Reivindicaciones
1. A system for obtaining spatial and temporal patterns of the velocity or a thermodynamic property of a fluid from scattered measurements, the system comprising: at least one sensor configured to acquire, for each time instant ti of a plurality Nt of time instances, a plurality Nc of scattered measurements (9) of a velocity or a thermodynamic property of a fluid (1) at scattered positions x ={xi1, xi2, ... , xiN C}; and a processing unit (10) configured to: determine, using the scattered measurements (9), an analytical approximation field ũ (x, ti) of the velocity or the thermodynamic property of the fluid (1) for each position x and time instant ti as a linear combination of a set of Nc radial basis functions, wherein the collocation points of the radial basis functions are set in the scattered positions {xi1, xi2, ..., xiN C} at the corresponding time instant ti; compute a temporal correlation matrix K, with dimension Nt × Nt, wherein each element Kij of the temporal correlation matrix K is computed as: K ij = 1 ‖ Ω ‖ ∫ Ω u ˜ x t i u ˜ x t j dΩ , <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0011" /> wherein Ω is the spatial domain where the scattered measurements (9) are acquired; decompose the temporal correlation matrix K via singular value decomposition, SVD; obtain the temporal modes ψi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the temporal modes ψi are the eigenvectors of the temporal correlation matrix K; and obtain the spatial modes ϕi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the ith spatial mode ϕi is computed as the inner product between the field ũ (x, ti) and the ith temporal mode ψi divided by σi, wherein σ i 2 <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0012" /> are the eigenvalues of the temporal correlation matrix K. 2. The system of claim 1, wherein the processing unit (10) is further configured to obtain the velocity or thermodynamic property of the fluid (1) at a position x and time instant ti using the temporal ψi and spatial ϕi modes of the proper orthogonal decomposition. 3. The system of any of claims 1 to 2, wherein the at least one sensor comprises a particle image velocimetry system (8) including a light source (5) and at least one camera (6). 4. The system of any of claims 1 to 2, wherein the at least one sensor comprises a plurality of sensor units (16) mounted on drones (13) scattered in the atmosphere (14). 5. The system of any of claims 1 to 2, wherein the at least one sensor comprises a plurality of sensor units mounted on buoys scattered at sea. 6. A method of obtaining spatial and temporal patterns of the velocity or a thermodynamic property of a fluid from scattered measurements, the method (100) comprising: acquiring (110), for each time instant ti of a plurality Nt of time instances, a plurality Nc of scattered measurements (9) of a velocity or a thermodynamic property of a fluid (1) at scattered positions x ={xi1, xi2, ... , xiN C}; determining (120), using the scattered measurements (9), an analytical approximation field ũ (x, ti) of the velocity or the thermodynamic property of the fluid (1) for each position x and time instant ti as a linear combination of a set of Nc radial basis functions, wherein the collocation points of the radial basis functions are set in the scattered positions {xi1, xi2, ... , xiN C} at the corresponding time instant ti; computing (130) a temporal correlation matrix K, with dimension Nt × Nt, wherein each element Kij of the temporal correlation matrix Kis computed as: K ij = 1 ‖ Ω ‖ ∫ Ω u ˜ x t i u ˜ x t j dΩ , <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0013" /> wherein Ω is the spatial domain where the scattered measurements (9) are acquired; decomposing (140) the temporal correlation matrix K via singular value decomposition, SVD; obtaining (150) the temporal modes ψi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the temporal modes ψi are the eigenvectors of the temporal correlation matrix K; and obtaining (160) the spatial modes ϕi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the ith spatial mode ϕi is computed as the inner product between the field ũ (x, ti) and the ith temporal mode ψi divided by σi, wherein σ i 2 <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0014" /> are the eigenvalues of the temporal correlation matrix K. 7. The method of claim 6, further comprising obtaining the velocity or thermodynamic property of the fluid (1) at a position x and time instant ti using the temporal ψi and spatial ϕi modes of the proper orthogonal decomposition. 8. The method of any of claims 6 to 7, wherein the scattered measurements (9) are acquired by a particle image velocimetry system (8). 9. The method of any of claims 6 to 7, wherein the scattered measurements (9) are acquired by a plurality of sensor units (16) mounted on drones (13) scattered in the atmosphere (12). 10. The method of any of claims 6 to 7, wherein the scattered measurements (9) are acquired by a plurality of sensor units mounted on buoys scattered at sea. 11. A non-transitory computer-readable medium for obtaining spatial and temporal patterns of the velocity or a thermodynamic property of a fluid from scattered measurements, comprising executable programming instructions stored thereon that, when executed by a processing unit (10), cause the processing unit (10) to: receive a plurality Nc of scattered measurements (9) of a velocity or a thermodynamic property of a fluid (1) at scattered positions x ={xi1, xi2, ... , xiN C} for each time instant ti of a plurality Nt of time instances; determine an analytical approximation field ũ (x, ti) of the velocity or the thermodynamic property of the fluid (1) for each position x and time instant ti as a linear combination of a set of Nc radial basis functions, wherein the collocation points of the radial basis functions are set in the scattered positions {xi1, xi2, ... , xiN C} at the corresponding time instant ti; compute a temporal correlation matrix K, with dimension Nt × Nt, wherein each element Kij of the temporal correlation matrix K is computed as: K ij = 1 ‖ Ω ‖ ∫ Ω u ˜ x t i u ˜ x t j dΩ , <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0015" /> wherein Ω is the spatial domain where the scattered measurements (9) are acquired; decompose the temporal correlation matrix K via singular value decomposition, SVD; obtain the temporal modes ψi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the temporal modes ψi are the eigenvectors of the temporal correlation matrix K; and obtain the spatial modes ϕi of the proper orthogonal decomposition of the velocity or thermodynamic property of the fluid (1), wherein the ith spatial mode ϕi is computed as the inner product between the field ũ (x, ti) and the ith temporal mode ψi divided by σi, wherein σ i 2 <img class="EMIRef" id="9613077c-6923-4c1f-a3c4-f590ed467b9b-ib0016" /> are the eigenvalues of the temporal correlation matrix K. 12. The non-transitory computer-readable medium of claim 11, further comprising executable programming instructions stored thereon that, when executed by the processing unit (10), cause the processing unit (10) to further obtain the velocity or thermodynamic property of the fluid (1) at a position x and time instant ti using the temporal ψi and spatial ϕi modes of the proper orthogonal decomposition.
