GB2039674A

GB2039674A - Heading reference apparatus

Info

Publication number: GB2039674A
Application number: GB7941524A
Authority: GB
Original assignee: Litton Systems Inc
Current assignee: Northrop Grumman Guidance and Electronics Co Inc
Priority date: 1978-11-30
Filing date: 1979-11-30
Publication date: 1980-08-13
Also published as: JPS5575612A; CA1131053A; DE2947863A1; FR2443048B1; FR2443048A1; IT1120047B; DE2947863C2; GB2039674B; IL58674A; IT7950925A0

Abstract

Automatic heading reference apparatus including two angular rate sensors such as two-degree-of-freedom gyroscopes (10, 12) and at least two accelerometers (16,15) mounted on a turntable (22) on a vehicle (30). The turntable (22) can be positioned about a vehicle vertical axis (24) in one or the other of two positions 180 degrees apart for alignment. After alignment, the turntable is caged into its zero degree position, and the instruments thereafter operate in a strap-down mode with the yaw, roll and pitch angles of the vehicle computed by computer mechanisms which are sensitive to signals from the gyroscopes and accelerometers. The outputs of the gyroscopes and accelerometers are read in the zero degree position. The turntable is then turned through 180 DEG and they are re-read. Adding and subtracting the readings in these two positions gives sum and difference signals which are related to the angles between vehicle-fixed and earth-fixed co- ordinates and the bias errors and scale factors of the rate sensors and accelerometers. <IMAGE>

Description

SPECIFICATION Automatic heading reference apparatus This invention pertains to automatic heading reference apparatus utilizing gyroscopes and accelerometers strapped down to a supporting vehicle and computing means to produce signals in earth-fixed coordinates.

Previously known reference apparatus require an external heading reference, usually magnetic, to establish and maintain heading, the accuracy being limited to that of the external source. Prior art inciudes: (1) A platform is supported on gimbals relative to the vehicle, and the platform is held locally level by signals from gyroscopes and accelerometers.

(2) A signal gyroscope is used and is suspended on gimbals with its spin axis vertical or horizontal. It is held in place, and its output signals are used to produce usable signals.

(3) Angular rates are supplied indirectly through gimbal resolvers.

According to one aspect of the invention there is provided a heading and attitude reference system for use in a vehicle having pitch, roll and yaw axes designated x, y and z, respectively, comprising: a turntable mounted for rotation about the z axis of said vehicle including means for positioning said turntable in a predetermined zero degree position and means for turning said turntable from said zero position into its 180 degree position; at least two angular rate sensors mounted on said turntable with their sensing axes parallel to x, y and z; at least two accelerometers mounted on said turntable with their sensing axes parallel to x andy; means for initially storing signals from said rate sensors and accelerometers when said vehicle is substantially stationary and said turntable is in its zero position;; means for controlling the turning of said turntable from its zero degree into its 180 degree position; means for combining signals from said rate sensors and accelerometers when said turntable is in its 180 degree position with said stored signals to produce sum and difference signals; and means for combining said sum and difference signals to produce accelerometer and rate sensor initial bias signals, rate sensor scale factor signals, and signals indicative of the initial attitude angles between said x, y and z axes and a reference set of coordinates.

A preferred embodiment uses a turntable which is pivoted for rotation about a yaw or azimuth "Z" axis in a vehicle, the turntable being motor driven between a predetermined zero degree position and a 180 degree position by a motor and gear drive. Detents at the zero and 180 degree positions precisely position the turntable. Positioned upon the turntable are two two-degree-of-freedom gyroscopes and at least two accelerometers. The gyroscopes are aligned to generate angular rate signals about andy axes normal to the z axis and about the z axis. The accelerometers are aligned to measure acceleration in the direction of the x and y axes. Optionally a third accelerometer measures acceleration along the z axis.

Gyroscope biasing errors and the initial tilt of the gyroscopes relative to gravity are first determined by measuring the outputs of the sensors of the gyroscopes and the accelerometers first in a zero, then in a 180 degree rotation, with the turntable first in the zero then in the 180 degree position.

After initial alignment, the outputs of the gyroscope and accelerometer sensors are delivered to computing means to substract out errors in the signals and to resolve the signals into earth coordinates. The resolved signals may then be used either by an operator or an autopilot to control a vehicle such as a helicopter, airplane, tank or truck.

It is therefore possible to produce signals which are measures of angular rate and angular position of a vehicle relative to an earth-fixed set of rectangular coordinates, e.g. where the earth-fixed set of co-ordinates are north-south, east-west and vertical.

