (Bh1, ..., BhM); a filtering step (23) of particles of the treated boxes (Bh1, ..., BhM) as a function of at least one datum representative of a real observation at the time step T + 1, delivering a following representation (REPT +1) at the time step T + 1.

Description

® FRENCH REPUBLIC

NATIONAL INSTITUTE OF INDUSTRIAL PROPERTY © Publication number: 3,060,795 (to be used only for reproduction orders)

©) National registration number: 16 63061

COURBEVOIE

©) Int Cl ⁸ : G 06 F17 / 10 (2017.01), G 06 F 7/38, G 01 W 1/00

A1 PATENT APPLICATION

©) Date of filing: 21.12.16. ©) Applicant (s): METEO-FRANCE Joint stock company (30) Priority: simplified - FR. ©) Inventor (s): BAEHR CHRISTOPHE, ROTTNER LUCIE, SUZAT FLORIAN and RIEUTORD THOMAS. (43) Date of public availability of the request: 22.06.18 Bulletin 18/25. ©) List of documents cited in the report preliminary research: Refer to end of present booklet (© References to other national documents ©) Holder (s): METEO-FRANCE Joint stock company related: simplified. ©) Extension request (s): @) Agent (s): CABINET PATRICE VIDON.

METHOD FOR CONSTRUCTING A THREE-DIMENSIONAL REPRESENTATION OF AN ATMOSPHERE, CORRESPONDING DEVICE AND PROGRAM.

FR 3 060 795 - A1 (3 / d The invention relates to a Method for constructing a three-dimensional representation of an atmosphere (REP. | ... REP _N ) evolving within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of sub-domains, called boxes, which include a plurality of particles representing the atmosphere in this sub-domain.

According to the invention, such a method comprises at least one iteration of an updating phase (20) of a current representation (REP _T ) of particles evolving within the atmospheric volume, this updating phase (20 ) comprising, for a current time step T:

a prediction step (21), from the current representation (REP _T ), of speeds and positions of the particles of each box of the atmospheric volume at a time step following T + 1, delivering an intermediate representation (REPi _{T +1} ) at time step T + 1;

a modification step (22) of the distribution of the particles in each box of the intermediate representation (REPi _{T + 1} ) delivering, a set of treated boxes (Bh ₁ , ..., Bh _M );

a filtering step (23) of particles from the treated boxes (Bh- |, ..., Bh _M ) as a function of at least one datum representative of a real observation at time step T + 1, delivering a representation next (REP _{T + 1} ) at time step T + 1.

REP _T

REPi _{T +} i>

_ £

Bh ₂ ;

DAT j-► • REPt-i i

Method for constructing a three-dimensional representation of an atmosphere, device and corresponding program

1. AREA

The invention relates to fluid dynamics. More particularly, the present technique relates to the representation of the evolution of a medium from observations of this medium. The present technique finds, for example, an application in the representation of a local atmosphere, considered as a physical medium whose state and dynamic characteristics are to be represented.

2. PRIOR ART

The representation of the evolution of physical environments is one of the keys to understanding the evolution of such physical environments, particularly in conditions of disturbed evolution, which can cause the environment to evolve rapidly. The atmospheric medium is typically a medium of this type. For an observed atmospheric environment, the atmosphere is, for example, modeled using digital particles whose evolution over time is to be represented. The atmosphere is therefore represented in the form of particles (fluid elements) whose speed and position, and their dynamic characteristics, change over time. In a way, the observed atmosphere is represented as the result of a representation of behaviors of particles which would be passively transported by the medium.

The problem, however, lies in the management of particles in a finite volume determined by the geometry of the observation system. Indeed, as the environment is not necessarily, in itself, made up of particles, the management of these particles and their number, and more particularly the management of their representation and the evolution of their representation during the time is an issue.

3. SUMMARY

The present technique makes it possible to solve at least some of the problems of the prior art. The present technique relates more particularly to a method of constructing a three-dimensional representation of an atmospheric medium.

More particularly, the invention relates to a method of constructing a three-dimensional representation of an atmosphere evolving within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of sub-domains, called boxes, which include a plurality of particles representing the atmosphere in this sub-domain.

Such a method comprises at least one iteration of a phase for updating a current representation of particles evolving within the atmospheric volume, this phase of updating comprising, for a current time step T:

a step of predicting, from the current representation, of the speeds and positions of the particles of each box of the atmospheric volume at a time step along T + l, delivering an intermediate representation at the time step T + l;

a step of modifying the distribution of the particles in each box of the intermediate representation delivering, a set of treated boxes; a step of filtering particles from the treated boxes as a function of at least one datum representative of a real observation at time step T + l, delivering a following representation at time step T + l.

According to a particular embodiment, the construction method comprises, prior to said updating phase:

a phase of obtaining and processing raw data coming from a measurement device, phase which delivers standardized data;

an initialization phase, during which representation parameters are selected and / or calculated, in particular by using the normalized data and other configuration data and in which an initialization of the representation is carried out, delivering an initial representation.

According to a particular characteristic, the step of modifying the distribution of the particles in each box of the intermediate representation comprises:

a step of obtaining, for at least one box, from the speeds and positions of the particles of the boxes previously predicted, at least one datum representative of a density of particles, called the density field of the Lagrangian particles; from the speeds and positions of the particles in the previously predicted boxes, a step of redistribution of outgoing particles, in at least one box, as a function of the density field of the Lagrangian particles and of a density field modeled; a step of management, within each box, of the particles previously redistributed, according to at least one law of representation of particles associated with said boxes.

According to a particular characteristic, the step of obtaining the density field of the Lagrangian particles comprises a step of calculating, for each box, of a density of particles at the time step T + l as a function of velocities and positions of the particles previously predicted boxes, delivering said so-called Lagrangian particle density field.

According to a particular characteristic, the step of redistribution of outgoing particles comprises, as a function of the density field of the Lagrangian particles and of the density field modeled:

a step of calculating, for each box, a weight, delivering a set of box weights, each weight being the result of a difference between a reference density from the density field modeled and a corresponding density in the density field of Lagrangian particles;

a step of random redistribution of outgoing particles, as a function of said set of weights of the boxes, delivering a reallocation matrix of outgoing particles; a step of random assignment, within the boxes, of each outgoing particle as a function of the outgoing particle reallocation matrix.

