Navigation instrument with tilt compensation and corresponding method

Description

Technical field

[0001] The invention relates to a navigation instrument, in particular an electronic compass, with tilt compensation, a portable device comprising this instrument, in particular a wristwatch, an associated method for determining orientation angles of the navigation instrument, a program for implementing the method in question and a computer-readable recording medium for this program. Technological background

[0002] Electronic compasses are nowadays mainly equipped for tilt compensation. This methodology consists of measuring the Earth's magnetic field along two or three axes, and first compensating the attitude (roll and pitch) of the compass (acquired by an accelerometer and / or gyroscope) in order to estimate the equivalent heading, as if the compass had been held horizontally, according to what is advisable to do in practice. These techniques are generally called "tilt compensation" or 6-DOF. For example, patent application EP 1 669 718 A1 illustrates an electronic compass with a measurement of the magnetic field along two axes with correction for pitch and roll.

[0003] The objective of these techniques is to be able to estimate the pitch and roll angles of the watch (the yaw being defined by the measurement of the Earth's magnetic field). Generally, the roll angle is calculated first, and the pitch angle second. The main problem with this method is that when the pitch approaches 90°, there is an instability in the roll calculation since the projection of the gravity vector on the roll measurement plane has a norm close to zero. The measurement noise of the accelerometer thus generates aberrant results ("gimbal lock" English term meaning gimbal lock in French).

[0004] In the particular context of an electronic compass mounted in a watch, in the case where the user does not use his watch horizontally to know the direction of North or a heading, there is a good chance that he will apply a strong pitch (corresponding generally to a rotation of the wrist so that he can look at his dial while his corresponding arm is raised) rather than a strong roll (corresponding generally to the angle formed between the forearm and the horizontal) to the watch he wears on his wrist when he observes it. This causes an instability that is intolerable from the point of view of the product.

[0005] Solutions exist, such as those described in US patent document 2004 / 0187328 and by ST (www.st.com) in the "Design Tip" DT5008, where certain angles are forced to 90° when the standard on the calculation axes is close to zero. US patent document 2004 / 0187328 proposes to fix a default angle value to solve the gimbal lock problem. This arbitrary choice can lead to erroneous heading values.

[0006] US 2013 / 0185018 describes an apparatus and method for estimating a yaw angle of a device in a gravitational reference system and for determining parameters used to extract a corrected static magnetic field to obtain nearby dynamic fields, using measurements from a magnetic sensor and other motion sensors. In particular, parameters are determined, at least in part analytically, to be able to convert measurement signals detected by the magnetic sensor into a local magnetic field, in particular correcting for an offset of the magnetic sensor, the scale used, effects related to the presence of soft iron and / or hard iron, and alignment deviations. Summary of the invention

[0007] The invention aims to overcome at least one of the drawbacks of the aforementioned state of the art. More particularly, the invention aims to reduce the noise sensitivity of a navigation instrument. To this end, the present invention relates to a navigation instrument comprising: - A first sensor configured to measure three components of a first vector, called the first measured vector, of a first terrestrial force field in a reference frame linked to said navigation instrument, called the onboard reference frame, and to generate first output signals representative of said three components; - A unit for calculating orientation angles of the navigation instrument, this calculation unit being connected to said first sensor to receive said first output signals and being configured to be able to calculate a first orientation angle and a second orientation angle of the onboard reference frame, and thus of the navigation instrument,with respect to a terrestrial reference frame, these first and second orientation angles being defined by two successive rotations that the first measured vector must undergo, around a first reference rotation axis (also called first reference axis) of the onboard reference frame for the first orientation angle and a second reference rotation axis (also called second reference axis) of the onboard reference frame for the second orientation angle, to align this first measured vector with a calculation vector having, in the onboard reference frame, three calculation components which are identical to three reference components, in the terrestrial reference frame,of a first reference vector which is predefined or predetermined in the terrestrial reference frame. This navigation instrument is remarkable in that the orientation angle calculation unit is configured to be able to determine the first and second orientation angles according to a given order of said two successive rotations and also according to a reverse order; and in that the calculation unit is arranged to be able to choose between said given order and said reverse order, to calculate the first and second orientation angles, according to a comparison between an indicator of a risk of error, quantifying a risk of instability of the calculation unit during the determination of the first and second orientation angles, and a predetermined threshold, said indicator of the risk of error being determined by the navigation instrument according to at least two of said first output signals.,

[0008] According to advantageous embodiments of the invention, the navigation instrument comprises one or more of the following technical characteristics, in all possible combinations: The error risk indicator is the norm of the projection of the first measured vector in a plane perpendicular to the first reference rotation axis; and the orientation angle calculation unit is configured to firstly determine the first orientation angle, by performing among said two successive rotations firstly the rotation of the first measured vector around the first reference rotation axis, when the error risk indicator is greater than said predetermined threshold. The value of the predetermined threshold is between 0.15 and 0.45 of the norm of the first measured vector, preferably between 0.20 and 0.30 of this norm.Alternatively, the error risk indicator is the absolute value of the second orientation angle when the first orientation angle is calculated before the second orientation angle; and the orientation angle calculation unit is configured to determine again the first and second orientation angles by firstly calculating the second orientation angle, by firstly performing among said two successive rotations the rotation of the first measured vector around the second reference rotation axis, when the error risk indicator is greater than the predetermined threshold, the calculation unit then retaining the values ​​of the first and second orientation angles determined again for these first and second orientation angles. In the previous alternative, the value of the predetermined threshold is between 65° and 80°, preferably between 70° and 75°.A predefined axis of the Earth reference frame is aligned with the first reference vector, preferably this first reference vector being aligned with a vertical axis. 1 z ⇀ of the Earth's reference frame. The first reference rotation axis corresponds to an axis 1 x ′ ⇀ in the embedded reference frame and the second reference rotation axis corresponds to an axis 1 y ′ ⇀ in the onboard reference frame, these first and second reference rotation axes being perpendicular. The navigation instrument comprises a second sensor configured to measure the three components of a second vector, called the second measured vector, of a second terrestrial force field in the onboard reference frame, this second measured vector being non-collinear with the first measured vector, and to generate second output signals representative of these three components; the navigation instrument further comprising a unit for determining a third orientation angle of this instrument relative to the terrestrial reference frame, this determination unit being connected to the second sensor to receive the second output signals and being configured to determine the third orientation angle from the calculated first and second orientation angles and the second measured vector.The calculation unit and the unit for determining the third orientation angle are formed by a single electronic unit which itself forms a central processing unit. The third orientation angle is defined by a rotation that the second measured vector must undergo, after having been reoriented in the onboard reference frame by applying to this second measured vector the first and second successive rotations, around a third reference rotation axis (also called third reference axis), perpendicular to the first and second reference rotation axes (and therefore corresponding to an axis . 1 z ′ ⇀ in the onboard reference frame), so that this second measured and reoriented vector, called the second reoriented vector, is located in a first reference plane of the onboard reference frame comprising the first and third reference rotation axes. The third orientation angle is determined by firstly applying to the second measured vector the first and second successive rotations, preferably in the order chosen between said given order and said inverse order to define the first and second orientation angles, so as to obtain the second reoriented vector, then by calculating the angle between a projection, in a second reference plane comprising the first and second reference axes, of the second reoriented vector and the first reference axis. The third orientation angle is considered as a heading of this instrument. The first measured vector is a vector of the Earth's gravitational force field.The first measured vector is determined by means of an accelerometer forming the first sensor. The second measured vector is a vector of the Earth's magnetic field, this second measured vector being determined by means of a magnetic sensor forming the second sensor. Alternatively, the first measured vector is a vector of the Earth's magnetic field, the first measured vector being determined by means of a magnetic sensor forming the first sensor. In the previous alternative, said three reference components are predetermined from data coming from a location device of the navigation instrument, in particular of the GPS type. In the aforementioned alternative, the second measured vector is a vector of the Earth's gravitational force field; the second measured vector being determined by means of an accelerometer which forms the second sensor.The navigation instrument is an electronic compass which comprises a magnetic North or geographic North indicator and a device for controlling this indicator, which are arranged to control the indicator so that it has an angle relative to the first reference axis which is equal to the opposite of the third orientation angle, preferably corrected for the deviation of the Earth's magnetic field at the location where the navigation instrument is located for the indication of magnetic North and, for the indication of geographic North, in addition to the declination of the Earth's magnetic field.The navigation instrument comprises a data display means indicating the true heading, said calculation unit being configured to calculate the true heading as a function of said heading, a first parameter quantifying the declination of the Earth's magnetic field and a second parameter quantifying the deviation of the Earth's magnetic field at the location where the navigation instrument is located.

