GB2272974A - Inertial guidance system - Google Patents

Abstract

An inertial guidance system for a strapdown aircraft navigation system has three accelerometers (AX, AY, AZ) for measuring acceleration in three mutually perpendicular axes (X, Y, Z). One accelerometer (AZ) is placed on the datum point of the unit; the other two accelerometers (AX, AY) are arranged to have their centres of percussion co-planar with the first accelerometer thereby to reduce the complexity of calculations required to effect error compensation due to lever arm effects. The displacements of the second and third accelerometers (AX, AY) from the first accelerometer are preferably arranged to be substantially equal and are along the X and Y axes respectively, thereby further simplifying error compensation. <IMAGE>

Description

INERTIAL GUIDANCE SYSTEM The present invention relates to an inertial guidance system incorporating accelerometers.

Inertial guidance systems for vehicles such as aircraft have been proposed and operate to determine the movement of a datum point (nominally fixed with respect to the vehicle) with respect to some navigation reference frame (e.g. local North, East and Down axes).

Inertial guidance systems always employ "accelerometers" which are sensors capable of measuring linear acceleration and may employ additional accelerometers or other sensors to determine angular motion such as gyroscopes.

In some cases it is physically arranged that the accelerometer input axes are maintained substantially in a fixed (or slowly varying) orientation with respect to the chosen navigation reference frame. In such cases the accelerometer outputs may be interpreted directly to give the motion of the vehicle.

Alternatively the accelerometer axes may be maintained substantially in alignment with the vehicles body axes and so in general do not remain fixed in alignment with respect to the chosen navigation reference frame due to vehicle rotations. Such systems are known as "strapdown" systems.

In strapdown systems the movement of the vehicle datum point with respect to the navigation frame is calculated from measurement of the motion in six degrees of freedom of a single reference point fixed with respect to the "Inertial Sensor Assembly" - a nominally rigid frame to which the motion sensors are attached. This point is hereinafter referred to as the ISA datum point. The data defining the motion of the ISA datum point is derived from measurements made by the accelerometers and any other motion sensors. It is often convenient to define the vehicle datum point to be identical with the ISA datum point.

It is often convenient to use a minimum of three single-axis linear accelerometers and three gyroscopes to provide the six measurements needed to fully define the motion of the datum point.

However, in general, it is not physically possible to arrange a set of three single axis accelerometers such that the points at which measurements are effectively made (herein referred to as the centres of percussion or Cs of P) of all three accelerometer coincide at the ISA datum point.

The fact that some of the accelerometers may have their centres of percussion displaced from the datum point means that the linear motion which they sense may differ from the true linear motion of the datum point. As a result of the lever-arm effect, purely angular motion about the ISA datum point may cause a linear acceleration to be present at the centre of percussion of one (or more) of the accelerometers leading to an ambiguous output. Such additional components are sometimes known as "Size Effect" accelerations. Since the physical configuration of the accelerometers is known and the angular motion of the ISA is sensed these Size Effects can be calculated and appropriate compensation introduced into the output of the accelerometers.Failure to apply Size Effect compensations accurately and at a sufficient rate to cope with the dynamic motion of the ISA may lead to significant errors in guidance in due time.

However the calculations involved in compensating for Size Effects in a set of three accelerometers may be substantial and the errors in calculating the compensation terms may be significant.

The present invention has arisen in an attempt to optimise the physical configuration of an Inertial Sensor Assembly suitable for strapdown applications and so reduce the number of calculations which are required to effect Size Effect compensations.

In accordance with the present invention, there is provided an inertial guidance system, comprising three accelerometers Ax, Ay, Az which are arranged to measure acceleration along three mutually perpendicular axes S,Y and Z, characterised in that the accelerometers are arranged to have their centres of percussion in a plane which includes two of said axes X and Y, and in that the centre of percussion of accelerometer Ax is displaced from the centre of percussion of accelerometer Az only along the direction of axis Y and that the centre of percussion of accelerometer Ay is displaced from the centre of percussion of accelerometer Az only along the direction of axis X.

Preferably the magnitude of the displacements between Ax and Az and between Ay and Az are arranged to be substantially equal.

