INERTIAL NAVIGATION SYSTEM WITH COMPENSATION OF ROLL SCALE FACTOR ERROR

Abstract

An inertial measurement system (200) for a longitudinal projectile, comprising a first, roll gyro to be oriented substantially parallel to the longitudinal axis of the projectile; a second gyro and a third gyro with axes arranged with respect to the roll gyro such that they define a three dimensional coordinate system. The system further comprises a controller (225, 250), arranged: —to compute a current projectile attitude from the outputs of the first, second and third gyros, the computed attitude comprising a roll angle, a pitch angle and a yaw angle; —for at least two time points, to compare the computed pitch and yaw angles with expected values for the pitch and yaw angles; —for each of said at least two time points, to calculate a roll angle error based on the difference between the computed pitch and yaw angles and the expected pitch and yaw angles; —to calculate a roll angle error difference between said at least two time points; —to calculate the total roll angle subtended between said at least two time points; —to calculate a roll angle scale factor error based on said computed roll angle error difference and said total subtended roll angle and apply the calculated roll angle scale factor error to the output of the roll gyro.

Claims

1. An inertial measurement system for a longitudinal projectile comprising: a first, roll gyro to be oriented substantially parallel to the longitudinal axis of the projectile; a second gyro and a third gyro with axes arranged with respect to the roll gyro such that they define a three dimensional coordinate system; a controller, arranged to: compute a current projectile attitude from the outputs of the first, second and third gyros, the computed attitude comprising a roll angle, a pitch angle and a yaw angle; for at least two time points, compare the computed pitch and yaw angles with expected values for the pitch and yaw angles; for each of said at least two time points, calculate a roll angle error based on the difference between the computed pitch and yaw angles and the expected pitch and yaw angles; calculate a roll angle error difference between said at least two time points; calculate the total roll angle subtended between said at least two time points; calculate a roll angle scale factor error based on said computed roll angle error difference and said total subtended roll angle; and apply the calculated roll angle scale factor error to the output of the roll gyro.

2. An inertial measurement system as claimed in claim 1, wherein the roll gyro is a MEMS gyro.

3. An inertial measurement system as claimed in claim 1, wherein the expected values for pitch and yaw angles as a function of flight time correspond to those expected from planar ballistic flight.

4. An inertial measurement system as claimed in claim 3, wherein the roll angle error is calculated as the angle whose tangent is the ratio of the rate of change of the calculated yaw angle to the rate of change of the calculated pitch angle.

5. An inertial measurement system as claimed in claim 4, further comprising a low pass filter arranged to filter out high frequency components of changes in the yaw angle and the pitch angle before calculation of the rate of change of the yaw angle and the rate of change of the pitch angle.

6. An inertial measurement system as claimed in claim 5, wherein a time constant of the low pass filter is increased at high roll rates and decreased at low roll rates.

7. An inertial measurement system as claimed in claim 1, wherein the expected values for pitch and yaw angles as a function of flight time are taken from a pre-computed flight trajectory which may be non-planar.

8. An inertial measurement system as claimed in claim 1, wherein the roll scale factor error is multiplied by a roll scale factor error gain factor before being applied to the output of the roll gyro.

9. An inertial measurement system as claimed in claim 8, wherein the gain factor is a fixed value.

10. An inertial measurement system as claimed in claim 8, wherein the roll scale factor error gain is proportional to the reciprocal of the instantaneous roll rate.

11. An inertial measurement system as claimed in claim 1, wherein the system has no linear accelerometers.

12. An inertial measurement system as claimed in claim 1, wherein the difference in time between the at least two time points is at least the time between samples of the roll gyro.

13. A method of correcting roll angle in an inertial measurement system for a longitudinal projectile, comprising: computing a current projectile attitude comprising a roll angle, a pitch angle and a yaw angle; for at least two time points, comparing the computed pitch and yaw angles with expected values for the pitch and yaw angles; for each of said at least two time points, calculating a roll angle error based on the difference between the computed pitch and yaw angles and the expected pitch and yaw angles; calculating a roll angle error difference between said at least two time points; calculating the total roll angle subtended between said at least two time points; calculating a roll angle scale factor error based on said computed roll angle error difference and said total subtended roll angle; and applying the calculated roll angle scale factor error to the output of a roll gyro.

14. A method as claimed in claim 13, wherein the roll angle error is calculated as the angle whose tangent is the ratio of the rate of change of the calculated yaw angle to the rate of change of the calculated pitch angle.

