Arrangement for determining the instantaneous angular position of a moving object

A simple accurate arrangement for determining the instantaneous angular position of a moving object comprises rotation acceleration sensors located in reference axes of the article. Because of the double integration, the low-frequency static angular signal obtained is not reliable so that a device for measuring the static angle is used which supplies these values accurately, it is true, but which is not reliable in high-frequency respects. A correct angular signal is obtained by filter circuits and mixing. A piezoelectric element is used in the rotation acceleration sensor, while the device for measuring the static angle is an electrolytic leveling instrument.

This invention relates to an arrangement for determining the instantaneous 
angular position of a moving object in which the angle between a reference 
plane in the object and a vertical plane coinciding with the direction of 
the force of gravity is determined, for which purpose a rotational 
acceleration sensor is arranged in the line of intersection of the two 
planes. The sensor is connected to determine the high-frequency components 
in an angular signal proportional to the angle to be measured for feed to 
a first processing circuit comprising a first integrator connected to a 
first input of a second integrator provided with a second input, while the 
arrangement comprises a second sensor which is connected to determine the 
low-frequency components in the angular signal for feed to a second 
processing circuit, in which a low-pass filter is included. The 
arrangement further comprises a summation circuit for summing the 
low-frequency and high-frequency components so that an output of the 
arrangement delivers the said angular signal. 
A determination of the angular position of an object, such as a vehicle, a 
vessel or an aeroplane, is of importance, for example, for stabilizing in 
a horizontal position a platform suspended on gimbals in the object or for 
accurately determining the direction in which the object moves or the 
position in space which the object occupies, for example expressed in 
coordinates. 
An arrangement by which the angular position can be determined is known 
from U.S. Pat. No. 3,824,386. 
With respect to the terrestrial surface, which is generally at right angles 
to the direction of the force of gravity, a rectangular coordinate system 
is assumed and such a system is also defined in the object. By rotation 
about the axes of the latter system, any position in space with respect to 
the terrestrial surface can be obtained. For measuring this rotation, a 
rotation acceleration sensor is arranged in each axis, by which the 
angular velocity and the angle of rotation can be found electronically by 
integrating once and twice in time respectively. However, in a static 
condition in which the angular position does not vary, the integrators 
should be very stable for a long time, which cannot be realized in 
practice. Only the data obtained by the sensor at higher frequencies are 
exact and are consequently very useful. In this known arrangement, it has 
been suggested to use additional sensors which deliver an accurate 
low-frequency static signal value, but which do not deliver, or deliver 
inaccurately, a similar high-frequency value. Thus, two angular 
acceleration sensors and a levelling instrument are used. 
A disadvantage of this arrangement is that several complicated computers 
and various function generators are required. The disadvantage is related 
inter alia, to the fact that rotations about two or three axes mutually 
influence each other because a component of the force of gravity active 
along an axis is influenced by rotations about the other axes. 
The invention is based on the idea that the circuitry can be considerably 
simplified if a sensor for the static angle is used which, at least in a 
given tolerance range, is not dependent upon the rotations about other 
reference axes. For this purpose, the arrangement of the kind mentioned in 
the opening paragraph is characterized in that the second sensor is an 
electrolytic levelling instrument and the second input of the second 
integrator is connected to an output of the second processing circuit. In 
addition, the output of the second integrator is connected to the output 
of the arrangement and to a first input of a comparison circuit included 
in the second processing circuit. A second input of the comparison circuit 
is connected to the low-pass filter which is connected to the electrolytic 
levelling instrument, and an output is connected to the output of the 
second processing circuit. 
Such an arrangement is particularly suitable for use in vehicles in which 
the tilting angle and the elevation angle remain within given limits. 
Advantageously an inexpensive system is obtained which can be used for 
vehicle navigation. The analogue circuitry is very simple, but by means of 
an inexpensive analogue-to-digital converter the analogue sensor signals 
can be digitized and handled in a microprocessor usually already present 
which, in view of the simplicity of the operations required, does not 
require much capacity. 
The electrolytic levelling instrument is known per se and is described, for 
example, in the "Handbook of Transducers for Electronic Measuring 
Systems", 1969, Prentice Hall Inc., Englewood Cliffs N.J., written by 
Harry N. Norton, on pages 155 and 156 and in FIGS. 2-10.