[0009] The invention also relates to a portable device provided with the navigation instrument. Advantageously, the portable device according to the invention, in particular a wristwatch, is remarkable in that this device is portable on the wrist of a user; and in that the first reference axis corresponds to the 6-12 o'clock axis and the second reference axis corresponds to the 9-3 o'clock axis (according to a conventional analog display of the time in a watch, the 6-12 o'clock axis being aligned with the longitudinal axis of the watch strap).

[0010] The invention also relates to a method for determining orientation angles, including at least a first and a second orientation angle, of a navigation instrument relative to a terrestrial reference frame, this method comprising the following steps: acquisition of the three components of a first vector, called the first measured vector, of a first terrestrial force field in a reference frame linked to said navigation instrument, called the on-board reference frame; determination of the first and second orientation angles of the on-board reference frame relative to the terrestrial reference frame, these first and second orientation angles being defined by two successive rotations of the first measured vector, around a first reference rotation axis of the onboard reference frame for the first orientation angle and a second reference rotation axis of the onboard reference frame for the second orientation angle, making it possible to align the first measured vector with a calculation vector having, in the onboard reference frame, three calculation components which are identical to three reference components, in the terrestrial reference frame, of a first reference vector which is predefined or predetermined in the terrestrial reference frame; determining the first and second orientation angles comprising a step of choosing between a given order for the two successive rotations and an inverse order; the choice between said given order and said inverse order, for calculating the first and second orientation angles, being based on a comparison between an indicator of a risk of error, quantifying a risk of instability during the determination of the first and second orientation angles, and a predetermined threshold, the indicator of the risk of error being determined based on at least two of said components of the first measured vector.

[0011] According to advantageous embodiments of the invention, the method for determining orientation angles comprises one or more of the following characteristics and / or steps, in all possible combinations: The error risk indicator is the norm of the projection of the first measured vector in a plane perpendicular to the first reference rotation axis, and the first orientation angle is calculated by performing, among said two successive rotations, firstly the rotation of the first measured vector around the first reference rotation axis when the error risk indicator is greater than said predetermined threshold. The value of the predetermined threshold is between 0.15 and 0.45 of the norm of the first measured vector, preferably between 0.20 and 0.30 of this norm.Alternatively, the error risk indicator is the absolute angular value of the second orientation angle when the first orientation angle is calculated, according to said given order, before the second orientation angle, and the second orientation angle is calculated by performing, among said two successive rotations, firstly the rotation of the first measured vector around the second reference rotation axis when the error risk indicator is greater than said predetermined threshold. In the previous alternative, the value of the predetermined threshold is between 65° and 80°, preferably between 70° and 75°. A predefined axis of the terrestrial reference frame is aligned with the first reference vector, preferably this first reference vector being aligned with a vertical axis. 1 z ⇀ of the Earth's reference frame. The first orientation angle and the second orientation angle are respectively a roll angle and a pitch angle, the roll angle being associated with a rotation around the first reference axis, corresponding to the axis 1 x ′ ⇀ in the on-board reference frame when the roll angle is determined first, and the pitch angle being associated with a rotation around the second reference axis, corresponding to the axis 1 y ′ ⇀ in the on-board reference frame when the pitch angle is determined first. The method further comprises a step of acquiring three components of a second vector, called the second measured vector, of a second terrestrial force field in the on-board reference frame, and a step of determining a third orientation angle from the calculated first and second orientation angles and the three components of the second measured vector.The third orientation angle is determined by firstly applying to the second measured vector said first and second successive rotations, preferably in the order chosen between said given order and said inverse order, to obtain a second measured and reoriented vector, called second reoriented vector, in the onboard reference frame, then by defining the third orientation angle as the angle between a projection of the second reoriented vector, in a reference plane comprising the first and second reference axes, and the first reference axis. The third orientation angle is a yaw angle of this instrument, this yaw angle being defined by a rotation of the navigation instrument around a third reference rotation axis, corresponding to a vertical axis. 1 z ⇀ in the Earth's reference frame, after roll and pitch corrections. The third orientation angle is considered a heading of the navigation instrument. The first measured vector is a vector of the Earth's gravitational force field, which is measured using an accelerometer. The second vector of a second Earth's force field is a vector of the Earth's magnetic field, which is measured using a magnetic sensor. Alternatively, the first measured vector is a vector of the Earth's magnetic field, the first measured vector being determined using a magnetic sensor. In the previous alternative, the second vector of a second Earth's force field is a vector of the Earth's gravitational force field, the second measured vector being determined using an accelerometer.In the aforementioned alternative, the three reference components are determined from data originating from a location device of the navigation instrument, in particular of the GPS type. The navigation instrument is an electronic compass. The navigation instrument comprises a means for displaying data indicating the true heading; and the method further comprises a step of determining the true heading as a function of said heading determined in one of the preceding steps, of a first parameter quantifying the declination and of a second parameter quantifying the deviation of the Earth's magnetic field at the location where the navigation instrument is located. The navigation instrument is configured to be mounted on or integrated into a portable device.The wearable device, in particular a wristwatch, is wearable on a user's wrist, the first reference axis corresponding to the 6-12 o'clock axis of a conventional analog time display by a watch and the second reference axis corresponding to the 9-3 o'clock axis.

[0012] The invention also relates to a program comprising instructions which, when the program is executed by a computer, cause this computer to implement the steps of the method according to the invention.

[0013] The invention further relates to a computer-readable recording medium comprising instructions which, when executed by a computer, cause the latter to implement the steps of the method according to the invention.

[0014] The measurements of the invention are advantageous because, from a mathematical point of view, the approach remains the same regardless of the angle calculated first. However, the result gives a heading that can be very different, depending on whether the two successive rotations are performed in the given order or in the reverse order, particularly in the case where the two angles are large (typically if the roll and pitch are equal to 45°). However, we know that for reasons of comfort, the user will generally use the watch with a roll close to 0° and a pitch that can vary greatly, particularly between -30° and 70°. Under these conditions, the heading measured by our proposal no longer suffers from the gimbal locking effect. In addition, the method makes it possible to determine the uncertainty associated with a measurement and guarantees numerical stability.Finally, the measurements of the invention are more precise than those obtained by the devices or systems in the prior art, since even when the pitch is close to 90°, an estimation of this angle is made. In the state of the art, in the same situation, at best a default value is assigned to the pitch. Brève description des figures