It is preferred that the ISA datum point is located within the physical confines of the ISA. Furthermore it is preferred that the accelerometer Az has its centre of percussion coincidental with said ISA datum point.

Conveniently, the system includes three gyroscopes, each measuring rotation about a respective one of said three axes.

In one embodiment the accelerometer Az measures acceleration in a nominally vertical axis, the accelerometers Ax and Ay measuring acceleration in nominally horizontal axes.

The invention finds particular application in strapdown navigation units for use in aircraft and other vehicles.

The present invention will now be described, by way of example only, with reference to the accompanying drawings in which: - Figure 1 is a schematic illustration which shows the effect of a single component of linear acceleration combined with a single component of angular motion on a sensor having its centre or percussion displaced from a datum point and Figure 2 is a diagrammatic view of part of a strapdown inertial guidance system. Parts have been omitted for clarity.

In the drawing of figure 1 there is a point P about which the guidance unit is notionally caused to rotate as is shown in relation to point Q as indicated by the arrow W.

The acceleration at the point Q induced by the acceleration A is modified by the rotation of the body about the point P.

As is well known the linear acceleration at the point Q, Aq is Aq = A + (r x W) + (r x W) x W (1) where W is the angular velocity vector (with respect to inertial axes) W is the rate of change of W r is the displacement from P to Q and x represents the vector cross-product operation i.e. the error in measurement of A due to the displacement r is Error = Aq - A = (r x W) + (r x W) x W This is the so called "Size Effect" error for which it is necessary to compensate.

In a system employing three single axis accelerometers the general error introduced into the output of each accelerometer due to the Size Effect can be illustrated mathematically as follows: Ex = - Rxx.(Wy2 + Wz2) + Rxy.(+Wz + Wx.Wy) - Rxz.(+Wy - Wx.Wz) Ey = - Ryy.(Wx2 + WZ2) + Ryx.(-Wz + Wx.Wy) - Ryz.(+Wx - Wy.Wz) Ez = - Rzz.(Wx2 + Wy2) + Rzx.(+Wy + Wx.Wz) - Rzy.(+Wx - Wz.Wy) Where EX is the Size Effect error from the accelerometer Ax Ey is the Size Effect error from the accelerometer Ay Ez is the Size Effect error from the accelerometer Az Rxx is the displacement of X accelerometer C of P from the datum in X direction Rxy is the displacement of X accelerometer C of P from the datum in Y direction Rxz is the displacement of X accelerometer C of P from the datum in Z direction Ryx is the displacement of Y accelerometer C of P from the datum in X direction Ryy is the displacement of Y accelerometer C of P from the datum in Y direction Ryz is the displacement of Y accelerometer C of P from the datum in Z direction Rzx is the displacement of Z accelerometer C of P from the datum in X direction Rzy is the displacement of Z accelerometer C of P from the datum in Y direction Rzz is the displacement of Z accelerometer C of P from the datum in Z direction Wx is the component of angular velocity of the ISA about the X axis Wy is the component of angular velocity of the ISA about the Y axis Wz is the component of angular velocity of the ISA about the Z axis Wx is the component of angular acceleration of the ISA about the X axis Wy is the component of angular acceleration of the ISA about the Y axis Wz is the component of angular acceleration of the ISA about the Z axis It will be appreciated that the calculations required to carrying out this general compensation are substantial, involving at least 15 different multiplications and 15 different additions or subtractions. Furthermore it is often convenient to estimate the angular acceleration terms from differencing of successive measurements of angular velocity. Three such terms are required in general. The invention is concerned with reducing the complexity of error correction.

The unit shown in Figure 2 comprises a casing C which is shown part cut-away. The casing C is attached to the floor F of an aircraft by means of anti-vibration mountings AV. The aircraft has six degrees of freedom of movement, namely translation and rotation along or about each of the three axes X, Y and Z. For the purpose of this description, the X axis is taken to be the longitudinal horizontal axis or "roll" axis, the Y axis is the lateral horizontal axis or "pitch axis and the Z axis is the vertical or "yaw" axis.