According to a second aspect of the invention there is provided an apparatus comprising a strapped down set of rate sensors for producing angular rate signals, wherein there are means for compensating said signals to eliminate signals of earth's rate components and means for removing bias errors from said signals.

According to a third aspect of the invention there is provided a method for determining the initial angular orientation of a Cartesian set of rate sensor and accelerometer axes relative to a set of reference axes and for determining the bias errors of said rate sensors and acclerometers, comprising:: positioning the sensing axes of said rate sensors and accelerometers in a first predetermined position designated zero degrees and reading the outputs of said gyroscopes and accelerometers; turning said rate sensors and accelerometers 180 degrees about one instrument axis; re-reading the output signals of said rate sensors and accelerometers; adding and subtracting the output signals in the 180 degree position to and from said signals in the zero degree position to obtain sum and difference signals which are related to the angles between the two sets of coordinates and the bias errors and scale factors of the rate sensors and accelerometers.

For a better understanding of the invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 shows a plan view of a turntable mounted for rotation about one axis relative to a vehicle and the gyroscopes, accelerometers and temperature sensor mounted thereon; Figure 2A is a schematic diagram of an alternative embodiment of the invention; Figure 2B is a schematic diagram of a preferred embodiment of the invention; Figures 3A, 3B and 3C show a schematic rotation of coordinates through a set of Euler angles; Figure 4 is a block diagram of a timer used in this invention during alignment; Figure 5 is a block diagram of means for producing initial bias signals and acceleration signals for the x and y accelerometers;; Figure 6 is a block diagram of means for producing initial ss andy signals; Figure 7 is a block diagram of means for producing an initial gyroscope biasing signal for one gyroscope; Figure 8 is a means for producing a scale factor signal for the z axis sensor on one of the gyroscopes; Figure 9 is a means for producing sum and difference signals for the two gyroscopes in different turntable positions during alignment; Figure 70 is a means for producing a signal of the value of a during alignment; Figure 7 7 is a means for producing a compensated signal of the angular rate signal about the x or y axis; Figure 12 is a means for producing a compensated signal of the acceleration of the vehicle along its x or y axis;; Figure 13 is a means for producing updated signals for interchanging signals between vehicle oriented coordinates and earth-fixed coordinates; Figure 14 is a mechanization for producing compensated a, (3 andy signals using the apparatus of Figure 13; and Figure 15 is a block diagram of the cut-out logic of Figure 14.

The apparatus of the invention comprises two two-axes angular rate sensors 10, 12 such as two-degree-of-freedom gyroscopes, each for generating angular rate signals which are measures of angular rate about two perpendicular axes. At least two, and preferably three, lineal acceleration measuring devices, 16, 18,20 such as accelerometers for generating signals which are measures of lineal acceleration, are positioned with their sensing axes forming an orthogonal set of axes. The rate sensors 10, 12 and accelerometers 16, 18,20 are fixedly mounted on a turntable 22 having a rotation axis 24. The accelerometers 16, 18, 20 are positioned with the sensing axis of accelerometer 20 defining a axis parallel to the axis 24.The sensing axes of each of the angular rate sensors 10,12 are parallel to the sensing axes of accelerometers 16, 18 and 20.

The turntable 22 can be turned about the axis 24 relative to the supporting vehicle 30. The periphery of the turntable 22 has gear teeth 32 thereon to engage a spur gear 34 which is driven by a motor 33. Detents 36,38 are positioned on opposite ends of a diameter of the turntable 22. A flexible pawl 40 has a roller 42 on the end thereof to roll on the periphery of the turntable 22 and to fit into the V-shaped detents 36,38 to hold the turntable in each of two precisely aligned positions 180 degrees apart. A raised tab 44 engages micro-switches 46,48 to stop the drive motor 33 of spur gear 34 when the roller 42 engages the detents 36, 38.

A right-handed set of orthogonal axes is defined in the vehicle30 with the z axis coinciding with axis 24.

Customarily the x, y and z axes are called the pitch, roll and yaw axes of the vehicle.

The sensing axes of the gyroscopes 10, 12 and the accelerometers 16, 18,20 are initially oriented as shown in Figure 2B.

The sensing axis wzio is parallel to the z axis. With the turntable 22 as shown, its spin axis SA10 and its other sensing axis xio are parallel to they and x axes respectively.

The sensing axis '12 is parallel to the z axis. With the turntable 22 as shown, its other sensing axis wry12 and its spin axis SA12 are parallel to they and x axes, respectively.

