Patent ID: 8868323

Claim:
A method for collaborative navigation between two or more platforms, the method comprising: establishing a communication link between a first platform having a first navigation filter and a second platform having a second navigation filter, the first navigation filter including a first state vector x 1 and a first covariance matrix P 1 , where: x 1 = [ a b ] ⁢ ⁢ P 1 = [ P a P ab P ba P b ] , the second navigation filter including a second state vector x 2 and a second covariance matrix P 2 , where: x 2 = [ a c ] ⁢ ⁢ P 2 = [ P a P ac P ca P c ] , wherein a, b, and c are state vector elements, with b and c being conditionally independent given a, wherein the first and second state vectors have at least one common state vector element (a), and the first and second covariance matrices have at least one common covariance matrix element (P a ); receiving at the first navigation filter an updated estimate of the common state vector element (a′) and an updated estimate of the common covariance matrix element (P′ a ) from the second navigation filter; replacing the state vector element a in the first navigation filter with the updated estimate of the common state vector element a′ from the second navigation filter; replacing the covariance matrix element P a in the first navigation filter with the updated estimate of the covariance matrix element P′ a from the second navigation filter; performing a conditional state update of the first navigation filter to produce an updated estimate of a state vector element b′, where: b′= b+ ( P ba ( P′ a ) −1 )( a′−a ); performing a conditional covariance update of the first navigation filter to produce an updated estimate of covariance matrix elements P′ b and P′ ba , where: P′ b =P b +( P ba ( P′ a ) −1 ) P ab , and P′ ba =P ba P a −1 P′ a .