Patent ID: 11941079
Assignee: SAFRAN ELECTRONICS & DEFENSE
Field: Measurement (Instruments)
Classification: CPC G | IPC G

Claim 8:
9. The method according to claim 8, wherein the first variables comprise a rotation matrix representing an attitude of the first carrier, and the second variables comprise a rotation matrix representing the attitude of the second carrier relative to the first carrier, and wherein the invariant Kalman filter uses an innovation comprising a vector Zv with the form:

Zv=log(({circumflex over (R)}1TR2{circumflex over (R)}21, {circumflex over (R)}1T(v2−{circumflex over (v)}1)+{circumflex over (R)}1TR2(ω×{circumflex over (x)}21)))

where:
{circumflex over (R)}1 is an estimate of the rotation matrix representing an attitude of the first carrier.
{circumflex over (R)}21 is an estimate of the rotation matrix representing an attitude of the second carrier relative to the first carrier,
{circumflex over (x)}21 is an estimate of a translation vector defining the second rigid transformation,
R2 is the rotation matrix representing an attitude of the second carrier in the reference frame,
v2 is the velocity vector of the second carrier in the reference frame,
ω is the angular velocity of the first carrier,
× designates a vector product,
log(⋅) designates a logarithm map of the Lie group.