Method and system of geolocation by direct calculation of movement elements

A method for determining the position of one or more objects able to move in a network, one or more objects being provided with an ability to measure distance to the other objects of the network, at least some of the coordinates of an object are known, wherein it comprises at least the following steps:

• defining a set of points Ai or anchors and the uncertainties associated with their coordinates, the coordinates of the anchors and the uncertainty as to the coordinates describing information on the position of the objects and the uncertainty as to this information,
• generating a set containing the estimated positions of the objects and defining an initial position of the points,
• measuring a set of distances between at least two objects Mi, Mj, with associated uncertainties, and executing the following steps:
• Step 1, for each object Mi, calculate a displacement
• δ
• →
• →
• i
• =
• ∑
• j
• ∈
• R
• i
• 
• δ
• →
• j
• →
• i
• corresponding to the vector sum of the ranging or measurement displacements over the set of available ranging measurements toward the object Mi and induced on this object Mi by all of the other objects having a ranging measurement from said object Mi, due to the relative ranging measurement rij between Mi and Mj and its uncertainty σrij, with Ri={rij} all of the available ranging measurements toward Mi, and
• δ
• →
• ->
• i
• =
• ∑
• j
• ∈
• R
• i
• 
• δ
• →
• j
• →
• i
• 
• 
• where
• 
• 
• δ
• →
• j
• →
• i
• =
• ϕ
• 
• (
• Δ
• ij
• ,
• σ
• rij
• )
• 
• M
• j
• 
• M
• i
• →
• 
• M
• j
• 
• M
• i
• →
• 
• with Δij the coordinates of MjMi, φ is a given displacement function,
• Step 2, for each object Mi, having an anchoring coordinate in a virtual anchor associated with a fixed anchor Ai, calculate a return displacement value {right arrow over (a)}→i to this anchor, with {right arrow over (a)}→i=Ψ({right arrow over (AiMi)}+{right arrow over (δ)}→i,{right arrow over (σ)}Ai), Ψ a displacement function,
• Step 3, apply, to each object Mi, a displacement equal to the sum of the ranging displacement {right arrow over (δ)}→i and the anchoring correction {right arrow over (a)}→i that were calculated previously,
• Step 4, calculate the square of the error term Δtot2 where
• Δ
• i
• 2
• =
• ∑
• j
• ≠
• i
• 
• Δ
• ij
• 2
• with Δij=rij−d(Mi,Mj), A is an error term between an estimation of the distance d(Mi, Mj) after displacement of the object in step 3 and the distance measurement provided by ranging devices on all of the nodes, compare this quantity with a stopping criterion defined beforehand by an operator if Δtot2≤Δfin2, or else max(|Δij|)<Maxdeviation,
• if this test is met, go to step 6,
• if not, Step 5, test whether a maximum number of iterations has been reached,
• if l<lmax then iterate l=l+1 and go to step 1, if not go to step 6,
• Step 6, end of the iterations, define the position of the objects corresponding to the best estimation of the actual position of the objects obtained for each object.