[0015] The invention will be described below in more detail with the aid of the appended drawings, given as non-limiting examples, in which: There Figure 1 represents a wristwatch in which a navigation instrument, in particular an electronic compass, is mounted, this Figure 1 including a front view of the wristwatch on the left and a simplified perspective view of this watch on the right; The Figure 2 illustrates an on-board reference frame linked to the wristwatch and a terrestrial reference frame; The Figure 3shows a succession of three rotations that a terrestrial reference frame should undergo in order for it to coincide with the on-board reference frame of a navigation instrument; The Figure 4a illustrates a projection of a vector of the Earth's gravitational field into a plane perpendicular to the axis 1 x ′ ⇀ of the on-board reference frame, defining a roll angle; The Figure 4b shows a first rotation and a second rotation of the vector of the Earth's gravitational field so as to make it coincide with a calculation vector whose components are proportional to those of the Earth's gravitational field in the Earth's reference frame; The Figure 5 includes two graphs illustrating the effect of measurement noise on the roll angle calculation; The Figure 6 shows an arbitration zone between the given order and the reverse order for two successive rotations relating to the roll and pitch of the navigation instrument; The Figures 7a to 7crepresent a series of graphs comparing heading values ​​versus pitch values ​​for various given roll angles with the given order and reverse order for both roll and pitch related rotations; and The Figure 8 schematically represents a portable object of the electronic type incorporating an electronic compass according to the invention. Detailed description of the invention

[0016] There Figure 1 represents a first embodiment of the invention in which the navigation instrument 4 (shown in the Fig.8 ) is an electronic compass incorporated in a wristwatch 2 which is shown in front view on the left and in perspective on the right (schematic representation without the bracelet which will be repeated in the other figures). The navigation instrument comprises a unit 8 for calculating orientation angles of the wristwatch which is incorporated in or formed by a central electronic unit (see Fig.8). A reference 1 x ′ ⇀ ; 1 y ′ ⇀ ; 1 z ′ ⇀ linked to the navigation instrument is represented in the Fig.1 . This reference frame is also called the onboard reference frame. Even if the onboard reference frame is linked to the navigation instrument, it can be defined with characteristics of the wristwatch 2 in which the navigation instrument is rigidly fixed. Consequently, advantageously, the onboard reference frame can therefore be defined with the axis 1 x ′ ⇀ and the axis 1 y ′ ⇀ aligned in sense and direction with the 6 o'clock-12 o'clock axis and the 9 o'clock-3 o'clock axis of the wristwatch 2, defining the general plane of the digital display or the analog display (namely of the main dial) of this wristwatch 2. The axis 1 z ′ ⇀ is chosen so as to be perpendicular and preferably dextrorotatory with respect to the axes 1 x ′ ⇀ 1 y ′ ⇀ and it is therefore directed towards the bottom of the wristwatch from the said general plane of the display.

[0017] The on-board reference frame makes it possible to determine the orientation of the navigation instrument relative to a predefined terrestrial reference frame as illustrated in Figure 2 . This orientation of the wristwatch 2 can vary significantly when the watch is worn by a user and the latter changes the position of the wrist on which he wears this wristwatch. It will be noted that the choice of an on-board reference frame 1 x ′ ⇀ ; 1 y ′ ⇀ ; 1 z ′ ⇀ just like that of a terrestrial reference frame 1 x ⇀ ; 1 y ⇀ ; 1 z ⇀ is arbitrary. This choice is essentially linked to usage conventions and / or the intended use of the navigation instrument. For example, the terrestrial reference frame is defined with an axis 1 z ⇀ oriented in the vertical direction from top to bottom (according to the NED orientation, acronym for North East Down in English), so that the axis 1 z ⇀ is aligned in sense and direction with the local gravity field (at the level of the navigation instrument). The local gravity field is characterized by a reference vector of the Earth's gravitational field, represented by the vector g ref ⇀ . The axis 1 x ⇀ of the frame of reference is oriented according to the direction of the magnetic or geographic north pole, as illustrated in Figure 2 . Preferably, the axis 1 x ⇀ results from the projection of a vector of the Earth's reference magnetic field into a plane perpendicular to the vector g ref ⇀ , the vector of the Earth's magnetic field pointing towards magnetic north, said vector being represented by the vector B ref ⇀ . In most inhabited regions on the surface of the Earth, the vector B ref ⇀ is substantially perpendicular to the vector g ref ⇀ and therefore the axis 1 x ⇀ is substantially collinear with the vector B ref ⇀ The third axis 1 y ⇀ is defined to be perpendicular and dextrorotatory to the axes 1 x ⇀ And 1 z ⇀ . The definition of the reference frame is not limited to the above-mentioned example. For example, the axis 1 x ⇀ could have been aligned with the vector B ref ⇀ and the axis 1 z ⇀ could have been obtained from the projection of the vector g ref ⇀ in a plane perpendicular to the axis 1 x ⇀ . The orientation of the axis 1 z ⇀ could also have been from bottom to top.

[0018] The orientation of the on-board reference frame relative to the terrestrial reference frame can be defined by a succession of three rotations defined by three orientation angles characterizing the movement that the terrestrial reference frame should undergo so that it merges with the on-board reference frame, as illustrated in Figure 3 .

[0019] As is known, the orientation of the on-board reference frame relative to the terrestrial reference frame is defined by three reference angles called yaw - pitch - roll. These angles are commonly used, particularly in aeronautics. The invention is however not limited to this choice of angles because there are other conventions such as Euler angles which are used in other technical fields in which the present invention is also applicable.

[0020] The first rotation, called yaw, is carried out around the axis 1 z ⇀ with an amplitude ψ. This first rotation makes it possible to determine the amplitude of the yaw movement of the wristwatch 2 (and consequently of the navigation instrument, in particular of the electronic compass). This amplitude also corresponds to the heading of the wristwatch 2 and therefore of the electronic compass. In a particular case where the wristwatch 2 is positioned so that the plane of the display of the wristwatch 2 is perpendicular to the field g ref ⇀ and therefore to the axis 1 z ⇀ , the yaw rotation directly indicates the heading of the navigation instrument. Indeed, the determination of the heading of the navigation instrument, and therefore of the wristwatch 2, is carried out by comparing the orientation of the actual wristwatch 2 with a fictitious positioning in which the 6 o'clock-12 o'clock axis of the wristwatch 2 would be aligned with the axis 1 x ⇀ , implying that the 6h-12h axis is aligned with the Earth's magnetic field vector B ref ⇀ The determination of the yaw angle and therefore of the heading is advantageously carried out from trigonometric calculations on the coordinates of a vector of the measured Earth's magnetic field. B ′ mes ⇀ These coordinates are determined by means of a magnetic sensor 10 arranged in the electronic compass 4 (see Fig.8 ). The coordinates B x , mes ′ , B y , mes ′ , B s , mes ′ of the Earth's magnetic field vector B ′ mes ⇀ are expressed in the embedded reference frame / reference system.

[0021] The second rotation, called pitching, takes place around the axis 1 y ∗ ⇀ of the reference frame obtained after the yaw rotation. The axis 1 y ∗ ⇀ corresponds to the axis 1 y ⇀ of the terrestrial reference frame having undergone the yaw rotation. The amplitude of the pitch is symbolized by the Greek letter θ. In the context of using a wristwatch 2, the pitch is generally similar to the rotational movement of the forearm that a person makes to look at the time on the display of the wristwatch 2 that he is wearing.

[0022] The third rotation, called rolling, takes place around the axis 1 x ∗ ⇀ , which corresponds to the axis 1 x ⇀ in the on-board frame of reference. The amplitude of the roll is symbolized by the Greek letter φ. When using a wristwatch 2, the roll generally resembles the rotational movement of the forearm relative to the horizontal.

[0023] The determination of the two roll and pitch angles can be carried out by comparing the position of the wristwatch 2 worn by the user to a virtual position in which the plane of the display of the wristwatch 2 would be flat (i.e. horizontal) and therefore perpendicular to the vertical axis 1 z ⇀ . To determine these two angles, the electronic compass has a sensor 6 (see Fig.8 ) which allows the measurement of the vector of the Earth's gravitational field in the on-board frame (linked to the watch), represented by g ′ mes ⇀ . Based on the measurement of components g x , mes ′ , g y , mes ′ , g z , mes ′ of the vector g ′ mes ⇀ in the on-board reference system of the wristwatch 2 to which the magnetic compass 4 is rigidly fixed, the pitch and roll angles can be easily deduced from trigonometric calculations, as explained below.