In an alternative embodiment (shown in Figure 2A), the spin axis SA12 is parallel to the z axis. With the turntable in a first position, its sensing axes (1)x12 and (1)y12 are parallel to the x and y axes, respectively.

With the turntable positioned as shown in Figures 2B and 2A, the accelerometer 16 senses acceleration Ax in the x direction, and the accelerometer 12 senses acceleration Ay in they direction, and the accelerometer 20 senses acceleration Az in the z direction.

A symbol over another symbol indicates that the other symbol represents a measured signal.

The x, y, z or pitch, roll and yaw axes of the vehicle do not, in general, coincide with the E-W, N-S and local vertical directions. To change measured signals in the vehicle coordinate system into components in a second set of coordinates, one may transform through a set of Euler angles. The Euler angle transformation is shown in Figures 3A, 3B and 3C. The first Euler angle rotation of coordinates, shown in Figure 3A, is about the z axis through an angle a to define a first intermediate right handed set of orthogonal coordinates x', y' and z. The second Euler angle rotation of coordinates, shown in Figure 3B, is about the x' axis through an angle B to define a second intermediate right handed set of orthogonal coordinates x', y", z". The third Euler angle rotation of coordinates, shown in Figure 3C, is about the y" axis through an angle y to define the right handed set of orthogonal coordinates x"', y", z"' which correspond to the directions, east, north and vertical.

The transformation between the x, y, z axes and the x"', y", z"' axes is a matrix [ T ] made up of sines and cosines of a, (3 andy.

Thus:

fi Wyt = {Fi1 {{Hj (1) Where #x, #y, o)z are signals which are measured by either rate sensor 10 or 12. QH is the horizontai, north-directed, y"' component of the earth's rotation rate, and Qv is the locally vertical z"' component of the earth's rotation rate.Equation (1) may also be written:

O #x ##H# = [P] ##y# (1A) #Y #z Similarly the measured accelerations âx, ay, âz may be transformed from one coordinate system to the other.

aE-W âx #aN-S# = [p] #ây# (2) aV âz It is convenient to express the accelerations in units of "g", the acceleration of gravity.

When the equations are transformed with the turntable 22 in its zero degree position and the supporting vehicle 30 at rest âxo = -Cos ss Sin γ + Bx (3) âyO = Sin ss + By (4) a20 = Cos ss Cos y + Bz (5) where Bx, By, Bz are the bias errors of the accelerometer.

When the turntable is turned to its 180 degree position, and the vehicle 30 still at rest, âx180 = Cos ss Sin γ + Bx (6) ây180 = -Sin ss + By (7) âz180 = Cos ss Cos γ + Bz (8) Taking the differences of equations (3) and (6) and of equations (4) and (7), # âx = -2 Cos ss Sin γ; (9) Aay = 2Sin(3 (10) Taking the sums of equations (3) and (6) and equations (4) and (7), # âx = 2Bx (11) # ây = 2 By (12) One may then determines and (3from equations (9) and (10),

From equations (11) and (12), Bx and Bx may be determined #âx Bx = (15) 2 #ây By = (16) 2 From equations (5) or (8) Bz=âzo (or âz180) -Cos ss Cos γ (17) Where the @# symbol means an estimated signal.

With the turntable 22 in its zero degree position, the gyroscopes 10 and 12 measure, x100 = (Cos α Sin ss Sin γ + Sin α Cos γ) #H (18) - (Cos ss Sin γ) #v -Mx10 Cos ss Sin γ + #x10 Cos ss Cos γ -Ax10 Sin ss Cos ss Sin γ + #x10 #y120 = (Cos αCos ss) #H + (Sin ss) #v + My Sin ss + #y12 Cos ss Cos γ -Ay12 Sin ss Cos ss Sin γ + #y12 #z100 = (Sin α Sin γ -Cos α Sin ss Cos γ) #H + (Cos ss Cos γ)#v + Mz10 Cos ss Cos γ - #z10 Cos ss Sin γ + Az10 Sin ss Cos ss Cos γ + E210 #z120 = (Sin αSin γ -Cos α sin ss Cos γ) #H + (Cos ss Cos γ) #v + Mz12 Cos ss Cos γ + #z12 Sin ss -Az12 Cos2 ss Sin ss Cos γ + #z12 Where M is a mass unbalance drift coefficient for mass unbalance of the designated gyroscope 10 or 12 in the direction of the designated axis.

A is the anisoelastic drift coefficient due to the anisoelasticity of the designated gyroscope 10 or 12 coupling into the quadrature; Q is the quadrature drift coefficient which occurs only in a dry tuned rotor gyroscope due to mass unbalance about the designated axis; E is the non-acceleration sensitive drift error in the gyroscope about the designated axis.