According to a particular characteristic, the step of managing the previously redistributed particles comprises:

a step of filling the boxes whose density is less than a reference density provided by the Eulerian field of modeled density, causing the creation of new particles;

a step of sampling of particles, within boxes whose particle density exceeds a value determined from the Eulerian field of density modeled, delivering said set of treated boxes;

According to a particular characteristic, the step of filtering particles from the treated boxes as a function of at least one datum representative of an actual observation at time step T + l comprises:

a step of calculating, for each particle of each box, a potential correlated with at least one current observation at time step T + l;

when a box comprises only harmful potentials for all of its particles, a step of resetting the speeds of the particles as a function of a current observation at time step T + 1 of said box; and a selection step, for each particle of each box, as a function of the potential of each particle and of said at least one current observation at time step T + l, delivering an updated representation at time step T + l.

According to another aspect, the invention also relates to a device for constructing a three-dimensional representation of an atmosphere evolving within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of sub-domains, called boxes, which include a plurality of particles representing the atmosphere in this sub-domain.

Such a device comprises means for updating a current representation of particles evolving within the atmospheric volume for a current time step T, these updating means comprising means for implementing:

prediction means, from the current representation of the velocities and positions of the particles of each box of the atmospheric volume at a time step along T + l, delivering an intermediate representation at the time step T + l; means for modifying the distribution of the particles in each box of the intermediate representation delivering, a set of treated boxes;

means for filtering particles from the treated boxes as a function of at least one datum representative of a real observation at time step T + l, delivering a following representation at time step T + l.

According to a preferred implementation, the different steps of the methods according to the invention are implemented by one or more software or computer programs, comprising software instructions intended to be executed by a data processor according to the invention and being designed to order the execution of the different process steps.

Consequently, the invention also relates to a program, capable of being executed by a computer or by a data processor, this program comprising instructions for controlling the execution of the steps of a method as mentioned above.

This program can use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code, such as in a partially compiled form, or in any other desirable form.

The invention also relates to an information medium readable by a data processor, and comprising instructions of a program as mentioned above.

The information medium can be any entity or device capable of storing the program. For example, the support may include a storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, or else a magnetic recording means, for example a floppy disk or a disc. hard.

On the other hand, the information medium can be a transmissible medium such as an electrical or optical signal, which can be routed via an electrical or optical cable, by radio or by other means. The program according to the invention can in particular be downloaded from a network of the Internet type.

Alternatively, the information medium can be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the process in question.

According to one embodiment, the invention is implemented by means of software and / or hardware components. In this perspective, the term module can correspond in this document as well to a software component, as to a hardware component or to a set of hardware and software components.

A software component corresponds to one or more computer programs, one or more subroutines of a program, or more generally to any element of a program or software capable of implementing a function or a set of functions, as described below for the module concerned. Such a software component is executed by a data processor of a physical entity (terminal, server, gateway, router, etc.) and is capable of accessing the hardware resources of this physical entity (memories, recording media, bus communication, electronic input / output cards, user interfaces, etc.).

In the same way, a hardware component corresponds to any element of a hardware (or hardware) set capable of implementing a function or a set of functions, according to what is described below for the module concerned. It can be a programmable hardware component or with an integrated processor for the execution of software, for example an integrated circuit, a smart card, a memory card, an electronic card for the execution of firmware ( firmware), etc.

Each component of the system described above naturally implements its own software modules.

The various embodiments mentioned above can be combined with one another for implementing the invention.

4. DRAWINGS

Other characteristics and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment, given by way of simple illustrative and nonlimiting example, and of the appended drawings, among which:

FIG. 1 presents a general view of the treatment of particles according to the present technique;

FIG. 2 describes an iteration of the phase of updating the representation;

FIG. 3 briefly describes the architecture of a representation initialization and updating device according to the present technique.

5. DESCRIPTION

5.1. Reminders of the principle

The general principle of the described technique consists in constructing a representation of an atmospheric medium (turbulent or laminar) as being the result of a representation of independent particles which are distributed in this medium and whose positions and successive speeds. An object being to represent as clearly as possible the evolution of these particles (position, speed, etc.) over time, in a given volume of representation. In the context of the present, as has been specified above, it is considered that the medium, such as for example the atmospheric medium, is divided into a set of volume units, called boxes. Indeed, due to the measurement geometry of the in-situ or remote sensing instruments, the reconstruction domain is limited and the exterior is not represented. Thus, the domain is divided into sub-domains, called boxes, such that each box contains only one observation point. Each box then has its own physical characteristics which are controlled by the related observation.

In addition, the representation of the environment is created and updated according to a behavior model. We represent the atmosphere under the conditions of the model: turbulent model leads to a turbulent representation. Conversely, a non-turbulent (laminar) representation is made from a laminar model.

In relation to FIG. 1, the representation construction method generally comprises: a phase for obtaining and processing (05) raw data (RAW) coming from the measuring device (MEAS) (LIDAR Doppler such as, for example, the WindCube ™ from LEOSPHERE or the DIABREZZA ™ from Mitsubishi Electric), a phase which delivers standardized data (DAT); an initialization phase (10), during which representation parameters are selected and / or calculated, in particular using the normalized data (DAT) and other configuration data (PAR) and in which in particular an initialization of the representation is made, thus delivering an initial representation (REPO); a succession of update phases (20) of the representation (REPO, REPI, ... REPN) (the number of update phases of the representation essentially depends on the frequency of obtaining data from the measuring device and the time during which the measurements were made): this succession of update phases represents the evolution of the atmospheric volume considered over time, each update phase corresponding to the passage of a time step T at a time step T + l. Successive representations can be saved or only used to extract data of particular interest.

Thus, as explained above, an update phase (20) of the representation performs a modification of the representation between two successive time steps. More particularly, each phase of updating the representation consists of a set of steps whose objective is to modify the representation of the medium so that it is representative of the evolution of the latter between the time step T and the time step T + l.

More particularly, in relation to FIG. 2, a phase for updating a representation, from a time step T to a time step T + 1 comprises the following steps:

a prediction step (21), from the current representation (REP _T ) of velocities and positions of the particles of each box of the atmospheric volume at a time step along T + l, delivering an intermediate representation (REPi _{T + 1} ) at time step T + l; a modification step (22) of the distribution of the particles in each box of the intermediate representation (REPi _{T + 1} ) delivering, a set of treated boxes (ehn. ^ Bhiv,);

a filtering step (23) of particles from the treated boxes (ΒΗ ^.,., ΒΙίμ) as a function of at least one datum representative of a real observation at time step T + l, delivering a following representation (REP _{T +1} ) at time step T + l.