[0024] With the knowledge of the amplitudes of the three rotations described above it is possible, as illustrated in Figure 3 , to bring virtually for example a wristwatch 2 from an initial virtual position in which it occupies a reference position in the terrestrial frame of reference to a final real position, when it is worn by the user. In the initial virtual position, the 6 o'clock-12 o'clock axis of the wristwatch 2 is aligned with the axis 1 x ⇀ and the general plane of the display (formed by the 6h-12h axis and the 9h-3h axis) is perpendicular to the vertical axis 1 z ⇀ . As previously stated, the yaw angle determined during the first rotation determines the heading of wristwatch 2. The second and third rotation angles determine the pitch angle and roll angle of the wristwatch.

[0025] The on-board reference frame relative to the terrestrial reference frame can therefore be defined by a reference frame transformation to describe a "solid" movement, in which the 3 orientation angles, namely yaw, pitch and roll, together define the angular displacements of the axes of the terrestrial reference frame ( 1 x ⇀ ; 1 y ⇀ ; 1 z ⇀ ) so as to make them coincide with the corresponding axes of the on-board reference frame ( 1 x ′ ⇀ ; 1 y ′ ⇀ ; 1 z ′ ⇀ ). This transformation of reference frame corresponds, for a point (x, y, z) in the terrestrial reference frame, to a change of coordinates which is expressed by the matrix product given in equation 1 below, this equation 1 providing the coordinates (x', y', z') of this point in the on-board reference frame. x ′ y ′ z ′ = R φ − 1 ⋅ R θ − 1 ⋅ R ψ − 1 x y z with R φ = 1 0 0 0 cos φ − sin φ 0 sin φ cos φ et R φ − 1 = R φ T R θ = cos θ 0 sin θ 0 1 0 − sin θ 0 cos θ et R θ − 1 = R θ T R ψ = cos ψ − sin ψ 0 sin ψ cos ψ 0 0 0 1 et R ψ − 1 = R ψ T Or RϕT< , R θ T< , R ψ T< are the transposed matrices of Rϕ , R θ And R ψ .

[0026] Since the electronic compass is incorporated in the wristwatch and, for this electronic compass, only the onboard reference frame is initially defined and known, and since the planned method consists of virtually bringing the onboard reference frame into coincidence with the terrestrial reference frame to determine the orientation angles of the portable device that is the wristwatch, in particular a heading of this portable device, we are then interested in the inverse reference frame transformation to that described above. Starting from a vector or several vectors having coordinates (x', y', z') in the onboard reference frame (the vectors having their origin at the point (0,0,0) in the onboard reference frame and also in the terrestrial reference frame), we seek to determine the coordinates (x, y, z) of this or these vector(s) in the terrestrial reference frame.Based on equation 1 given previously, the mathematical relationship, in matrix form, between a vector (x', y', z') expressed in the onboard reference frame and this same vector (x, y, z) expressed in the terrestrial reference frame is given by equation 2 below. This property will be used in the remainder of the description of the invention for calculating the orientation angles of the portable device incorporating the electronic compass. The matrix relationship of equation 2 defines a transition matrix allowing, for a point or a vector, to pass from the onboard reference frame to the terrestrial reference frame (i.e. for the expression of its coordinates). x y z = R ψ ⋅ R θ ⋅ R φ x ′ y ′ z ′

[0027] Since the coordinates of a point can define the end of a vector whose origin coincides with the common origin of the on-board and terrestrial reference frames, as indicated previously, equation 2 thus makes it possible to establish a relationship between the measured vector g ′ mes ⇀ defined in the embedded reference and the same vector g mes ⇀ defined in the Earth reference frame. This relationship is as follows: g x , mes g y , mes g z , mes = R ψ ⋅ R θ ⋅ R φ g x , mes ′ g y , mes ′ g z , mes ′

[0028] Also, the relationship between the measured vector B ′ mes ⇀ defined in the embedded reference and the same vector B mes ⇀ defined in the terrestrial reference system is as follows: B x , mes B y , mes B z , mes = R ψ ⋅ R θ ⋅ R φ B x , mes ′ B y , mes ′ B z , mes ′

[0029] However, the calculation of orientation angles starts from the assumption that the measured vectors g ′ mes ⇀ , B ′ mes ⇀ in the embedded reference frame are collinear with reference vectors g ref ⇀ , B ref ⇀ which correspond to them and whose components in the terrestrial reference frame are predefined or predetermined. Thanks to equations 3 and 4, it is possible to determine the components of each of the measured vectors g ′ mes ⇀ , B ′ mes ⇀ in the Earth reference frame, as follows: g x , ref g x , ref g z , ref = k 1 ⋅ g x , mes g x , mes g z , mes = k 1 ⋅ R ψ ⋅ R θ ⋅ R φ g x , mes ′ g y , mes ′ g z , mes ′ B x , ref B y , ref B z , ref = k 2 ⋅ B x , mes B y , mes B z , mes = k 2 ⋅ R ψ ⋅ R θ ⋅ R φ B x , mes ′ B y , mes ′ B z , mes ′

[0030] It is therefore possible to calculate the orientation angles by solving equations 5a and 5b. However, this approach to finding the orientation angles is far from being advantageous in all circumstances, because there may be singular solutions (e.g. gimbal lock). For this reason, according to the invention, a more sophisticated approach has been developed, as explained below.

[0031] In the case of a passage from the on-board reference frame (that of the measurement) to the terrestrial reference frame (that of the reference vectors whose expression is at least partially known in this terrestrial reference frame) for a measured point or vector, we observe in equation 2 that the succession of reference rotations is: first the roll (angle ϕ), then the pitch (angle θ) and finally the yaw (angle ψ). Preferably, the roll and pitch angles are determined, in a first step, on the basis of the measurement of a vector of the gravitational field g ′ mes ⇀ (having a norm g), this first step being followed by the determination of the yaw and therefore of the heading during a second step, the calculation of the yaw being based on the measurement of a vector of the Earth's magnetic field B ′ mes ⇀ .

[0032] The first step is therefore to determine the roll and pitch angles from equation 5a. The choice of an appropriate terrestrial reference frame with a gravitational field vector aligned with the vertical axis 1 z ⇀ allows for simplifying calculations and better anticipating a risk of dial blocking, as explained in the equations below. g ref ⇀ = k ⋅ R ψ ⋅ R θ ⋅ R φ ⋅ g mes ′ ⇀ with g ref ⇀ = 0 0 g z , ref = 0 0 g z et g mes ′ ⇀ = g x , mes ′ g y , mes ′ g z , mes ′ = g x ′ g y ′ g z ′

[0033] Equation 5a can be rewritten and simplified as follows: R ψ − 1 ⋅ g ref ⇀ = R ψ T ⋅ g ref ⇀ = g ref ⇀ = k ⋅ R θ ⋅ R φ ⋅ g mes ′ ⇀

[0034] And so: cos ψ sin ψ 0 − sin ψ cos ψ 0 0 0 1 ⋅ 0 0 g z = 0 0 g z = k ⋅ cos θ 0 sin θ 0 1 0 − sin θ 0 cos θ ⋅ 1 0 0 0 cos φ − sin φ 0 sin φ cos φ ⋅ g x ′ g y ′ g z ′

[0035] The roll angle resulting from equation 5a, in the case of a first measured vector which is collinear with a first vertical reference vector, is given by the following trigonometric relationship: φ = arctan g ′ y / g ′ z

[0036] The pitch angle is then given by: θ = − arctan g ′ x / g ∗ z with g ∗ z = g ′ y ⋅ sin φ + g ′ z ⋅ cos φ

[0037] Advantageously, it follows from equation 6 that the roll angle ϕcorresponds to the angle between the projection of the Earth's gravitational field vector g mes ′ ⇀ in the reference plane Y'- Z' (perpendicular to the axis 1 x ′ ⇀ ) and the axis 1 z ′ ⇀ , as illustrated in Figure 4a .