With the turntable 22 in its 180 degree position, #x10180 = -(Cos α Sin ss Sin γ + Sin α Cos γ) #H + (Cos ss Sin γ) #v + Mx10 Cos ss Sin γ + #x10 Cos ss Cos γ -Ax10 Sin (3Cos (3 Sin y + #x #y12180 = -(Cos αCos ss) #H - (Sin ss) #v - My12 Sin ss + #y12 Cos ss Cos γ -Ay12 Sin ss Cos ss Sin γ + #y12 #z10180 = (Sin α Sin γ -Cos α Sin ss Cos γ) #H + (Cos ss Cos γ) #v + Mz10 Cos ss Cos γ + #z10 Cosss Sin γ -Az10 Sin ss Cos ss Cos γ + eZ10 #z12180 = (Sin αSin γ -Cos α Sin ss Cos γ) #H + (Cos ssCos γ) #v + Mz12 Cos ss Cos γ - #z12 Sin ss + Az12 Cos2ss Sin γ Cos γ + ez12 Taking the differences and sums of equations (18) and (22) and equations (19) and (23), ##x10 = 2 (Cos α Sin ss Sin γ + Sin α Cos γ) #H - 2 (Cos ss Sin γ) #v - 2Mx10 Cos ss Sin γ ##x10 = 20x10 Cos ss Cos γ - 2Ax10 Sin ss Cos ss Sin α + 2#x10 ##y12 = 2 (Cos a Cos ss) #H + 2 (Sin (3)Qv + 2M,12Sin(3 ##y12 = 2 #y12 Cos ss Cos γ - 2 Ay12 Sin ss Cos ss Sin γ + 2#y12 Combining equations (26) and )28)

It should be noted that the gyroscope drift coefficients Q and A do not appear in equation (30) because they have cancelled in the difference equations (26) and (28).Also note that M x10 and My12 are for different gyroscopes, and errors in knowledge of the values are expected to be uncorrelated so that their effects on the estimate of a is in a Root Sum Squared sense rather than a direct sense.

The drift parameters of the gyroscopes may be estimated from equations (27) and (29).

Take the sum of equations (20) and (24) and of equations (21) and (25).

##z10 = 2 (Sin α Sin γ - Cos α Sin ss Cos γ) #H + 2 (Cos ss Cos γ) #v + 2 Mz10 Cos ss Cos γ + 2E210 ##z12 = 2 (Sin α Sin γ - Cos α Sin ss Cos γ) #H + 2 (Cos ss Cos α) #v + 2 Mz12 Cos ss Cos γ) + 2E212 From which estimates of the drift terms can be made.

Since the instruments are rotated through a known angle of 180 degrees about the z axis, the scale factor for #z10 and #z12 may be estimated.

where #z10 = a210 (t) due to earth rate +##(t) and # TT(t) is the rate of rotation of the turntable 22 about the z axis during rotation from zero to 180 degrees.

Assume ##(t) is a constant ## (by making gear 34 turn at a constant speed).

and the scale factor may be estimated

Similarly

Note that the preferred orientation also provides two sources of "azimuth" body rate (a) measurements about the z axis, thereby permitting averaging or optimally mixing or even selecting to improve performance. This is important because the azimuth angle (a) is not readily bounded as the pitch and roll angles may be by use of the x andy accelerometers 16 and 18.

Alignment with the alternate gyroscope orientation of Figure 2A is now considered.

The acceleration measurements are the same as in equations (3) through (8), and the difference and sum of equations (9) through (12) are the same. Equations (13) through (17) are also the same.

For the zero degree position of the turntable 22, #x120 = (Cos α Sin ss Sin γ + Sin α Cos γ) #H - (Cos ss Sin γ) #v - Mx12 Cos ss Sin γ + #x12 Sin ss + Ax12 Sin ss Cos ss Cos γ + #x12 #y120 = (Cos α Cos ss) #H + (Sin ss) #v + My12 Sin ss - #y12 Cos ss Sin γ -Ay12 Cos2 ss Sin γ Cos γ; + #y12 The equations for #x100 and #z100 are the same as equations (18) and (20), respectively.

When the turntable 22 is turned to the 180 degree position.

#x12180 = - (Cos a Sin ss Sin γ + Sin a Cos γ) QH + (Cos ss Sin γ)#v + Mx12 Cos ss Sin γ - #x12 Sin ss - Ax12 Sin ss Cos ss Cos γ + #x12 #y12180 = - (Cos α Cos ss) #H - (Sin ss) #v - 2My12 Sin ss + #y12 Cos ss Sin γ + Ay12 Cos2 ss Sin γ Cos γ + #y12 The equations for #x10180 and #z10180 are the same as equations (22) and (24), respectively.