The methods implemented in this reconstruction system, and more particularly for this updating phase, are linked to the representation of the continuous medium, and turbulent by point particles.

When the evolution of the system is modeled (represented), the particles interact with each other, but are not linked to the domain measured. Thus, to properly represent the domain of reconstruction by particles, specific management rules have been defined: these rules allow in particular to manage outgoing particles, regions of the domain which are in deficit of particles (which harms the representation) and regions which are, on the contrary, over-represented.

In general, the proposed methods are based on random redistributions minimizing the difference to an ideal distribution of particles: this is more particularly the case of the modification step. When a particle is replaced randomly in a box, we always use the same rule, which consists in drawing according to a uniform law the position of the replacement and giving the replaced particle a speed characteristic of the box where it is replaced.

Initially the outgoing particles are stored in the domain. To do this, the delivery box is drawn randomly according to a rule which favors boxes whose density deviates from the ideal distribution. Then replace this outgoing particle in the box according to the rule prescribed above.

Then, when a box is too much in deficit compared to an ideal distribution (particles in this box) we take a particle in the system by first choosing a box (this choice favors a sample in the too full boxes), then by taking a particle from the box with a uniform choice. The replacement in the target box follows the rule presented above. The operation is repeated as long as boxes are lacking in representation (that is to say as long as the quantity of particles in this box deviates from an “ideal” quantity of particles, according to a density target, ideal for a given box). The ideal quantity relates to the distribution of the particles as a function of the modeling of the medium, and is explained below, in connection with a particular embodiment.

Finally, we carry out a treatment on the boxes which contain an excess of particles compared to the ideal distribution. Particles are taken from these excess boxes in the same way as above, then the particles are replaced randomly in one of the destination boxes. The choice of the box favors those which are the least filled. The particles are then randomly positioned inside this box.

In a general embodiment, the distribution of the particles in the boxes follows a predetermined distribution law: the distribution law determines the choice of either Lagrangian or Eulerian representation. In a specific embodiment, such as that presented below, a law of uniform distribution of the particles is preferred: this law is used at the initialization of the system. This distribution law is then updated over time according to what we have learned from the environment: that is to say according to successive observations.

In the following, therefore, we present a particular embodiment of the general principle which has just been presented previously.

5.2. Description of an embodiment

In this embodiment, we detail the different steps implemented to build a three-dimensional representation. In this embodiment, the representation is based on the use of Lagrangian stochastic particles scattered in the reconstruction domain. To function properly, the reconstruction system uses several elements:

a turbulent stochastic Lagrangian model;

particle filtering relative to the observation to obtain the best representation;

a method to keep its quality in the representation of the medium by particles evolving freely according to the Lagrangian model.

In this embodiment, the method of constructing the representation is described for a posteriori processing. It is however possible to carry out a reconstruction online, in real time. In this case, the steps for preprocessing the raw data in particular are modified to correspond to the sequential arrival of the data.

5.2.1. Preprocessing phase, processing of time steps and shaping of raw data

The objective of this phase is to normalize the data that is used to build the representations. This optional phase only concerns ex-post processing: it makes it possible to “comb” the data, that is to say, to fill in the missing data. There is also an equivalent phase for data processing in real time. This processing is slightly different from the a posteriori processing in the sequence of actions: in the case of a posteriori processing, as soon as we locate missing data, we go directly to the next observation and in the real time case, there is an absence of data and we wait until the next observation.

ίο

Anyway, in the case of deferred time (a posteriori), this phase includes the following stages:

05a- Reading the time file

This step takes as input a file comprising measurement times and outputs a raw vector of the observation times and statistical elements on the measurement times. More particularly, this step comprises a reading of the time file, calculates statistical data on the time steps, and determines the nominal time step. It also includes a step of determining the maximum time step for detecting missing times (see step 05f).

05b- Time vector creation

This step determines the complete vector of the observation times, with indexing of the absent times as a function of the raw vector of the observation times previously calculated. More particularly, it performs a creation of the time vector from the present times and by completing the missing times with the nominal time steps. This step also delivers a file of observation times corresponding to the times of the different data observed.

05c- Reading of the radial winds file

This stage delivers a raw matrix of the radial winds according to a file containing the measurements of the radial winds, resulting from the measuring device (Lidar Doppler like for example the WindCube ™ of LEOSPHERE or the DIABREZZA ™ of Mitsubishi Electric).

An example of a measurement file for a 5-beam Lidar is as follows:

Timestamp Shoot T 40m 60 m 80 m 100m CNR (dB) Radial speed (m / s) CNR (dB) Radial speed (m / s) CNR (dB) Radial speed (m / s) CNR (dB) Radial speed (m / s) 1900/01/01 00: 00: 00.00 O 14.0 -2.34 -0.29 -0.30 -0.54 0.80 -0.56 0.94 -0.62 1900/01/01 00: 00: 01.00 Z 14.0 -2.28 -0.80 -0.53 -1.09 1.31 -0.63 1.65 -0.56 1900/01/01 00: 00: 02.00 NOT 14.0 -2.66 -6.21 -0.37 -6.85 1.24 -6.93 1.45 -7.10 1900/01/01 00: 00: 03.00 E 14.0 -2.79 2.29 -1.22 2.27 0.11 1.56 0.37 1.44 1900/01/01 00: 00: 04.00 S 14.0 -2.59 5.10 0.05 6.74 1.31 6.84 1.42 6.86

05d- Processing of missing data

This step delivers a corrected radial wind matrix, as a function of the raw radial wind matrix previously obtained and of the complete time vectors with indexing of the absent times. More particularly, we call absent data, a time when there are no observations on the entire domain. The missing data are therefore partial. The missing times of the time vector give absent winds, therefore NaN (from the English “Not a Number”), over the entire domain observed for these times (this means that there is no observation for the no time considered).

05e- Processing of outliers

The objective of this step is to delete the outliers, that is to say the data, which, taking into account the measurements made, are greater or less than the possible data. It takes as input the matrix of radial winds previously obtained and replaces the outliers, those which exceed a predetermined threshold, by an absence of value (NaN).

At the end of this stage, one thus has a matrix of radial winds, having missing data (NaN) for certain time steps considered. It is therefore necessary to take these missing data into account for further processing, and in particular for the construction of the representation.

