This invention relates to a system for estimating the position, speed and orientation of a vehicle (10), comprising means for determining the components of two noncollinear constant unit vectors b, b according to vehicle body axes; means for determining the components of said noncollinear constant unit vectors {right arrow over (g)}t, {right arrow over (e)}t according to Earth's axes; means for determining the three components of angular velocity b of the vehicle in body axes; means for correcting said angular velocity b with a correction uω and obtaining a corrected angular velocity {circumflex over (ω)}b=b+uω; a control module (14) implementing a control law to calculate said correction uω, where said control law is:
uω=σ(b×ĝb+<?img id="custom-character-00007" he="3.13mm" wi="1.78mm" file="US20070213889A1-20070913-P00901.TIF" alt="custom character" img-content="character" img-format="tif" ?>b×êb) [1]
where σ is a positive scalar,
such that upon using said corrected angular velocity {circumflex over (ω)}b=b+uω as input to a module for integrating the kinematic equations, the latter are stable in the ISS sense and the error in the estimation of the direction cosine matrix {circumflex over (B)} and of the Euler angles {circumflex over (Φ)} is bounded.