Forming the sum and difference equations from equations (40) and (42) and equations (41) and (43).

Assx12 = 2(CosaSinBSiny+ SinaCosy)gH - 2 (Sin 13 Sin y) #v - 2 Mx12Cos ss Sin y + 2 #x12 Sin ss + 2Ax12 Sin ss@@ Cos ss Cos γ ##x12 = 2#x12 ##y12 = 2 (Cos α Cos ss) #H + 2 (Sin ss) #v + 2My12 Sin ss - 2 #y12 Cos ss Sin γ - 2 Ay12 Cos2 ss Sin γCos γ ##y12 = 2#y12 Using equations (44) and (46), an estimate of azimuth angle (a) about the z axis is made:

Similar gyroscope bias drift estimates may be made from equations (45) and (47) ##x12 #x12 = ##y12 # = Ey12 2 Equation (33) is also valid for this mechanization.

An estimate for Kzl2 can also be made as in equation (39).

Note from equation (48) that this second configuration produces error terms which could become important during alignment when pitch and roll angles ss and y become significant (for example, greater than six degrees). Also note that only one gyroscope 10 measures a, but two gyroscopes 10 and 12 measure ss.

Hence in this embodiment errors in a cannot be reduced by combining or selecting, but errors in ss can be reduced by combining. However, this redundancy features is not important in P because the accelerometers can produce an independent measure of ss.

The above equations and description implement the alignment of the apparatus of this invention.

It is likely, in a preferred embodiment of the invention, that a general purpose digital computer or processor would be used to receive the output signals of the gyroscopes and the accelerometer. Those output signals would either be in digital form or be converted to digital form. The computer would then produce output signals, probably in digital form.

For purposes of explanation the computer functions have been shown in Figures 4-15 in block form. One may consider the blocks to be portions of a general purpose computer, software for a computer, or an analog computer.

Figure 4 shows a timer 59 which may be started with a start signal or energized from a switch. Initially, the timer should enable the turntable motor to place the turntable 22 in its zero degree position and enable the computers of Figures 5 and 9 to store the output signals of the gyros and accelerometers in the storage memories 60, 62. The timer 59 then sends a signal to the turntable motor to index the turntable 22 into its 180 degree position. The timer 59 then enables the storage memories 60, 62 to deliver their stored signals to the various summers 64, 66, 68, 70, 72, 74, 76, 78, 80, 82 for adding or subtracting the outputs of the sensors on the gyroscopes 10, 12 and the accelerometers 16, 18,20. The sum and difference signals of Figure 5 are then stored in storage memories 84,86,88,90 for future use.The outputs of summers 72,74,76,78,80,82, if desired, also may be entered into storage (not shown).

Equations (13) and (17) are mechanized in Figure 6 The #ay/2 input is obtained from Figure The a20 is obtained from the memory 60 of Figure 5. The B signal is delivered by an adder 92 receiving LaY/2 signals from memory 90 and sin (3signals from sin generator 94. The output of the adder 92 is then integrated by integrator 96 to produce the ss signal. Sin ss and cos ss signals are then produced by sin generator 94 and cos generator 98.

taX/2 is divided by cos through a divider 100, and the resultant signal is delivered to an adder 102. The adder 102 also receives input from sin generator 104. The output of adder 102 is integrated by integrator 106 to produce outputsignal y. They signal is delivered to sin generator 104 and cos generator 108 to produce sin y and cos y signals.

Cos generators 98 and 108 are connected into multiplier 110 with adder signal 112.

The output signal ssz is stored by memory 114.

In Figure 7 the costs sin ss and cos y outputs of Figures 6 and 10 are connected into multiplier 116 whose output is connected into adder 118. The sin a input to multiplier 120 is obtained from sin generator 122 of Figure 10. The sin y input to multiplier 120 is from sin generator 104 of Figure 6. The output of multiplier 120 is subtracted in summer 118.

For a given latitude, known a priori, at the position of alignment, one can generate a signal proportional to the horizontal component of earth's rotation at that latitude. The signal is then delivered to multiplier 124 where it is multiplied by the output of adder 118. The adder 126 receives the output of multiplier 124, the output of multiplier 128 and the output of adder 80 of Figure 9 to mechanize equation 33. The cos ss and cos y inputs to multiplier 128 are obtained from Figure 6. The , input to multiplier 128 is the calculated vertica I component of earth's rotation for the particular known latitude where the alignment occurs.