15. A method as claimed in any claim 13, wherein the method makes no use of linear accelerometers.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0031] One or more non-limiting examples will now be described, by way of example only, and with reference to the accompanying figures in which:

[0032] FIG. 1a shows a projectile in flight;

[0033] FIG. 1b illustrates the attitude of the projectile;

[0034] FIG. 2 shows an inertial navigation system; and

[0035] FIG. 3 shows a roll control process in detail.

[0036] FIG. 1a illustrates a rocket 100 in flight. Its trajectory 110 is shown in broken line. The rocket 100 has a nose 101, tail 102 with fins 103. Fins 103 may be static or they may be movable so as to provide directional control so as to alter the flight path of the rocket 100.

[0037] In inertial navigation terminology, the orientation of a body/platform is described in terms of the three Euler angles ‘heading, ‘elevation’ and ‘bank’. The equivalent terms yaw′, ‘pitch’ and ‘roll’ are also in use. The body orientation is generally referred to using the term ‘attitude’. Although strictly speaking the term ‘attitude’ refers only to the elevation and bank angles, in this document, the more general definition is used. Therefore in this document, the term ‘attitude’ refers to all three of heading, elevation and bank (or equivalently yaw, pitch and roll).

[0038] A ‘quaternion’ is a 4-element hyper-complex number used in inertial navigation as a convenient method of maintaining and propagating heading/attitude angles. Use of quaternions avoids the numeric singularities that can occur when Euler angles are manipulated directly. The use of quaternions in navigation systems is well known and is not described further here.

[0039] In FIG. 1b the attitude 125 of the rocket 100 is shown with respect to the axes 120 of the navigation frame of reference. The projection of the attitude 125 onto the horizontal plane is shown by dotted line 126. The heading or yaw angle of the rocket is shown by the angle 121, the elevation or pitch angle of the rocket is shown by the angle 122 and the bank or roll angle of the rocket about its longitudinal axis is indicated by arrow 123. The rocket 100 is rotating anti-clockwise when viewed from behind as shown.

[0040] FIG. 2 illustrates in a general way how the scale factor estimation process fits in with the normal attitude integration process. The raw inputs of the inertial navigation system 200 are the roll, pitch and yaw rates from the body mounted gyroscopes indicated at 210, 211 and 212 respectively.

[0041] In a standard navigation system (ignoring for the moment the additional roll control functions of this example), the gyroscope outputs 210, 211, 212 are integrated by the attitude integration function 225.

[0042] As mentioned earlier, this example does not require linear accelerometers in order to function. However, in more complex systems where body mounted linear accelerometers are provided, the attitude integration function may also take into account other corrections such as Earth Rate Correction, Transport Rate Correction, Coriolis & Centripetal Correction and Gravity Correction. Each of these corrections are based on the position and velocity data derived from the accelerometers. These corrections and the associated transformations between reference frames are all well-known and understood and will therefore not be described further here. However, to aid understanding, the symbols in FIGS. 2 and 23 have the following meanings:

C.sub.b.sup.n Transformation matrix−body to navigation reference frames
Ω.sub.ib.sup.b Body rotation rate in the body frame of reference
θ Inertially derived Elevation (pitch) angle
φ Inertially derived Bank (roll) angle
ψ Inertially derived Heading (yaw) angle
φ.sub.error Bank (roll) angle error estimate
δφ.sub.error Change in Bank (roll) angle error estimate
{dot over (φ)} Inertially measured roll rate

[00001]$\frac{\partial \theta }{\partial t}$

Inertially derived Elevation (pitch) angle rate

[00002]$\frac{\partial \psi }{\partial t}$

Inertially derived Heading (yaw) angle rate
Δt Time interval.

[0043] The Scale Factor estimation process 250 is indicated in FIG. 2 in dashed lines, as an addition to the conventional attitude integration function 225 indicated in solid lines. This complete process is designed to operate during the early flight phase of a surface launched rocket or other high roll-rate projectile, when the roll rates are typically high (e.g. 10 Hz to 20 Hz).

[0044] The inertial navigation system 200 of FIG. 2 combines two of the outputs from the attitude integration function (Elevation θ and Heading ψ angles) with the IMU roll axis rate measurement ({dot over (φ)}) 210 to derive an estimate of the roll axis scale factor error, which is then available to correct the roll axis rate measurement.

[0045] FIG. 3 shows the inertial navigation system 200 in more detail.