[0038] Then it follows from equation 7 that the pitch angle i corresponds to the angle between a work vector, resulting from the rotation of the Earth's gravitational field vector g mes ′ ⇀ in the reference plane X' - Z' (perpendicular to the axis 1 y ′ ⇀ ) and the axis 1 z ′ ⇀ , as illustrated in Figure 4b .

[0039] There Figure 4b illustrates that the roll and pitch angles are defined by two successive rotations that the measured Earth's gravitational force field vector should undergo g ′ mes ⇀ , first around the axis 1 x ′ ⇀ for roll rotation and then around the axis 1 y ′ ⇀ for pitch rotation, to align this measured vector with the axis 1 z ′ ⇀ .

[0040] The vector of the gravitational field measured in the onboard frame g ′ ref ⇀ can be determined by an accelerometer that provides output signals representative of the three components of this vector. However, it has been observed that the three signals corresponding to the three components each present noise whose amplitude is not negligible and can strongly disturb the measurement of the orientation angles if no suitable measures are taken. It will be noted that, for each of the three components of the measured vector, the noise is a random effect not depending on the amplitude of the measurement signal. The noise is therefore problematic when calculating the attitude of the portable device. Indeed, the calculation of the roll angle is done on a projection, and therefore potentially on a vector of low amplitude. As the noise is statistically invariant on each measurement axis, the uncertainty in the measurement increases when the amplitude of the measured and projected vector decreases. In the example presented in Fig. 5where the roll rotation is performed before the pitch rotation, we observe in the Y'- Z' plane (defined by the axes / vectors 1 y ′ ⇀ And 1 z ′ ⇀ of the on-board reference) that the noise generates a much larger error on the roll angle when the standard is low (see the image on the right relative to the image on the left).

[0041] Mathematically, problems arise when we are close to a case of gimbal lock, which occurs when the roll rotation axis becomes substantially collinear with the pitch rotation axis. Note that the roll value has a direct impact on the calculated yaw value. We realize that if the calculated roll value is unstable, the yaw value and therefore the heading indicated by a needle or other display will also be unstable.

[0042] According to the invention, the order of the calculation of the orientation angles can be reversed in order to avoid this instability which appears when the projection of the measured vector in the Y'- Z' plane is too small. Thanks to this measurement, the norm of the projection of the measured vector g ′ mes ⇀ in the X'- Z' plane (defined by the axes / vectors 1 x ′ ⇀ And 1 z ′ ⇀ of the onboard reference frame), used to calculate the pitch angle θ, then remains within an acceptable range. This phenomenon is explained because, as the acceleration is of constant norm, if its projection is of low norm in one plane, it is necessarily large in the other perpendicular planes.

[0043] The order of calculation of the roll and pitch angles is therefore either in a given order or in a reverse order. The given order first involves a roll rotation followed by a pitch rotation. For the reverse order, an inversion of the given order is provided with a pitch rotation which is calculated first and then a roll rotation. It will also be noted that these rotations applied to a vector measured in the on-board reference frame correspond to a correction of the roll and pitch presented by the portable device incorporating or equipped with the electronic compass according to the invention and therefore to rotations in the opposite direction ( -ϕ ; - i ) of the embedded reference frame, so that this embedded reference frame is virtually reoriented with its axis 1 z ′ ⇀ collinear to the vertical axis / vector 1 z ⇀ of the terrestrial reference.

[0044] For the above-mentioned order, the roll and pitch angles are determined by the equations 6 and 7 given previously. For the reverse order, the simplified equation 5a is replaced by the following equation 5c: R ψ − 1 ⋅ g ref ⇀ = R ψ T ⋅ g ref ⇀ = g ref ⇀ = k ⋅ R φ ⋅ R θ ⋅ g mes ′ ⇀

[0045] The pitch angle resulting from equation 5c, in the case of a first measured vector which is collinear with a first vertical reference vector, is given by the following trigonometric relationship: θ = − arctan g ′ x / g ′ z

[0046] The roll angle is then given by: φ = arctan g ′ y − g ′ x ⋅ sin θ + g ′ z ⋅ cos θ

[0047] It should be noted that, in general, Rϕ · R θ is not equal to R θ · Rϕ , so that the inversion of the two successive rotations considered has an influence on the yaw value subsequently calculated to obtain a heading for wristwatch 2. We will come back to this later.

[0048] The choice of the order of calculation of the roll and pitch angles can be based on different criteria. For example, a first criterion exploits the norm (or the square of the norm) of the projection of the vector g ′ mes ⇀ in the Y'- Z' plane. If this standard is less than a given value, the order of calculation of the angles is reversed (calculation of the pitch first, then the roll). Alternatively, a second proposed criterion concerns the value of the pitch angle when this value is determined according to the given order (calculation of the roll first, then the pitch). If it turns out that the pitch is greater than a given angle, the calculation of the two angles considered here is carried out a second time with the pitch which is calculated first.

[0049] The first criterion, called basic, aims to ensure that the limit of the standard projected onto the Y'- Z' plane (defined by the axes 1 y ′ ⇀ And 1 z ′ ⇀ of the on-board reference) is significantly greater than the maximum noise standard. In this way, a certain precision is ensured for the calculation of the roll angle. Advantageously, this condition can be achieved by comparing the projection of the measured vector g ′ mes ⇀ in the Y'- Z' plane and a predetermined threshold value (limit radius as illustrated in Fig. 6 ). A condition for switching to pitch first would be that the projection of the vector g ′ mes ⇀ projected has a norm less than a given threshold value. For example, the predetermined threshold value is between 0.15 and 0.45 of the norm of the measured vector g ′ mes ⇀ , preferably between 0.20 and 0.30 of this standard. These values ​​are particularly favorable for a navigation instrument mounted on or in a wristwatch. Indeed, it turns out that the user tends to look at his watch with his forearm positioned horizontally, with a wrist turned approximately 30° to 60° in pitch. Thus, in an advantageous embodiment of the invention, the choice to use the reverse order occurs when the pitch exceeds a threshold value of between 70° and 75° (see alternative criterion). Indeed, it is advantageous to avoid the order being reversed in a useful range of 30° to 60° for pitch when the user looks at his watch, hence the choice of an angle of the aforementioned threshold value.

[0050] Other value ranges can be chosen for the threshold value depending on the scope of application of the navigation instrument, for example a range centered around cos (45°), i.e. 0.707. This selection optimizes the reduction of the influence of measurement noise for the calculated values, but it risks causing instability in the heading display for an electronic compass incorporated in a wrist-worn object, and possibly more repetition of the roll and pitch angle calculation sequence due to this instability. Indeed, as the order given and the reverse order for the roll and pitch rotations applied to the measured vector g ′ mes ⇀ leads to a different yaw / heading value, if the pitch angle varies around the threshold value during use of the electronic compass, the indicated heading will, without further action, be recalculated at each change in the result of the comparison defined by the criterion for choosing the order of the two rotations in question. The second criterion, called alternative, is substantially equivalent to the first criterion. It is based on the comparison between the pitch angle calculated according to the given order and a threshold value between 65° and 80°, preferably between 70° and 75°.