Equation 34 may be mechanized the same as equation 33.

Figure 8 mechanizes equation (38), and equation (39) may be mechanized in a similar fashion. The output of adder 80 of Figure 9 is delivered to an adder 130. A signal which is a measure of the known angular velocity of turntable 22 is added into adder 130. The output of adder 130 is divided into joe by the divider 132 to produce aKzO signal.

Figure 10 mechanizes equation 30. The sin ss, cos ss, sin y, cos y inputs are from Figure 6. The Qv input is known from knowledge of local latitude atthe initial calibration position. The Mx10, Mya2, inputs are known constants of the gyroscopes. The "'Y12/2 212 and the ##x10/2 inputs are from Figure 9. The sin ss, cos ss terms are delivered to divider 134 to produce a tan (3 signal. The tan ss signal is multiplied in multiplier 136 by the sin y signal. The output of multiplier 136 is delivered to adder 138.

The MX,0 and Q v signals are added in adder 140 and the sum signal is delivered to multiplier 142 where it is multiplied by cos ss and sins. The output of multiplier 142 is added in adder 144to 8' X10/2. The output of adder 144 is delivered to divider 146.

The My,2 and #y signals are added in adder 147 and the sum signal is delivered to multiplier 149 where it is multiplied by sin (3. The output of multiplier 149 is added, in adder 152, to ' v12/2, and the sum signal is delivered to divider 146. The output of divider 146 is delivered to adder 138 and thence to multiplier 148. A cos (3over cos signal is produced in divider 150. The signal from 150 is delivered to multiplier 148, and the output of multiplier 148 is delivered to multiplier 152.

A tan a signal is delivered by tan generator 154 toadder 152. The output of adder 152 is integrated by integrator 156 to produce an a signal. Tan a and sin a signals are produced by tan generator 154 and Sin generator 122, respectively.

Figures 11-15 are mechanizations of the heading reference of this invention in its operative mode.

Figure 11 shows a typical computer which continuously removes various E, Q, A and M bias errors from the output signals of the gyroscopes. #x is an output from a gyroscope 10 sensor. The Ks, is a computer scale factor which is known. The temperature sensor 50 adjacent to the gyroscopes and accelerometers produces a temperature signal which modifies the scale factor in a known way. These signals are delivered to multiplier 160, and the produced signal is delivered to adder 162.

A temperature sensitive correction factor is delivered from multiplier 164 to adder 162. The ax is delivered from a circuit substantially identical to Figure 12 but with ax and Bx inputs. Mx is known, and the temperature signal comes from sensor 50.

The multiplier 166 receives known signals Ax10, #x10 E which are known contants of gyroscope 10.

The ax and by signals come from circuits like Figure 12. The B and y signals are updated pitch and roll angle signals from Figure 14. Multiplier 166 has a multiplying factor which is temperature sensitive in a known function of temperature.

The initial bias corrections of equation (27) during alignment, from Figure 9, are added in adder 168 from the updated signal output of multiplier 166. Storage means (not shown) may be needed to hold the signal of Figure 9.

The output of adder 168 is subtracted in adder 162 to produce e x signal which is the sum of the component of earth rate about the x axis and the relative angular rate about the x axis.

A circuit similar to that of Figure 11 also may be used to calculate #y and oz.

There is a circuit like Figure 12 for each x, y accelerometer channel. The accelerometer signal is delivered to a temperature sensitive multiplier 170. The scale factor KSF is known, and temperature signals are received from sensor 50. Bias signals such as By are delivered from Figure 5 to a temperature sensitive multiplier which receives temperature signals from sensor 50. The outputs of multipliers 170, 172 are added in adder 173 to produce an ay signal which has a component due to gravity unless ss = 0, plus a true acceleration signal.

Figures 13 and 15 are portions of Figure 14.

In Figure 13, the known latitude signal (which may be obtained by any technique) is delivered to sin and cosine generators 174 and 176. An # signal proportional to earth rotation is also delivered to generators 174, 176. The Q sin Q and # cos Q outputs of generator 174, 176 are delivered to sin, cos matrix mechanization 178. The mechanization 178 mechanizes three equations having sines and cosines therein and represented by a matrix [P]T. The matrix [PiT terms are delivered from time delay block 190. The outputs of mechanization 178 are Qx, Qy and #2 signals, the components of earth's rotation about axes x, y, z.The outputs of 178 are delivered to adders 182, 184, 186 where they are subtracted out of the sensed signals Wx, Wy, o, from Figure 11. The corrected signals are delivered to the matrix updating mechanism 188 which updates the information in matrix mechanization blocks 178 and 180. The block 180 mechanizes matrix equation [P] and block 178 mechanizes [PiT.