To monitor the motions relative to each axis the unit includes three gyros (not shown) which monitor rotation about the axes and three accelerometers AX, AY and AZ to measure translation along the axes. Each accelerometer has a centre of percussion P which is the important point to consider when positioning of the accelerometers is decided.

In order to reduce the compensation required, one accelerometer, in this case AZ, is placed with its centre of percussion P coincidental with the unit datum point D. Thus no compensation is required for this accelerometer, i.e.

the vertical accelerometer. In order that the Z axis effect can be removed from the horizontal accelerometer AX, AY, these are arranged to be co-planar with AZ in the XY plane.

Such an arrangement only requires compensation in the X and Y directions and this compensation is further simplified by arranging for each of the accelerometers AX, AY to be displaced from AZ by the same amount, r. Thus the compensation required in each case is very similar.

This can be shown mathematically in equation 2: for Az, Rzx = Rzy = Rzz = 0 and error Ez = 0 for Ay, Ryx = r; Ryy = Ryz = 0 and error Ey = -r.Wz + r.Wx.Wy for Ax, Rxy = r; Rxx = Rxz = 0 and error Ex = rWz + r.Wx.Wy Thus the calculations required for compensation have been reduced to 3 different multiplications and 2 additions (or subtractions).

Only one angular acceleration term is required in this case.

It will be appreciated that while the preferred arrangement eliminates the Z axis compensation, any arrangement which place all accelerometers in a plane containing two axes will simplify the compensation as only two cases need be considered.

The gyros in the unit do not require compensation as the lever arm effects are not encountered.

Claims (9)

1. An inertial guidance systems, comprising three accelerometers which are arranged to measure acceleration along three mutually perpendicular axes, characterised in that the accelerometers are arranged to have their centres of percussion in a plane which includes two of said axes and in that a first accelerometer is displaced from a second accelerometer along the first of said two axes and a third accelerometer is displaced from the first accelerometer along the second of said two axes.

2. A system as claimed in Claim 1, characterised in that the displacements between first and second, and first and third accelerometers is arranged to be substantially equal.

3. A system as claimed in Claim 1 or 2, comprising a datum point relative to which motion is measured which is within the physical confines of the unit.

4. A system as claimed in Claim 3, wherein the centre of percussion of the first accelerometer is coincidental with the datum point.

5. A system as claimed in any one of the preceding claims, which also includes three gyroscopes, each measuring rotation about a different one of said three axes.

6. A system as claimed in any one of the preceding claims, wherein the first accelerometer measures acceleration in a nominally vertical axis, the second and third accelerometers measuring acceleration in nominally horizontal axes.

7. A strap down (as herein defined) navigation unit, comprising an inertial guidance system as claimed in any one of the preceding claims.

8. An aircraft navigation system comprising a system as claimed in any one of the preceding claims.

9. An inertial guidance system substantially as described herein with reference to the drawings.

9. An inertial guidance system substantially as described herein with reference to the drawings.

Amendments to the claims have been filed as follows 1. An inertial guidance system, comprising three accelerometers which are arranged to measure acceleration along three mutually perpendicular axes, accelerometers being arranged to have their centres of percussion in a plane which includes two of said axes and so that a first accelerometer is displaced from a second accelerometer along the first of said two axes and a third accelerometer is displaced from the first accelerometer along the second of said two axes.

2. A system as claimed in Claim 1, in which the displacements between first and second, and first and third accelerometers are arranged to be substantially equal.

3. A system as claimed in Claim 1 or 2, comprising a datum point relative to which motion is measured which is within ,the physical confines of the unit.

4. A system as claimed in Claim 3, wherein the centre of percussion of the first accelerometer is coincidental with the datum point.

5. A system as claimed in any one of the preceding claims, which also includes three gyroscopes, each measuring rotation about a different one of said three axes.

6. A system as claimed in any one of the preceding claims, wherein the first accelerometer measures acceleration in a nominally vertical axis, the second and third accelerometers measuring acceleration in nominally horizontal axes.

7. A strap down navigation unit, comprising an inertial guidance system as claimed in any one of the preceding claims.

8. An aircraft navigation system comprising a system as claimed in any one of the preceding claims.