Method and a system for determining the geometry and/or the localization of an object

Abstract

A method for determining the geometry and/or the localisation of an object comprising the steps of: sending one or more signals by using one transmitter; receiving by one or more receivers the transmitted signals and the echoes of the transmitted signals as reflected by one or more reflective surfaces building by a computing module a first Euclidean Distance Matrix (EDM) comprising the mutual positions of the receivers; adding to the EDM matrix a new row and a new column, the new row and a new column comprising time of arrivals of said echoes and computing its rank or distance to an EDM matrix determining the geometry and/or the position of the object based on said rank or distance.

1 . A method for determining the geometry and/or the position of an object, comprising the steps of
 sending one or more signals with one transmitter;   receiving by one or more receivers the transmitted signals and echoes of the transmitted signals reflected by one or more reflective surfaces;   building with a computing module a first Euclidean distance matrix corresponding to mutual positions of the receivers;   adding to said matrix a new row and a new column, the new row and a new column corresponding to the time of arrivals of at least some of said echoes, and computing the rank of the modified matrix, or computing the distance between the modified matrix from a true Euclidean Distance Matrix;   determining the geometry and/or the position of the object based on the computed information.   
     
     
         2 . The method of  claim 1 , wherein only first order echoes are considered. 
     
     
         3 . The method of  claim 1 , wherein only echoes received during a predetermined time window are considered. 
     
     
         4 . The method of  claim 1 , said object being a convex room, said transmitter being a loudspeaker, each receiver being a microphone, said geometry being a 2D geometry, the number of receivers being 3. 
     
     
         5 . The method of  claim 1 , said object being a convex room, said transmitter being a loudspeaker, each receiver being a microphone, said geometry being a 3D geometry, the number of receivers being higher than 4. 
     
     
         6 . The method of  claim 1 , said object being a receiver, said transmitter being a satellite, said receiver being a mobile device. 
     
     
         7 . The method of  claim 1 , comprising determining the geometry and/or the localisation of an object comprising the step of labelling echos. 
     
     
         8 . The method of  claim 1 , comprising determining which of the peaks of the impulse response received by each receiver correspond to which reflective surface. 
     
     
         9 . The method of  claim 1 , comprising verifying if the augmented matrix still verify the rank property according which a EDM in Rn has a rank at most n+2, n being an integer and positive number. 
     
     
         10 . The method of  claim 9 , comprising testing at least some echoes combination and selecting the combination for which the rank property is satisfied. 
     
     
         11 . The method of  claim 1 , comprising augmenting said EDM matrix by a vector t formed by the TOA from the transmitter to each receiver. 
     
     
         12 . The method of  claim 1 , comprising determining the location of the transmitter by using least-squared distance trilateration. 
     
     
         13 . The method of  claim 1 , comprising multi-dimensional scaling. 
     
     
         14 . The method of  claim 13 , comprising applying a s-stress criterion. 
     
     
         15 . A system for determining the geometry and/or the localisation of an object, comprising:
 a transmitter for sending one or more signals;   one or more receivers for receiving the transmitted signals and the echoes of the transmitted signals as reflected by one or more reflective surfaces;   a first computing module for building a first Euclidean Distance Matrix (EDM) corresponding to mutual positions of the receivers;   a second computing module for adding to the EDM a new row and a new column, the new row and a new column comprising time of arrivals of said echoes and computing its second rank or its distance from the first EDM;   a third computing module for determining the geometry and/or the position of the object based on said second rank or distance.   
     
     
         16 . The system of  claim 15 , the first, second and third modules being the same module. 
     
     
         17 . The system of  claim 15 , the transmitter being a loudspeaker, the receiver being a microphone, the object being a room comprising said loudspeaker and said microphone. 
     
     
         18 . The system of  claim 15 , the transmitter being a satellite, the receiver a mobile device, the object being said mobile device. 
     
     
         19 . A computer program product, comprising:
 a tangible computer usable medium including computer usable program code for determining the geometry and/or the localisation of an object, the computer usable program code being used for
 building a first Euclidean Distance Matrix (EDM) comprising the mutual positions of the receivers; 
 adding to the EDM a new row and a new column, the new row and a new column comprising time of arrivals of echoes of the signals transmitted by a transmitter as reflected by one or more reflective surfaces and received by one or more receivers and computing its rank or its distance to the first EDM; 
 determining the geometry and/or the position of the object based on said rank or distance.