The up-dating block 188 receives [PI signals from block 190 and performs matrix multiplication as indicated in block 188 to produce an updating increment for each term of [P] and [PiT. The incremental output of block 188 is added to [P] in adder 192. The output of adder 192 is time delayed by 190, and the updated matrix terms are delivered to blocks 178, 180 and 188.

Blocks 194,196,198 of Figure 14togetherform Figure 13. The adders 182, 184, 186 correspond to the same adders in Figure 13, and the outputs a, (3,t' from the Euler angle resolver 206 Figure 13 correspond to the same outputs in Figure 14.

Additional feedback circuitry to adders 182, 184 to stabilize the mechanization is shown in Figure 14. The feedback loops, in turn may be cut out in accordance with logic built into blocks 200, 202. That logic is shown in Figure 15.

In Figure 14 the (3 signal is delivered to the cut out logic 200. and the r signal is delivered to logic 202.

Signal ay has subtracted therefrom in adder 210 a gravity component g sin ss from sin generator 212 which, in turn receives a ss signal from block 194. The output of adder 210 is delivered to logic 200 and to adder 214.

The output of adder 214 is integrated by integrator 216 and a part of the output signal is fed back through scaler 218 to adder 214. The output of integrator 216 is further scaled by scaler 222 and fed back through cutout switch 220 to adder 182.

The ss output of 194 is delivered through a cos generator 230 to a multiplier 232. The γ outout of block 196 is delivered through (g times) sin generator 234 to the multiplier 232. The output of multiplier 232 is a gravity term which is subtracted in adder 236 from the signal ax. The output of adder 236, labelled baX, is delivered to cut out logic 202 and to adder 238. The output of adder 238 is integrated by integrator 240, and the output is scaled by scaler 242 and fed back to adder 238.

The output of integrator 240 is also scaled by scaler 244 to deliver a scaled feedback signal through cut out switch 246 to adder 184.

The "z10 and "Z12 outputs are added by adder 186 to 2Qz, and the output is multiplied by 1/2 in multiplier ~ 250 to produce an averaged signal which is delivered to block 198, which is part of Figure 13, to produce an a signal.

The cut out logic is shown in Figure 15. The symbols (3oL òaXOLs yOL and hayOL are predetermined thresholds at which the various loops open.

The symbols (3cL (haXcLf YCL and òayCL are thresholds at which the loops re-close, and they are slightly lower than the corresponding open loop thresholds to prevent relay chattering.

In summary the apparatus of this invention is a heading and attitude reference unit which uses strapped down gyroscopes together with accelerometers to generate accurate vehicle attitude and heading as well as vehicle angular rates.

It should also be noted that the particular errors due to M, Q, A and E are peculiar to dry tuned flexure suspended rotor gyroscopes. Other kinds of gyroscopes as well as other angular rate sensors could be used.

For example, nuclear magnetic resonance gyroscopes and laser gyroscopes could be used. Other kinds of gyroscopes and rate sensors would, of course, have their own error sources and those error sources could be identified by the initial sensing with the turntable first in one position then turned 180 degrees.

Although the invention has been described in detail above, it is intended that the invention shall not be limited by that description alone but in combination with the appended claims.

Claims

1. A heading and attitude reference system for use in a vehicle having pitch, roll and yaw axes designated x, y and z, respectively, comprising: a turntable mounted for rotation about the z axis of said vehicle including means for positioning said turntable in a predetermined zero degree position and means for turning said turntable from said zero position into its 180 degree position; at least two angular rate sensors mounted on said turntable with their sensing axes parallel to x, y and z; at least two accelerometers mounted on said turntable with their sensing axes parallel to x and y; means for initially storing signals from said rate sensors and accelerometers when said vehicle is substantially stationary and said turntable is in its zero position; means for controlling the turning of said turntable from its zero degree into its 180 degree position;; means for combining signals from said rate sensors and accelerometers when said turntable is in its 180 degree position with said stored signals to produce sum and difference signals; and means for combining said sum and difference signals to produce accelerometer and rate sensor initial bias signals, rate sensor scale factor signals, and signals indicative of the initial attitude angles between said x, y and z axes and a reference set of coordinates.

