Navigation instrument with tilt compensation and associated method

A navigation instrument (4) comprising:

• a first sensor (6) configured to measure three components of a first vector, called first measured vector, of a first terrestrial force field (;
• ) in a reference frame (;
• ;
• ) linked to said navigation instrument, called on-board reference frame, and generate first output signals which are representative of said three components (g′x,mes, g′y,mes, g′z,mes;
• B′x,mes, B′y,mes, B′z,mes), the on-board reference frame defining a first reference axis of rotation and a second reference axis of rotation
• an orientation angle (φ, θ, ψ) calculation unit (8) of the navigation instrument, said calculation unit being connected to said first sensor (6) to receive said first output signals and being configured to determine a first orientation angle (φ) and a second orientation angle (e) of said on-board reference frame, and thus of the navigation instrument (4), with respect to a terrestrial reference frame (, , ) other than the on-board reference frame, said first and second orientation angles being defined by two successive rotations that the first measured vector must undergo, around the first reference axis of rotation for the first orientation angle and the second reference axis of rotation for the second orientation angle, to align said first measured vector with a calculation vector having, in the on-board reference frame, three calculation components which are identical to the three components, in the terrestrial reference frame, of a first reference vector (;
• ) which is predefined or predetermined in the terrestrial reference frame, wherein the terrestrial reference frame is linked to the earth;
• wherein the orientation angle calculation unit (8) is configured to determine the first and second orientation angles in a given order for said two successive rotations and also in reverse order;
• and wherein the calculation unit (8) is arranged to choose between said given order and said reverse order, to determine the first and second orientation angles, based on a comparison between a risk of error and a predetermined threshold, said risk of error quantifying a risk of instability of said calculation unit during the determination of the first and second orientation angles and being determined by the navigation instrument according to at least one of said first output signals, and
• wherein the navigation instrument is an electronic compass (4) which comprises an indicator (18) of magnetic North or geographic North and wherein the electronic compass (4) controls an angle of the indicator relative to the first reference axis of rotation, the angle depending on said first and second orientation angles.