05f- Search restart

This is the objective of this step. It is necessary to define time steps (moments) when the construction must start from 0 rather than continuing. Indeed, when the missing data spread over a too long time period, the numerical evolution of the representation (ie without observation) can deviate too significantly from the real evolution (ie if there had been observations). It is therefore preferable to define restart times. This is the role of this stage. It takes as input the matrix of radial winds and predefined thresholds (defining options for further processing or restarting) and it delivers a matrix of radial winds for processing (the matrix which is used later). As an indication, when the data are absent for a period of around seven times the nominal time step, a restart is implemented. When the absence period is more reduced (2 to 3 times the nominal time) the construction processing will continue, however omitting the filtering step based on actual data.

05g- Creation of the observed radial winds matrix

On the basis of the preceding data, and in particular on the basis of the matrix of the radial winds, this step prepares a complete matrix of the radial winds and a file of the radial winds cleaned and usable on the basis of this matrix, that is to say say whose missing data have been filled.

At the end of this preprocessing phase, there is a matrix reproduction of the data from the capture, normalized and timed reproduction. Depending on the embodiments, it is possible to have a single three-dimensional matrix, retracing the evolution of the measurements over time, or even a plurality of matrix, each matrix being associated with a determined time step.

5.2.2. Initialization phase and determination of reference winds

As explained above, this phase makes it possible to initialize the construction system, namely to initialize in particular the particles in the domain and to obtain first constructions of the representation with a view to its successive updates (this is the representation REP ₀ at the step time T = 3). This phase includes the following stages:

10a- Definition of global and geometric parameters

This step takes as input: Physical quantities, Physical constants of the model, Predefined parameters of the reconstruction system, Geometric quantities of the measurement system, Statistical quantities of the observation system.

It outputs system variables

The reconstruction system uses a certain number of parameters depending on the measurement geometry, the physics used, the reconstruction / filtering algorithm.

Note: as explained above, the domain is divided into sub-domains called boxes, such that in each box there is an observation given by the measurement system. Thus, a box is, in this embodiment, defined as a volume around at least one observation.

10b- Creation of 3D winds

This step provides a first three-dimensional estimate of the "initial" winds. It uses the complete matrix of radial winds, obtained during the preprocessing and geometric variables of the observation system to deliver a complete matrix of 3D winds. Two situations can arise:

for systems with oblique sight (LIDAR Doppler system having several sightings and allowing the calculation of the horizontal component of the wind speed), it is necessary to deduce the three-dimensional wind from the radial winds: to do this, we project the three components of direction of the oblique winds on the 2 horizontal axes and the vertical axis by basic trigonometric formulas (calculations carried out starting from sine and cosine of the angle of inclination of the aiming to find the horizontal and vertical components of the wind); The “NaN” present on a sight give “NaN” in the three directions.

for systems returning the wind only in the direction of sight (Lidar system

Doppler with only one ray, for example vertical), this step is not necessary.

10c- Declaration of variables

This purely formal step allows you to declare and initialize the processing variables used later.

lOd- Special treatment of times 1 and 2

The reconstruction method uses, to determine the commands at time step N, the wind estimates of time steps Tl & T-2. The Lagrangian model of particles uses what are called commands which make it possible to conform the evolution of the model to observations. These commands are learned as and when the observations processed and the filtering are carried out. We consider as being the time T = l, the first time where the measurements are not absent (measurements without "NaN"). The time loop update of the representation thus starts at the 3 ^rd time step and the time T = 1 and T = 2 are pretreated.

In the event of a restart (i.e. missing data over too long a period of time, see step 05f), the reconstruction process is restarted at this step.

An order is an entry which has a particular role in the model and which determines how the system evolves. The command itself evolves over time, depending in particular on observations, and determines the behavior of the system. In the present, at least one order is available per box. The filtering technique allows you to learn the command of a box from the observations of this box. The models of each box are not necessarily identical. Thus, the evolution of orders, as and when filtering by observations, is not identical for each box. Concretely, the command is a number, which is integrated into the Lagrangian model of particles and which participates, iteration after iteration, in the evolution of this model. The Lagrangian model, in itself, gives the evolution of the position and the speed of the particles. The model is therefore composed of a function (defining the model) and two commands (or a command u (t) composed of 2 numbers) causing the model to vary.

More precisely, in this embodiment, there are two groups of commands per box: one group of commands is the local variance of the speed increments and the other is the local average evolution of the speed increments (a group of commands includes three numbers each time because the observations are in 3D). The model gives the evolution of the position and the speed. The model is a function and 2 commands (or an u (t) command made up of two numbers).

This particular processing step for times 1 and 2 is divided into three sub-steps:

10d: a - Case of missing observations in times 1 and 2: In this sub-step, on the basis of the complete 3D wind matrix of times 1 & 2, we process the missing data of these matrices (one matrix per no time). A search for missing data in the observed domain (signed by NaN) is carried out and the replacement of this missing data is carried out: a missing data is replaced by the barycenter of the regular values around the NaN. If the NaNs are on the ends of the domain, the last valid values are then copied. 10d: b - Placement of particles in the boxes according to a representation law On the basis of the complete 3D wind matrices of times 1 & 2 (previously updated), we make a first estimate of the Eulerian field of modeled density (ie - to say of the model, model which one then makes evolve according to the observations). The state vector of a particle contains the position of this particle, its speed and its membership box. We build a first representation of the medium by placing particles in the medium to sample a target probability law for positions.

When the target law is the uniform law: the positions are chosen randomly by drawing them according to a uniform law. This is the case, for example, with a treatment of the WindCube V2. This simplified case is part of the more complex case in which the law is not uniform. The objective is then uniformity and the boxes are of equivalent densities (Eulerian field of uniform density).

When the target law is another probability law which is time invariant, the positions are sampled according to this law.

When the target law is a time-dependent probability law, additional steps are integrated compared to the stationary case: o the positions are initialized by a draw according to a sequence with low irregularity ("low discrepancy") to represent the best possible l uniformity with few particles.

o we define an Eulerian field of modeled density of particles,, to serve as an initial condition for the evolution of itself (that is to say of this Eulerian field of modeled density) according to a scheme in finite volumes.

For times T = 1 & T = 2, once the positions of the particles are fixed, their membership box is determined, the speed of each particle is chosen by adding noise (here Gaussian choice for centered dispersion) to its observation reference. For a given particle, the reference observation is the observation of the box to which the particle belongs.