[0051] The approach proposed by the invention is notably based on the observation that, despite and whatever the noise, it is always possible to bring the measured gravitational vector back onto the axis 1 z ′ ⇀ with relatively good accuracy in determining roll and pitch angles. Indeed, despite noise in the measurement of the gravitational vector, the calculation of the roll of a measured vector coplanar to the Y'- Z' plane (defined by the vectors 1 y ′ ⇀ And 1 z ′ ⇀ ) is always relatively accurate and the calculation of the pitch of a vector measured coplanar to the X'- Z' plane (defined by the vectors 1 x ′ ⇀ And 1 z ′ ⇀ ) is always relatively accurate. Then, once the roll has been calculated first and the corresponding rotation applied to the measured vector, the measured vector thus reoriented is in the X'- Z' plane so that the pitch can then be calculated with good accuracy. Similarly, once the pitch has been calculated first and the corresponding rotation applied to the measured vector, the measured vector thus reoriented is in the Y'- Z' plane so that the roll can then be calculated with good accuracy. It is therefore understood that it is the first calculation of an orientation angle of the electronic compass which is critical since it is based on a projection in a reference plane and the norm of this projection can be relatively small, so that the noise occurring during the measurement can strongly distort the result of the first angle then calculated by the calculation unit 8 of the electronic compass 4, as explained previously.Thanks to the invention, good or sufficient precision is ensured for this first calculation by selecting between 'roll first' and 'pitch first'.

[0052] The second step is to determine the yaw to obtain the heading. This step consists of solving equation 5b given previously. The choice of a judicious terrestrial reference frame simplifies the calculation steps, in particular when the projection of the reference Earth magnetic field vector B ref ⇀ , corresponding to a second reference vector, in a plane perpendicular to the axis 1 z ⇀ is collinear with the axis 1 x ⇀ ; which is the case for the terrestrial reference frame NED defined at the beginning. In this case we have the following equation for the magnetic vector measured by the magnetic sensor: B x , ref B y , ref B z , ref = B x , ref 0 B z , ref = k 2 ⋅ B x , mes B y , mes B z , mes = k 2 ⋅ R ψ ⋅ R θ ⋅ R φ B x , mes ′ B y , mes ′ B z , mes ′

[0053] Equation 10a corresponds to the 'roll first' alternative and for the 'pitch first' case we have an equation 10b similar to equation 10a but with an inversion of the rotation matrices Rϕ And R θ . The yaw angle ψ can be determined by first applying to the measured Earth's magnetic field vector B ′ mes ⇀ , in the onboard reference frame, two successive rotations corresponding to a roll rotation and a pitch rotation according to an order chosen between said given order and said reverse order, as previously explained, so as to obtain a vector of the measured and reoriented Earth's magnetic field B ∗ mes ⇀ , then calculating the angle between a projection, in the reference plane X'- Y' defined by the axis 1 x ′ ⇀ and the axis 1 y ′ ⇀ , of the reoriented Earth's magnetic field vector B ∗ mes ⇀ and the axis 1 x ′ ⇀ . Starting from equations 10a and 10b, we obtain the following simplified equation: B x , ref 0 B z , ref = k 2 ⋅ R ψ B x , mes ∗ B y , mes ∗ B z , mes ∗ with according to the given order: B x , mes ∗ B y , mes ∗ B z , mes ∗ = R θ ⋅ R φ B x , mes ′ B y , mes ′ B z , mes ′ in reverse order: B x , mes ∗ B y , mes ∗ B z , mes ∗ = R φ ⋅ R θ B x , mes ′ B y , mes ′ B z , mes ′

[0054] From equation 10a or 10b, the yaw / heading angle is therefore given by the following equation: ψ = − arctan B y , mes ∗ / B x , mes ∗

[0055] All the calculation steps described above can be carried out by the central processing unit 14 of the electronic compass 4. The determination of the heading is based on the yaw angle calculated with the equation 12 by a unit 12 for determining a heading, which can be formed by the same electronic circuit as the unit 8 for calculating the roll and pitch angles. In a variant, the electronic compass comprises an indicator 18 of the magnetic North or the geographic North and a device 16 for controlling this indicator (see Fig. 1 And Fig. 8 ). The control device 16 may be arranged to control the indicator 18 so that it has an angle relative to the axis 1 x ⇀ equal to the opposite of the yaw angle, preferably corrected for the deviation of the Earth's magnetic field at the location of the navigation instrument for indicating magnetic North and, for indicating geographic North, in addition to the declination of the Earth's magnetic field.

[0056] The electronic compass 4 preferably comprises a data display device 20 indicating the true heading (see Fig. 1 And Fig. 8), the unit 12 for determining a heading being configured to calculate the true heading as a function of the heading provided by the equation 12 given previously, of a first parameter quantifying the declination of the Earth's magnetic field and of a second parameter quantifying the deviation of the Earth's magnetic field at the location where the navigation instrument is located. In particular to determine the declination and deviation of the Earth's magnetic field, the portable object 2 further comprises a geolocation device. The electronic compass 4 may have a non-volatile memory in which information relating to the declination and deviation are stored and / or a program designed to determine them in particular on the basis of the geolocation.In addition, the portable object may have wireless communication means allowing in particular the acquisition of the declination and deviation of the magnetic field depending on the location of the portable object incorporating the electronic compass.

[0057] A comparative study was conducted to demonstrate that the choice of rotation order between the given order (roll then pitch) or the reverse order (pitch then roll) has relatively little importance on the result of the calculation of the yaw angle, and therefore of the heading, in the context of the application of a wristwatch 2. Indeed, the order of the roll and pitch rotations normally influences the calculation of the roll angle and the pitch angle because, as already indicated, the matrix product is not commutative ( R θ · Rϕ ≠ Rϕ · R θ ). There Figure 7ashows that in the absence of roll (the forearm wearing the wristwatch equipped with the electronic compass being horizontal), the permutation between the given order and the reverse order has no impact. This observation is important, because it turns out that a user tends to look at his watch on his wrist with his forearm positioned substantially horizontally, with a wrist turned in particular by 30° to 60° in pitch. Thus, in an advantageous embodiment of the invention, the choice to use the reverse order occurs when the pitch exceeds 70°, but one could also choose another threshold value, for example 60°. Indeed, it is advantageous, as already explained, to avoid the order being reversed in a usual pitch range to avoid instability in the succession of sequences for calculating the orientation angles and / or an increase in the number of these calculation sequences, hence the (arbitrary) choice of an angle greater than 60°, in particular 70°.As long as the roll remains low, which is practically the case in general, even when operating beyond this value, the user of the watch will not notice any difference when switching from the given order to the reverse order (. Fig. 7a ). As a reminder, this inversion makes it possible to reduce the influence of measurement noise on the determination of the orientation angles of the navigation instrument (in particular an electronic compass), to increase the precision of the heading measurement and also to reduce any possible instability of the successive results given by a succession of calculation sequences, such instability resulting in an oscillation of the needle indicating the North and / or of the heading value displayed.

[0058] It should be noted, however, that for a relatively low roll (see Fig. 7b: 10° roll), a significant deviation of up to 10° is already observed in the 0°-90° range, in particular about 5° to 8° in the 40°-60° range, which corresponds to common values. Thus, avoiding the predetermined threshold value being located in or corresponding to the usual pitch range is advantageous. The Fig. 7c shows that as the roll angle increases, the difference in the heading result between the given order and the reverse order increases. Thus, for a roll angle of 45° and in a pitch range of 0° to 30°, the difference in the heading value can reach 20°.

[0059] The invention is not limited to the portable device of the first embodiment described above. Indeed, the inversion of the order of rotations not only makes it possible to advantageously reduce the sensitivity to measurement noise when predicting two orientation angles but also to no longer suffer from the gimbal locking effect for many objects, such as a transport vehicle or a flying object. In general, the inversion of the order of rotations according to the invention operates as a filter aimed at reducing the effect of the noise of the measurement of at least one vector of a terrestrial force field and at eliminating the gimbal locking when determining the orientation angles of an object relative to a terrestrial reference frame.