[0046] The detail of the Scale Factor Estimation function 250 is indicated in FIG. 3 by the dashed line. The parameter φ.sub.error is derived from the measurement of roll rate and the derived Elevation and Bank Euler angles (θ and ψ) in the following manner:

[0047] φ.sub.error is derived as a correction to the existing Bank (roll) estimate, the correction being the ratio between the Heading (yaw) rate and the Elevation (pitch) rate as calculated from the attitude integration module 225. In other words, the Bank angle error is the angle having the ratio of Heading (yaw) rate to Elevation (pitch) rate as its trigonometric tangent. This calculation is based on the assumption that the rocket trajectory is purely planar i.e. it maintains the same fixed heading throughout the flight. The elevation angle in such flight is also expected to decrease at a constant, predictable rate. This calculation is based on the assumption that any deviation in Heading (yaw) angle must have arisen through errors in the Bank (roll) angle calculation. This technique may however be extended to applications involving non-planar trajectories (e.g. spinning artillery shells) using prior knowledge of the expected heading profile. In such cases, a similar calculation can be made using the deviation of the calculated Heading (yaw) angle compared with the expected/predicted Heading (yaw) angle and assuming that any such deviations have arisen through errors in the Bank (roll) calculation.

[0048] The Heading (yaw) and Elevation (pitch) rates are continuously calculated as the time derivative of low-pass filtered forms of the Heading (yaw) and Elevation (pitch) angles from the attitude integration module 225. The low pass filter gain is varied according to the roll rate, to accommodate the effect of roll rate on the characteristics of unwanted modulations in the heading and elevation angles. The frequency and magnitude of the unwanted modulations are related to roll rate, therefore the low pass filter performs better if adjusted by the roll rate. The scheme implemented in this example uses the roll rate (i.e. {dot over (φ)}) to adjust the time constant of the low pass filter 315. The time constant is increased at high roll rates and decreased at low roll rates so that there is more smoothing of theta and psi at high roll rates. This reflects the fact that, at high roll rates, the roll angle error will generally be larger than at low roll rates (because the underlying issue is gyro scale factor error). It is the size of the roll angle error that determines the numeric size of the time derivatives of theta and psi, hence these will be larger and more observable at high roll rates. This allows more smoothing to be applied whilst still maintaining sufficient sensitivity in terms of determining the roll angle error. It will be appreciated that this is just one possible approach. There are other ways of manipulating the low pass filter 315 that could be used instead. The particular choice of algorithm is not critical.

[0049] Referring to FIG. 3, the Heading (yaw, psi) and Elevation (pitch, theta) angles are extracted from the attitude integration module 225 and fed into low pass filter 315 which filters out unwanted high frequency components. Time derivatives of Elevation (pitch) angle,

[00003]$\frac{\partial \theta }{\partial t}$

and Heading (yaw) angle,

[00004]$\frac{\partial \psi }{\partial t}$

are calculated by time-derivative module 320 and the ratio of these time derivatives is calculated in Ratio module 325. The ratio is output as the roll angle error (φ.sub.error) 330.

[0050] The φ.sub.error parameter 330 is then used to estimate the Roll Rate Scale Factor error in the following manner: [0051] 1. A time interval, Δt, is determined by the Control function 350; the time interval is set in accordance with the dynamic characteristics of the host platform and can vary from the IMU data sample rate up to an extended period of many seconds. [0052] 2. The change in the φ.sub.error parameter is computed over the time interval Δt by Difference module 355. [0053] 3. The corrected Roll Rate measurement 360 (i.e. the raw gyro rate output 210 corrected by the scale factor adjustment module 358) is integrated by Integration module 365 to estimate the total subtended Roll angle over the time interval Δt. [0054] 4. The ratio of these two derived parameters is calculated in ratio module 370 and is used as an estimate for the residual Scale Factor error δφ.sub.error/∂{dot over (φ)}dt at the end of the time interval Δt. [0055] 5. A Gain factor 372 (κ), normally <1, is applied to ensure overall stability. [0056] 6. Successive residual Scale factor error estimates are accumulated by Summing module 375 to form the total Scale Factor error estimate. [0057] 7. The total Scale Factor error estimate is applied as a correction to the Roll Rate measurement by scale factor adjustment module 358.

[0058] This process applies improved techniques and achieves improved performance by providing the ability to calibrate the Roll Rate Scale Factor error under prolonged high roll rate conditions and from early in the flight trajectory. The process results in a more accurate and earlier correction to the IMU Roll axis Scale Factor error. Additionally this process has no reliance upon a full navigation solution (e.g. it is not reliant on linear accelerometers) and can be applied to simpler guidance applications and rate-only IMUs, thus saving on cost and simplifying implementations.