10d: c - Time 2 estimates: the purpose of this sub-step is to determine the commands of the Lagrangian Stochastic model at time 3 from the particles at times 1 & 2.

The Lagrangian stochastic model contains two terms that control the model and determine the evolution of particles. These two commands are medium terms of large scales (compared to particles). In the case of a model driven by observations, these commands are learned using the particles which have been filtered by the observations. There is one set of commands per box. For the times T = 1 & T = 2, the particles are not filtered, the velocities of the particles as they are used to estimate these commands which are used to start the time loop at time T = 3.

It is specified that with the choice made of a Gaussian dispersion around the observations, one of the commands corresponds to the increment of the speeds observed in each box and the other depends on the variance of the Gaussian chosen. But the step presented here calculates the commands on the particles without considering the previous Gaussian choice.

At the end of the initialization phase, we therefore have a model and a representation that we will be able to develop thanks to the data of the following time steps (the matrices of successive radial winds at times T = 3, ..., T, T + 1, T = N). It is this evolution of the construction of the representation which is described below, in the update phase.

5.2.3. Time loop for updating representations

The time loop processes the particles sequentially as long as observations (observation matrices) are available. This treatment comprises three stages, presented previously. These steps are detailed here for this embodiment of the proposed technique. The first step is an evolution of the particles in speed and position according to the commands learned during the previous updates.

The second step concerns the management of the representation of the medium by the particles. First, the particles out of the reconstruction domain are replaced inside. Second, the positions of the particles are treated to correspond to a target spatial representation law (defined at least in part by the Eulerian field of modeled density).

The last step filters the particles according to their relevance to their reference observation. From there came the different estimates.

The current time step is noted T, and the evolution predicts the state of the system at the time step T + l.

The three steps are presented below, according to the numbering used in Figure 2.

5.2.3.1. Particle velocity and position prediction (step 21)

The prediction of speeds and positions uses a Lagrangian model of behavior of fluid elements. For turbulent conditions, a specific model is used. This model can deal with turbulence in 1D, 2D or 3D with vertical couplings to take into account the buoyancy terms (Archimedes thrust) or vertical gradients. For laminar flow conditions or for stable turbulence conditions, other suitable models can be used.

Step 21 of predicting the positions and velocities of the particles at time T + 1 itself comprises four sub-steps.

21: under processing of missing data

From the observations (observation matrix (s)), it is determined whether data are missing. When observation data is missing, it must be “replaced” by “simulation” data. This sub-step delivers, for the Lagrangian model, NaN commands or flags when the data is missing.

The Lagrangian model uses commands which are learned on the average increments filtered by the observation of time steps T, T-l. When the observation T + 1 is missing, the last commands learned by filtering are used.

21: b-under a step of definition of the variable time step

The purpose of this sub-step is to determine the current time step from the time vector. We define the local time step for the evolution model, it is the difference between the times recorded for the observation at the current and previous time step.

21: c-sub-step for determining speed changes

From the Matrix of the speeds filtered from the previous time step (i.e. from the previous iteration), we define a Matrix of the speeds at the next time step. The evolution of particle velocities is given by the Lagrangian model. The evolution of a particle takes into account the position and the speed of the other particles with operators of spatial averages which maintain a coherence of large scale in the movement of the particles. This step predicts the speeds at time step T + l.

21: d-sub step for determining changes in positions

From the matrix of the positions of the preceding time step, one defines a Matrix of the predicted positions. The evolution of the positions of the particles is the expression of the integration of the velocities, with an error term because we use a simplest decentered Euler scheme. This error term is a Gaussian noise centered with a variance determined beforehand. This step predicts the positions at time step T + l.

5.2.3.2. Evolution of the density eulerian field (step 21-0)

The purpose of this step is to determine the density Eulerian field at the current time step. To do this, we base ourselves on the Eulerian field of density at the previous time step.

The density Eulerian field evolves according to a classical transport equation with a numerical scheme in finite volumes with free conditions at the edges. We use a mesh modeled on the boxes defined for the reconstruction. The Eulerian wind field at time step T used for the advection scheme is then calculated by average over the particle velocities for all grid points at time step T which has been created and filtered. After this evolution step, we have the density eulerian field at time step T + l.

In the case of a stationary field, this step is omitted, this is why this step is designated as being optional.

5.2.3.3. Modification of the distribution: conditioning in the domain and representation by particles of the fluid (step 22)

This stage constitutes the heart of the construction technique. It is a question of managing the representation of the fluid by the particles in all the field without leaving gaps in the representation and without destroying the structures learned by the system (resulting from the preceding iterations). This step deals with the positions of the particles. After this, the selection step will process the particle velocities. If the particle velocities are controlled by filtering, the positions of these particles are not filtered and therefore these positions must be treated appropriately. This stage is divided into two main sub-stages which are: the treatment of particles which have left the domain after their a priori evolution; and the treatment of the particles within each box so that the representation retains its spatial coherence with respect to a reference evolution (the model).

First, for these treatments, we use an Eulerian field of particle density that must be calculated for each box.

22: a - Calculation of the Eulerian field of density of Lagrangian particles

The positions of the Lagrangian particles predicted at the time step T + l are used to calculate in each box the density of the Lagrangian particles. We then obtain an Eulerian field of the densities of Lagrangian particles at time T + l. This Eulerian field of particle densities (derived from particles, themselves derived from the evolution of observations) is compared to the Eulerian field of modeled density (step 10d: b in which we defined the model for times 1 & 2) ( note 3) to decide on redistributions of Lagrangian particles. The particles which left the reconstruction domain after the reconstruction step do not contribute to the estimation of this Eulerian field of particle densities.

22: b - Redistribution of outgoing particles

After the step of predicting the positions of the Lagrangian particles, some were able to leave the area of interest. These outgoing particles no longer participate in the reconstruction and must be repositioned inside the representation. We try to fill the boxes that are in deficit of particles after the prediction step. This happens when more particles have come out than come in. This step implements a random draw, based on a calculated weight, from a box for reassigning an outgoing particle. Then in the selected box, a particle is replaced. This process is iterated as many times as there are particles to store. The weight function (for the random draw of the reassignment box) is relative to the difference between the eulerian density of Lagrangian particles and the target representation which is calculated by the eulerian field of modeled density. The outgoing particles are stored in a temporary matrix (X °, V °).