[0060] In a second embodiment, the navigation instrument makes it possible to determine two orientation angles of a system in the framework of spherical coordinates. The navigation instrument therefore makes it possible to determine the two orientation angles of the axis 1 r ⇀ of the on-board reference system based on the measurement of a terrestrial magnetic field vector determined via a geolocation means.

[0061] The first embodiment proposes to firstly calculate the roll and pitch angles as a function of the measurement, in a reference frame linked to the navigation instrument, of a gravitational field vector g ′ mes ⇀ , then the yaw angle from the measurement in the same on-board reference frame of an Earth's magnetic field vector B ′ mes ⇀ This order can be reversed with a first step of calculating the yaw and roll angle from a measurement, still in a frame of reference linked to the navigation instrument, of a vector of the Earth's magnetic field B ′ mes ⇀ , then the pitch angle from the measurement, in this on-board frame of reference, of a terrestrial gravitational field vector g ′ mes ⇀ This example shows that the choice of the axes of the reference frames considered, as well as the given order of rotations, is arbitrary.

Claims

1. 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 ( g ′ mes ⇀ ; B ′ mes ⇀ ) in a reference frame ( 1 x ′ ⇀ , 1 y ′ ⇀ , 1 z ′ ⇀ ) 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 ′ ); - an orientation angle (ϕ, θ, ψ) calculation unit (8) of the navigation instrument, this calculation unit being connected to said first sensor (6) to receive said first output signals and being configured to be able to calculate a first orientation angle (ϕ) and a second orientation angle (θ) of said on-board reference frame, and thus of the navigation instrument (4), with respect to a terrestrial reference frame ( 1 x ⇀ , 1 y ⇀ , 1 z ⇀ ), these first and second orientation angles being defined by two successive rotations that the first measured vector must undergo, around a first reference axis of rotation ( 1 x ′ ⇀ ) of the on-board reference frame for the first orientation angle and a second reference axis of rotation ( 1 y ′ ⇀ ) of the on-board reference frame for the second orientation angle, to align this first measured vector on a calculation vector having, in the on-board reference frame, three calculation components which are identical to three reference components, in the terrestrial reference frame, of a first reference vector ( g ref ⇀ ; B ref ⇀ ) which is predefined or predetermined in the terrestrial reference frame; characterised in that the orientation angle calculation unit (8) is configured to be able to determine the first and second orientation angles in a given order for said two successive rotations and also in reverse order; and in that the calculation unit (8) is arranged to be able to choose between said given order and said reverse order, to calculate the first and second orientation angles, based on a comparison between an indicator of a risk of error, quantifying a risk of instability of said calculation unit during the determination of the first and second orientation angles, and a predetermined threshold, said indicator of the risk of error being determined by the navigation instrument according to at least two of said first output signals.

2. The navigation instrument according to claim 1, characterised in that said indicator of the risk of error is the norm of the projection of the first vector measured in a plane perpendicular to the first reference axis of rotation; and in that the orientation angle calculation unit (8) is configured to first determine the first orientation angle, by performing among said two successive rotations firstly the rotation of the first vector measured around the first reference axis of rotation, when said indicator of the risk of error is greater than said predetermined threshold.

3. The navigation instrument according to claim 2, characterised in that the value of the predetermined threshold is comprised between 0.15 and 0.45 of the norm of the first measured vector, preferably between 0.20 and 0.30 of this norm.

4. The navigation instrument according to claim 1, characterised in that said indicator of the risk of error is the absolute value of the second orientation angle when the first orientation angle is calculated before the second orientation angle; and in that the orientation angle calculation unit (8) is configured to again determine the first and second orientation angles by first calculating the second orientation angle, by firstly performing among said two successive rotations the rotation of the first measured vector around the second reference axis of rotation, when said indicator of the risk of error is greater than said predetermined threshold; the calculation unit (8) then retaining the values of the first and second orientation angles determined again for these first and second orientation angles.

5. The navigation instrument according to claim 4, characterised in that the value of the predetermined threshold is comprised between 65° and 80°, preferably between 70° and 75°.

6. The navigation instrument according to one of the preceding claims, characterised in that a predefined axis of the terrestrial reference frame is aligned with the first reference vector, preferably this first reference vector being aligned with a vertical axis 1 z ⇀ of the terrestrial reference frame.

7. The navigation instrument according to the preceding claim, characterised in that the first measured vector is a vector of the terrestrial gravitational force field.

8. The navigation instrument according to the preceding claim, characterised in that the first measured vector is determined by means of an accelerometer (6) forming said first sensor.

9. The navigation instrument according to one of the preceding claims, characterised in that the first reference axis of rotation corresponds to an axis 1 x ′ ⇀ of the on-board reference frame and the second reference axis of rotation corresponds to an axis 1 y ′ ⇀ of the on-board reference frame, these first and second reference axes of rotation being perpendicular.

10. The navigation instrument according to one of the preceding claims, characterised in that said instrument includes a second sensor (10) configured to measure the three components of a second vector, called second measured vector, of a second terrestrial force field in the on-board reference frame, this second measured vector being non-collinear with the first measured vector, and to generate second output signals representative of these three components; and in that the navigation instrument further comprises a unit (12) for determining a third angle of orientation of said on-board reference frame, and thus of this navigation instrument, relative to the terrestrial reference frame, this determination unit being connected to said second sensor (10) to receive said second output signals and being configured to determine the third orientation angle from said calculated first and second orientation angles and the second output signals.

11. The navigation instrument according to the preceding claim, characterised in that said calculation unit (8) and said unit (12) for determining the third orientation angle are formed by one and the same electronic unit which itself forms a central electronic unit (14) of the navigation instrument.

12. The navigation instrument according to claim 10 or 11 dependent on claim 9, characterised in that the third orientation angle is defined by a rotation that the second measured vector must undergo, after having been reoriented in the on-board reference frame by an application to this second measured vector of said first and second successive rotations, around a third reference axis of rotation, perpendicular to the first and second reference axes of rotation and corresponding to the third axis 1 z ′ ⇀ of the on-board reference frame, so that the second measured and reoriented vector, called second reoriented vector, is located in a first reference plane of the on-board reference frame comprising the first and third reference axes of rotation.

13. The navigation instrument according to claim 12, characterised in that the third orientation angle is determined by first applying to the second measured vector said first and second successive rotations, preferably in the order chosen between said given order and said reverse order to define the first and second orientation angles, so as to obtain the second reoriented vector, then by calculating the angle between a projection, in a second reference plane comprising the first and second reference axes of rotation, of the second reoriented vector and the first reference axis of rotation.

14. The navigation instrument according to one of claims 10 to 13, characterised in that the second measured vector is a vector of the terrestrial magnetic field, this second measured vector being determined by means of a magnetic sensor (10) forming said second sensor.

15. The navigation instrument according to one of claims 10 to 14, characterised in that the third orientation angle is considered as a heading of this instrument.

16. The navigation instrument according to one of claims 1 to 5, characterised in that the first measured vector is a vector of the terrestrial magnetic field, this first measured vector being determined by means of a magnetic sensor (10) forming said first sensor.

17. The navigation instrument according to claim 16, characterised in that said three reference components are predetermined from data originating from a location device of the navigation instrument, in particular of the GPS type.

18. The navigation instrument according to claim 16 or 17 combined with one of claims 10 to 13 dependent on one of claims 1 to 5, characterised in that the second measured vector is a vector of the terrestrial gravitational force field.

19. The navigation instrument according to claim 18, characterised in that the second measured vector is determined by means of an accelerometer (6) which forms said second sensor.

20. The navigation instrument according to one of claims 10 to 15 dependent on claim 9, characterised in that this instrument is an electronic compass (4) which comprises an indicator (18) of magnetic North or geographic North and means (16) for controlling this indicator, which are arranged to control the indicator (18) so that it has an angle relative to the first reference axis of rotation equal to the opposite of the third orientation angle, preferably the correction of the deviation of the terrestrial magnetic field at the location of the navigation instrument for the indication of magnetic north and, for the indication of geographic north, in addition to the declination of the terrestrial magnetic field.

