System and global method for geolocation using imprecise distance and anchor position measurements

A method for determining a position of one or more objects Mi capable of moving in a network, the one or more objects being provided with an ability to measure distance to other objects of the network, each object comprising a communication means, wherein the method comprises at least the following steps:

• having coordinates of points Ai measured by at least a device for determining an absolute position of said coordinates of points and an uncertainty as to these coordinates, describing information on a position of all or some of the objects to be located, called anchored objects,
• measuring by a distance measurement device or ranging device at least one inter-object distance between at least one or more pairs of objects Mi, Mj, with an uncertainty value associated with each measurement, and executing by a processor the following steps:
• calculating an initial vector X representative of the estimated positions for nodes whose position is sought,
• calculating a criterion C(x) by using an observed measurement vector containing all inter-object distance measurements available for the objects having a position to be estimated and measured coordinates of objects said to be anchored, a covariance matrix representing statistical variation on the measurement vector and a theoretical measurement vector Mes(X) corresponding to the observed measurement vector , and
• minimizing this criterion C(x) and determining the coordinates of the position of one object or of said objects corresponding to this minimum, X=Arg Min[C(X)].