The various stages of the redistribution of the outgoing particles are detailed below. 22: b-l Calculation of the weight of each box in the domain

In this step, we seek to determine the boxes for reassigning outgoing particles. More particularly, we seek to determine a function which makes it possible to determine a kind of privilege of reassignment, although the reassignment in itself is done at random. To obtain this set of weights, we use the Eulerian field of density of the Lagrangian particles (projection on the grid), and the Eulerian field of density modeled and we obtain an Eulerian field of the weight of the boxes (i.e. a set of box weights).

We define a weight function such that: the more the Lagrangian density (Eulerian field of density of Lagrangian particles) of a box deviates by default from the target Eulerian density (Eulerian field of modeled density), the greater its weight. To calculate the weights of each box, W (x, y), we define a potential function G ^w (x, y), the weight being deducted a posteriori by normalization. The potential function G ^w calculates the distance between the two input Eulerian fields (distance between the Eulerian density field of Lagrangian particles and the density density field modeled) to normalize it between 0 and 1.

Thus, for a box of coordinates (x, y) if we note p ^L (x, y) the Lagrangian density (of the Eulerian field of density of Lagrangian particles), p ^E (x, y) the Eulerian density (of Eulerian field of modeled density), it is possible to give the potential function several empirical expressions. It is for example feasible to choose as function G ^w (x, y) = max (l - p _E (xy)> θ) ^or βίθ ^η G ^w (x, y) = max (tan (l - θ) ^or d Others This potential function must be decreasing and limited.

All the weights of the boxes are expressed by a Eulerian field W (x, y) =

G ^w (xy),. ,, ...

_r —— · —— of the weight of the boxes.

; GW (x, y) dx dy ^H

22: b-2 Random draw according to the calculated weights of a reassignment box

The next step consists in obtaining, randomly, a reassignment box as a function of the Eulerian field W of the weight of the boxes (set of weights W) in order to obtain a matrix of the coordinates N ^R of the reassignment boxes.

The set of weights W (x, y) allows the reassignment boxes to be drawn randomly, and relative to the weight of each box. It is a random drawing of discrete random variables (the reallocation coordinates) according to the probabilities W (x, y). The reallocation coordinates N ^R (x, y) are stored in a matrix. So for each outgoing particle, we select a reassignment box. The Lagrangian density p ^L (x, y) is then updated.

22: b-3 Put the particles back in a box

Using the matrix of coordinates N ^R of the reassignment boxes, the outgoing particles are reassigned and a temporary matrix (X °, V °) is obtained, comprising all the particles which have been reassigned. For each reassignment box N ^R (x, y), a position is drawn inside this box, in a uniform or almost uniform manner, which will be the new position X °. There are several possibilities for choosing the speed of this particle. A dispersion around the predicted average value of the box is a possibility. The dispersion can be Gaussian or follow the local pseudo-random function, for example by randomly drawing the fluctuation in the predicted speed of a nearby particle.

Be that as it may, the outgoing particles are thus replaced in the domain by favoring regions that are poorly represented.

22: c - Management of particles according to a representation law

The next step is to determine if the boxes are properly filled with the particles. This step makes it possible to ensure that the number of particles in the boxes is relatively homogeneous with regard to a law of representation of the particles in the boxes: it is necessary to fill, according to this law, the boxes which are too little filled and on the contrary eliminate overfilled boxes. Each box is filled according to the orders associated with this box. Thus, the representation law can be common to all the boxes while individualized commands can be applied to each of the boxes, modifying the result provided by the representation law.

After having stored the outgoing particles, it is necessary to process the representation of the domain to have sufficient information and therefore particles in sufficient number everywhere in the domain, without destroying the structures which may appear and without changing the number of particles.

To do this, we have p ^E (x, y) the Eulerian density (of the modeled density Eulerian field) which is the target; and p ^L (x, y) the Lagrangian density (of the Eulerian field of density of Lagrangian particles) which must be modified to have the most relevant representation.

Note that this step is placed before the selection step which will filter the speeds which will have been badly chosen by the resampling and perfect the representation.

The various stages of the redistribution of the outgoing particles are detailed below.

22: c-l Filling of the too little filled boxes

As before, we use the Eulerian field of density of Lagrangian particles, and the Eulerian field of density modeled to provide a new matrix of Lagrangian particles and a new one of the Eulerian field of density of Lagrangian particles.

It is first necessary to detect the boxes under-representation then fill them to reach the target. The under-representation criterion relates to the target and not to an absolute criterion. It is necessary to allow the representation system to keep sparse boxes if this is the case in the target. Several detection methods exist to give the detection threshold. Detection can take place if p ^L (x, y) is less than a fraction of p ^E (x, y) while ensuring that p ^E (x, y) is not too small. The method used in this embodiment is the conjunction of the events p ^L (x, y) < ^{Lag threshold} and p ^E (x, y)> ^{Eul threshold} . The number of particles to be added is then N ^A i ° ^ut (x, y) = K ^Particles (p ^E (x, y) - p ^L (x, y)). The delivery procedure is identical to that of step 22: b-3 which is iterated as many times as necessary (as long as there are too few boxes filled).

During this operation, new particles are created. The Eulerian field of density of Lagrangian particles p ^L (x, y) is then updated (one thus obtains one of the Eulerian field of density of Lagrangian particles).

22: c-2 Elimination of particle overflow

As before, we use the Eulerian field of density of Lagrangian particles (previously updated), and the Eulerian field of density modeled to provide a new matrix of Lagrangian particles and an Eulerian field of density of Lagrangian particles.

Filling to avoid underrepresented areas creates new Lagrangian particles. We must now take some to stay with a constant global number. The number to be taken is provided by the previous step: N ^Pre i ^event = N ^A i ° ^ut (x, y).

To do this, we proceed as in steps 22: b1 and 22: b-2, by defining a potential function, then by choosing sampling boxes. Then in each selected box, the particle or particles are removed. The vector of the sample boxes has the length N ^{Pre ievement} _e j- box numbers can be repeated.

The potential function is different from that used in step 14: bl. It is a matter of favoring the heavier boxes for direct debits. Again several empirical functions are possible. For example G ^w (x, y) = atan can be used.

The choice of the sampling box is identical to step 14: b-2, by a random drawing according to the weights W (x, y). A vector of sample collection boxes B is then ^created .