21. The navigation instrument according to claim 15 or claim 20 dependent on claim 15, characterised in that this instrument comprises a device (20) for displaying data indicating the true heading, said calculation unit (8) being configured to calculate the true heading according to said heading, of a first parameter quantifying the declination of the terrestrial magnetic field and a second parameter quantifying the deviation of the terrestrial magnetic field at the location where the navigation instrument is located.

22. A Wearable device (2) comprising the navigation instrument according to one of the preceding claims.

23. The wearable device according to the preceding claim, characterised in that this device, in particular a wristwatch (2), is wearable on the wrist of a user; and in that the first reference axis of rotation ( 1 x ′ ⇀ ) corresponds to the 6-12 o'clock axis and the second reference axis of rotation ( 1 y ′ ⇀ ) corresponds to the 9-3 o'clock axis of this device wearable on the wrist.

24. A method for determining the angles of orientation of a navigation instrument (4) with respect to a terrestrial reference frame ( 1 x ⇀ , 1 y ⇀ , 1 z ⇀ ), this method comprising the following steps: - acquisition of the three components of a first vector, called first measured vector, of a first terrestrial force field in a reference frame ( 1 x ′ ⇀ , 1 y ′ ⇀ , 1 z ′ ⇀ ) linked to said navigation instrument, called on-board reference frame; - determination of a first angle of orientation and of a second angle of orientation of the on-board reference frame with respect to the terrestrial reference frame, these first and second orientation angles being defined by two successive rotations of the first measured vector, around a first reference axis of rotation of the on-board reference frame for the first orientation angle and a second reference axis of rotation of the on-board reference frame for the second orientation angle, allowing to align the first measured vector with a calculation vector having, in the on-board reference frame, three calculation components which are identical with three reference components, in the terrestrial reference frame, of a first reference vector which is predefined or predetermined in the terrestrial reference frame; said determination comprising, to calculate the first and second orientation angles, a step of choosing between a given order for the two successive rotations and a reverse order based on a comparison between an indicator of a risk of error, quantifying a risk of instability during the determination of the first and second orientation angles, and a predetermined threshold, said indicator of the risk of error being determined based on at least two of said components of the first measured vector.

25. The method according to claim 24, characterised in that said indicator of the risk of error is the norm of the projection of the first vector measured in a plane perpendicular to the first reference axis of rotation; and in that, when said indicator of the risk of error is greater than said predetermined threshold, the first orientation angle is calculated based on said given order by firstly performing, among said two successive rotations, the rotation of the first vector measured around the first reference axis of rotation.

26. The method according to claim 25, characterised in that the value of the predetermined threshold is comprised between 0.15 and 0.45 of the norm of the first measured vector, preferably between 0.20 and 0.30 of this norm.

27. The method according to claim 24, characterised in that said indicator of the risk of error is the absolute value of the second orientation angle when, in said given order, the first orientation angle is calculated before the second orientation angle; and in that, when said indicator of the risk of error is greater than said predetermined threshold, the first and second orientation angles are again calculated in said reverse order by performing, among said two successive rotations, firstly the rotation of the first vector measured around the second reference axis of rotation; the values of the recalculated first and second orientation angles then being retained for these first and second orientation angles.

28. The method according to claim 27, characterised in that the value of the predetermined threshold is comprised between 65° and 80°, preferably between 70° and 75°.

29. The method according to one of claims 24 to 28, characterised in that a predefined axis of the terrestrial reference frame is aligned with the first reference vector, preferably this first reference vector being aligned with a vertical axis 1 z ⇀ of the terrestrial reference frame.

30. The method according to one of claims 24 to 29, characterised in that the first measured vector is a vector of the terrestrial gravitational force field.

31. The method according to the preceding claim, characterised in that the first measured vector is determined by means of an accelerometer (6).

32. The method according to one of claims 24 to 31, characterised in that the first orientation angle and the second orientation angle are respectively a roll angle and a pitch angle, the roll angle being associated with a rotation around the first reference axis of rotation, corresponding to the axis 1 x ′ ⇀ of the on-board reference frame when the roll angle is determined first, and the pitch angle being associated with a rotation around the second reference axis of rotation, corresponding to the axis 1 y ′ ⇀ of the on-board reference frame when the pitch angle is determined first.

33. The method according to one of claims 24 to 32, characterised in that the method further comprises a step of acquiring three components of a second vector, called second measured vector, of a second terrestrial force field in said on-board reference frame ( 1 x ′ ⇀ , 1 y ′ ⇀ , 1 z ′ ⇀ ), this second measured vector being non-collinear with the first measured vector, and a step of determining a third orientation angle of the on-board reference frame, and thus of said navigation instrument, with respect to the terrestrial reference frame from the first and second calculated orientation angles and from the three components of the second measured vector.

34. The method according to claim 33, characterised in that the third orientation angle is determined by first applying to the second measured vector said first and second successive rotations, preferably in the order chosen between said given order and said reverse order, to obtain a second measured and reoriented vector, called second reoriented vector, in the on-board reference frame, then by calculating the angle between a projection of the second reoriented vector in a reference plane, comprising the first and second reference axes of rotation, and the first reference axis of rotation.

35. The method according to claim 33 or 34 dependent on claim 32, characterised in that the third orientation angle is a yaw angle of the navigation instrument, this yaw angle being defined by a rotation of the on-board reference frame around a third reference axis of rotation, corresponding to the vertical axis 1 z ⇀ in the terrestrial reference frame, after roll and pitch corrections.

36. The method according to claim 35, characterised in that the third orientation angle is considered as a heading of the navigation instrument.

37. The method according to one of claims 33 to 36 dependent on claim 30 or 31, characterised in that the second vector of a second terrestrial force field is a vector of the terrestrial magnetic field; and in that said second vector is measured by means of a magnetic sensor (10).

38. The method according to one of claims 24 to 29, characterised in that the first vector of a first terrestrial force field is a vector of the terrestrial magnetic field; and in that said first vector is measured by means of a magnetic sensor.

39. The method according to claim 38 combined with claim 33 or 34 dependent on any one of claims 24 to 29, characterised in that the second vector of a second terrestrial force field is a vector of the terrestrial gravitational force field.

40. The method according to the preceding claim, characterised in that the second vector of a second terrestrial field is measured by means of an accelerometer (6).

41. The method according to any one of claims 38 to 40, characterised in that said three reference components are determined from data coming from a location device of the navigation instrument, in particular of the GPS type.

42. The method according to one of claims 24 to 41, characterised in that said navigation instrument is an electronic compass (4).

43. The method according to claim 36, characterised in that said navigation instrument comprises means (20) for displaying data indicating the true heading; and in that the method further comprises a step of determining the true heading according to said heading determined in one of the preceding steps, of a first parameter quantifying the declination and of a second parameter quantifying the deviation of the terrestrial magnetic field at the location where the navigation instrument is located.

44. The method according to one of claims 24 to 43, characterised in that the navigation instrument is configured to be mounted on or integrated into a wearable device (2).

45. The method according to the preceding claim, characterised in that the wearable device, in particular a wristwatch (2), is wearable on a user's wrist; and in that the first reference axis of rotation ( 1 x ′ ⇀ ) corresponds to the 6-12 o'clock axis, and the second reference axis of rotation ( 1 y ′ ⇀ ) corresponds to the 9-3 o'clock axis.

46. A computer program comprising instructions which, when the program is executed by a computer, cause this computer to implement the steps of the method according to one of claims 24 to 45.

47. A computer-readable recording medium comprising instructions which, when executed by a computer, cause this computer to carry out the steps of the method according to one of claims 24 to 45.