2. Apparatus as recited in Claim 1 in which said means for combining said sum and difference signals comprises: means for producing a signal which is a measure of the initial pitch angle in response to the said difference signal of the said y axis accelerometer; means for producing a signal which is a measure of the initial roll angle in response to said pitch angle signal and said difference signal of said x axis accelerometer; means for producing a signal which is a measure of x axis accelerometer bias in response to said sum signal of said x axis accelerometer; means for producing a signal which is a measure of y axis accelerometer bias in response to said sum signal of said y axis accelerometer;; means for producing a signal which is a measure of the initial drift parameters about the x axis of a first said rate sensor in resonse to said sum signal of rotation rate of said first rate sensor about the x axis and to signals which are a measure of earth rate; means for producing a signal which is a measure of the initial drift parameters about they axis of a second said rate sensor in response to said sum signal of that second said rate sensor about the y axis and to said earth rate signals;; means for producing a signal which is a measure of the initial yaw angle in response to said roll and pitch angle signals, to said difference signals of the angular rate about the x axis of one said rate sensor and of the angular rate about they axis of the other said rate sensor, to a signal which is a measure of a component of angular velocity due to earth's rotation, and to signals which are measures of the acceleration sensitive drift coefficient of both said rate sensors; and means for producing a signal which is a measure of the initial drift rate of said rate sensors about the z axis in response to said pitch, roll and yaw signals, to said component of earth's rate signal, and to said sum signals of the angular rate of each respective rate sensor about its z axis.

3. Apparatus as recited in claim 2 and further comprising means for producing a signal which is a measure of the scale factors about the z axis of said rate sensors in response to signals which measure the rotation of said turntable, and said sum signals about the z axis of rate sensors.

4. Apparatus as recited in claim 3 in which said signals are responsive to instrument temperature and further comprising means for generating a temperature signal and for modifying said other signals in response to said temperature signal.

5. Apparatus recited in claim 4 and further comprising means for storing said signals for use during the operative mode of said apparatus.

6. Apparatus as recited in claim 5 and further comprising: means for continuously modifying the angular rate signal about said x axis from said first rate sensor to remove instrument drift rate errors; means for continuously modifying the angular rate signal about said y axis from said second rate sensor to remove instrument drift rate errors; means for resolving earth's rate signals into components about said x, y and z axes; means for substracting said earth's rate signal components from the respective modified angular rate signals;; means for producing direction signals which are measures of the rotation of said instruments about said reference coordinate axes including means responsive to said initial pitch, roll and yaw angle signals, continuously to update means for producing direction signals, and means for resolving said updated signals to produce updated pitch, roll and yaw angle signals.

7. Apparatus as recited in Claim 6 and further comprising feedback means for bounding errors in the pitch and roll angle signals.

8. Apparatus as recited in Claim 7 in which said bounding signals are pitch and roll signals obtained in response to said accelerometer signals.

9. Apparatus as recited in Claim 8 and further comprising logic means for selectively disconnecting and reconnecting said bounding signals in response to the magnitude of said pitch and roll angles and to vehicle acceleration signals.

10. Apparatus as recited in Claim 9 in which said bounding means is disconnected in said x channel in response to either the pitch angle signal or they axis vehicle acceleration signal exceeding predetermined thresholds; said bounding means is disconnected in said y channel in response to either the roll angle signal or the x axis vehicle acceleration signal exceeding predetermined thresholds; said x channel bounding means is reconnected in response to both the pitch angle signal and they axis vehicle acceleration signal being below predetermined thresholds; and said y channel bounding means is reconnected in response to both the roll angle signal and the x axis vehicle acceleration signal being below predetermined thresholds.

11. An apparatus comprising a strapped down set of rate sensors for producing angular rate signals, wherein there are means for compensating said signals to eliminate signals of earth's rate components, and means for removing bias errors from said signals.

12. A method for determining the initial angular orientation of a Cartesian set of rate sensor and accelerometer axes relative to a set of reference axes and for determining the bias errors of said rate sensors and accelerometers, comprising: positioning the sensing axes of said rate sensors and accelerometers in a first predetermined position designated zero degrees and reading the outputs of said gyroscopes and accelerometers; turning said rate sensors and accelerometers 180 degrees about one instrument axis; re-reading the output signals of said rate sensors and accelerometers; adding and subtracting the output signals in the 180 degree position to and from said signals in the zero degree position to obtain sum and difference signals which are related to the angles between the two sets of coordinates and the bias errors and scale factors of the rate sensors and accelerometers.

13. A heading and attitude reference system substantially as hereinbefore described with reference to the accompanying drawings.

14. A method for determining angular orientation substantially as hereinbefore described with reference to the accompanying drawings.