The vector B ^Sampling _is traversed and in each selected box (with redundancies) a particle is taken. The choice of the sampled particle is done randomly. This draw can meet several laws. We can collect according to the uniform law. This can also be according to the complement of the likelihood of the particle. The likelihood function, which is a potential, is defined in the next section.

Once the samples are finished, the Eulerian field of density of Lagrangian particles p ^L (x, y) is updated.

At the end of this stage, we therefore have a new representation, updated to stabilize the number of particles represented in the different boxes. Of course, the above is only an indicative embodiment of how this modification step can be implemented. It is entirely conceivable, for example, to carry out the elimination of the overflow at the same time as the filling of the too little filled boxes, one serving as a reservoir for the other, then to reassign the outgoing particles in the boxes again too little filled. The central point of this step is to keep the same number of Lagrangian particles while keeping, for each box, a density of particles from previous iterations (density from the Eulerian field of modeled density).

5.2.3.4. Filtering of homogenized particles: selection according to observation (step 23)

The two previous stages of prediction and conditioning / representation / modification of the domain form the evolution-a priori part of the construction process. These stages allow us to propose a global state, the reconstructed system, made up of possibilities, the particles.

The selection stage makes it possible to filter these possible states so as to retain only those which are likely with respect to the observation which is made of the reconstructed system. After filtering the reconstructed system constitutes the best accessible state of the atmosphere, a posteriori, having regard to the observation which is made of it, the representation of the fluid which has been set up and the Lagrangian modeling which has been chosen.

Filtering consists of a selection of particles in each box using observation of the box. This selection is of genetic type and uses the definition of a potential function G ^Y (x, y) for each box (x, y). As we seek to estimate the posterior probability given the a priori probability (implementation of a nonlinear filtering), the potential function G ^Y (x, y) is given by the probability of likelihood of the Bayes rule. The type of genetic selection defines an algorithm class, a class in which, for the case of the invention, the particles which are considered "suitable" are kept and the particles "not adapted" are deleted.

To carry out this operation, in this embodiment, the following four steps are implemented:

23: a - Calculation of the particle potential

First, a calculation is made of the potential of the particles. To do this, we use the Lagrangian Particle Matrix and the Field of observations. At the output, a vector of potential G ^Y of the Lagrangian particles is delivered.

A potential function G ^{Y, b} is deduced from an observation equation (the link between a state and its observation) or more precisely from the probability density function of the observation noise. The observation equation which can have the form: Y _t = H (v {* ^eel ) + B ° ^bs where V / ^eel is the real wind that we are trying to estimate, H is a function called transfer function which makes it possible to pass from the physical quantity to the quantity observed and B ° ^bs is the noise of observation that is to say the random disturbance of the measurement system, and it is supposed to know in advance the distribution law of probabilities of this observation noise. The potential function G 'is then deduced from the observation equation.

For each particle the potential relative to the current local observation Y _t ^b +1 is calculated, where b = (x, y) is the position of the box to which the particle belongs. This potential G ^{Y, b} (Xt + i, V _t ' ₊ i) measures for each particle (Xt + i, V _t ' ₊₁ ) a likelihood of the particle relative to its speed V _t ' ₊₁ regardless of its position X [ ₊₁ in box b.

23: b - Treatment of all harmful potentials in a box

It is possible that all the particles in a box are inconsistent with respect to the observation. For example if the wind model gave inconsistent speeds to all the particles in a box. The sum of the potentials is calculated for each box. When a box has all harmful potentials (the potential function is always positive or zero), then the sum is zero and the speed of the particles is reset with a Gaussian dispersion around the current local observation The positions remain unchanged. The potential of these particles is then updated as in the previous step 23: a.

23: c - Treatment of missing observations

We must again deal with the case of missing observations. From the field of observations, we define a vector of flags with missing observations

In case of missing (isolated) observations, there is no selection and therefore no step 23: d. A flag vector (boolean) is created. The flag vector is also used in the estimation step 24: c.

23: d - Genetic selection according to speeds

From the potential vector G ^y and the Matrix of Lagrangian particles, we update the Matrix of Lagrangian particles to produce a new representation based on observation.

The particle potential vector relative to the observations G ^Y makes it possible to make a genetic selection which performs the conditioning of the velocities of the particles to the observations. Genetic selection consists of a first acceptance / rejection step. The acceptance rate is given by the potential. If a particle is accepted, the predicted speed is unchanged. In the event of rejection, the particle is replaced by another present in the same box drawn at random according to the potentials. This draw is identical to that described in 22: bl and 22: b-2 with creation of weights and draw according to them. All the particles present in the box can be removed, including that which has been rejected. In the end, particles can thus be duplicated (or more) within a box or disappear.

At the end of this genetic selection step, all the particles (Xt + i, V _t ' ₊₁ ) have velocities which have been filtered by observation (filtering of the possible velocities). It should be noted that particles with unsuitable speeds will have positions that are also unsuitable and therefore have been eliminated. The Eulerian field of density of Lagrangian particles is not affected in this step since the deliveries are made inside each box.

The set of filtered particles (Xt + i, V _t ' ₊₁ ) gives the best knowledge of the random environment with regard to the observations that have been made. It is then possible to calculate the estimates of the dynamic quantities of the reconstruction system.

5.2.3.5. Estimates

In this embodiment, a final step is implemented, within the updating phase. This last step (24) of the time loop makes it possible to provide the fields or quantities necessary for the next time step, but also for the estimation of dynamic quantities such as speed or turbulent parameters. All these quantities can also be recorded in output files at each time step. The estimates are divided into four successive stages.

24: a - Calculation of new density fields

In this embodiment, the modeled density Euler field which is used in the next time step is simply the final Lagrangian particle density Euler field.

24: b - Estimated speeds

For each box, the average speed of the filtered particles is the estimate of the speed of the fluid in this box. It is a simple arithmetic average. This average is obtained, per box, from the Matrix of Lagrangian particles and we obtain a Matrix of the estimated velocities.

24: c - Estimates of the model commands

It is the same calculation as that made in step 10d: c. For each gearbox, the average of the temporal increments of the speeds and the quadratic mean of the temporal increments are calculated. This calculation therefore uses the filtered velocities of the times T and T + l. Missing observations (Vector of missing observation flags) allow missing data to be ignored. We obtain as output a new Matrix of commands from the Lagrangian Stochastic model, to be used in the following iteration.

24: d - Estimates of turbulent parameters

According to the calculated parameter, the turbulent parameters are calculated globally, or by box, from the Matrix of Lagrangian particles, then they are stored in matrices to be saved in files thereafter. These turbulent parameters can be said to be rapid and correspond to instantaneous spatial averages. Or be slow and be calculated by time averages over several time steps. These estimated parameters are not used in the reconstruction system but for posterior uses.

5.3. Other features and benefits

There is described, in relation to FIG. 3, a device for constructing representations implemented to manage the initialization and the updating of a representation of an atmosphere as a function of real observations, according to the method described previously.

For example, the representation construction device comprises a memory 31 comprising for example a buffer memory, a general processing processor 32, equipped for example with a microprocessor, and controlled by a computer program 33, these processing units putting implementing data processing methods as described above to update the representation as and when the measured data is taken into account.

On initialization, the code instructions of the computer program 33 are for example loaded into a memory 31 before being executed by the processing processor 32. The processing processor 32 receives as input at least one datum representative of a request to generate a virtual screen. The processing processor 32 implements the steps of the processing method, according to the instructions of the computer program 33 to update the representation.

For this, the representation construction device comprises, in addition to the memory 31, communication means, such as network communication modules, data transmission means and data transmission circuits between the various components of the construction device. representations and database management interfaces.

The means described above can take the form of a particular processor implemented within a specific device. According to a particular embodiment, the device for constructing and updating representations implements a particular application which is responsible for carrying out the operations described above, this application being for example provided by the manufacturer of the processor in question in order to allow the use of said processor.

Claims (4)

Method for constructing a three-dimensional representation of an atmosphere (REP ₁ ... REP _n ) evolving within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of sub-domains, called boxes, which include a plurality of particles representing the atmosphere in this sub-domain, a method characterized in that it comprises at least one iteration of an update phase (20) of a current representation (REP _T ) of particles evolving at within the atmospheric volume, this updating phase (20) comprising, for a current time step T: a prediction step (21), from the current representation (REP _T ), of the velocities and positions of the particles of each box of the atmospheric volume at a time step along T + l, delivering an intermediate representation (REPi _{T + 1} ) at time step T + l; a modification step (22) of the distribution of the particles in each box of the intermediate representation (REPi _{T + 1} ) delivering, a set of treated boxes (Bhn. ^ BhM); a filtering step (23) of particles from the treated boxes (Bhi, ..., Bh _M ) as a function of at least one datum representative of a real observation at time step T + l, delivering a following representation (REP _{T + 1} ) at time step T + l. Construction method according to claim 1, characterized in that it comprises, prior to said updating phase (20): a phase of obtaining and processing (05) raw data (RAW) coming from a measurement device (MEAS), phase which delivers standardized data (DAT); an initialization phase (10), during which representation parameters are selected and / or calculated, in particular using the normalized data (DAT) and other configuration data (PAR) and in which an initialization of the representation is performed, delivering an initial representation (REP ₀ ). Construction method according to claim 1, characterized in that the modification step (22) of the distribution of the particles in each box of the intermediate representation (REPi _{T + 1} ) comprises: a step of obtaining, for at least one box, from the speeds and positions of the particles of the boxes previously predicted, at least one datum representative of a density of particles, called the density field of the Lagrangian particles; from the speeds and positions of the particles in the previously predicted boxes, a step of redistribution of outgoing particles, in at least one box, as a function of the density field of the Lagrangian particles and of a density field modeled; a step of management, within each box, of the particles previously redistributed, according to at least one law of representation of particles associated with said boxes. Method according to claim 3, characterized in that the step of obtaining the density field of the Lagrangian particles comprises a step of calculating, for each box, a density of particles at the time step T + l as a function of speeds and of positions of the particles of the previously predicted boxes, delivering said so-called density field of Lagrangian particles. Method according to claim 3, characterized in that the step of redistribution of outgoing particles comprises, as a function of the density field of the Lagrangian particles and of the density field modeled: a step of calculating, for each box, a weight, delivering a set of box weights, each weight being the result of a difference between a reference density from the density field modeled and a corresponding density in the density field of Lagrangian particles; a step of random redistribution of outgoing particles, as a function of said set of weights of the boxes, delivering a reallocation matrix of outgoing particles; a step of random assignment, within the boxes, of each outgoing particle as a function of the outgoing particle reallocation matrix. Method according to claim 3, characterized in that the step of managing the previously redistributed particles comprises: a step of filling the boxes whose density is less than a reference density provided by the Eulerian field of modeled density, causing the creation of new particles; a step of sampling of particles, within boxes whose particle density exceeds a value determined from the Eulerian field of density modeled, delivering said set of treated boxes; Construction method according to claim 1, characterized in that the step of filtering (23) particles from the treated boxes (Bh ₁ , ..., Bh _M ) as a function of at least one datum representative of an actual observation at time step T + l includes: a step of calculating, for each particle of each box, a potential correlated with at least one current observation at time step T + l; when a box comprises only harmful potentials for all of its particles, a step of resetting the speeds of the particles as a function of a current observation at time step T + 1 of said box; and a selection step, for each particle of each box, as a function of the potential of each particle and of said at least one current observation at time step T + l, delivering an updated representation at time step T + l. Device for constructing a three-dimensional representation of an atmosphere (REP ₁ ... REP _N ) evolving within a predetermined atmospheric domain, the predetermined atmospheric domain being divided into a set of sub-domains, called boxes, which include a plurality of particles representing the atmosphere in this sub-domain, a device characterized in that it comprises means for updating (20) a current representation (REP _T ) of particles evolving within the atmospheric volume, for a current time step T, these updating means (20) comprising: predicting means (21), from the current representation (REP _T ) of velocities and positions of the particles of each box of the atmospheric volume at a time step along T + l, delivering an intermediate representation (REPi _{T + 1} ) at time step T + l; means for modifying (22) the distribution of the particles in each box of the intermediate representation (REPi _{T + 1} ) delivering, a set of treated boxes (Bhn. ^ BhM); means for filtering (23) particles from the treated boxes (Bh ^. ^ Bhivi) as a function of 5 minus a datum representative of a real observation at time step T + l, delivering a following representation (REP _{T + 1} ) at time step T + l. 9. Product computer program downloadable from a communication network and / or stored on a medium readable by computer and / or executable by a 10 microprocessor, characterized in that it comprises program code instructions for the execution of a construction method according to claim 1, within a device, when executed on a processor. MEAS 1/2