FIG. 1 shows an embodiment of an angle acceleration sensor, such as can be 
used in accordance with the invention. 
On a base plate 1 is secured a supporting bracket 2, in which a shaft 3 can 
rotate resiliently within given limits. The shaft 3 has secured to it 
spacer members 4 and 5, which support cylinders 6 and 7, which produce 
mass inertia. 
The spacer member 4 has secured to it an arm 8, to which a piezo-electric 
strip 9 is mounted. 
The other end of this strip is secured to a block 10 on the base plate 1. 
When the base plate 1 moves so that the shaft 3 performs a rotation about 
the reference axis 11, the strip 9 will bend due to the mass inertia of 
the cylinders 6 and 7 which, as known, produces an electrical charge at 
electrodes provided on the strip, which charge is proportional to the bend 
and hence to the angular acceleration. 
FIG. 2 shows an electrolytic levelling instrument 12 provided with an 
electrolyte 13, a gas bubble 14, a counterelectrode 15 and measurement 
electrodes 16 and 17. The electrolyte resistance between the electrodes 15 
and 16 constitutes with the resistor 18 one branch of a bridge circuit. 
The electrolyte resistance between the electrodes 15 and 17 constitutes 
with the resistor 19 the other branch of the bridge circuit which is 
supplied from a source at terminals 20 and 21. The bridge unbalance is 
measured between the electrodes 16 and 17 by means of an amplifier circuit 
22, which supplies to the output 23 a direct voltage proportional to the 
unbalance and hence to the asymmetry of the electrolyte resistances. This 
asymmetry depends upon the position of the gas bubble 14 and hence upon 
the angle the line 24 of the levelling instrument encloses with the 
vertical line on the terrestrial surface. In the case of an A.C. source 
apply to the bridge circuit, the amplifier circuit 22 comprises further 
rectifier circuits. 
The levelling instrument 12 is not suitable to supply all information about 
the angle of the oblique position because the electrolyte is too mobile 
and will react to lateral forces and fluctuations. However, the levelling 
instrument supplies over a longer time, in which the electrical bridge 
output signal is averaged, correct information about the static angle and 
very slow variations of this angle. 
In FIG. 3, which shows the arrangement according to the invention, a 
low-pass filter 25 is connected to the levelling instrument of FIG. 2. The 
filter consists of resistor 26 connected to the output 23 and a capacitor 
27. This filter 25 forms part of a second processing circuit 28, which 
also comprises a comparison circuit 29. 
The piezeo-electric sensor 9 is connected by electrodes 30 and 31 to a 
charge amplifier 32, which supplies to the input 33 of a first processing 
circuit 34 a voltage proportional to the bend of the sensor strip 9. In 
this first processing circuit 34, the voltage is integrated in a first 
integrator 35 so that a signal proportional to the angular velocity is 
present at the output 36. When used in a vehicle it may be assumed that 
the latter will not rotate at a constant speed about a reference axis so 
that the angular velocity will contain only alternating components which 
can be measured via a high-pass filter. This filter is constituted by a 
capacitor 37 connected in series with a resistor 38, a feedback resistor 
39 and an operational amplifier 40. The angular velocity signal is 
available at the output 41. 
The output 36 is further connected to a first input 42 of a second 
integrator 43 comprising an operational amplifier 44, a capacitor 45 and a 
resistor 46. Due to this second integration, a signal proportional to the 
angle becomes available at the output 47. In fact this angular signal is a 
summation of successive angular rotations from which the angle of the 
oblique position is determined in that when starting the arrangement an 
initial condition corresponding to the angle of the oblique position is 
set up in the integration circuit. However, due to the presence of a 
device for measuring the absolute angle in the form of the levelling 
instrument 12, this initialising operation is not necessary. This can be 
seen as follows. The filtered angular signal of the levelling instrument 
12 present across the capacitor 27 is supplied to a second input 48 of the 
comparison circuit 29, the first input 49 of which is connected to the 
output 47 supplying the angle signal. The output 50 of the comparison 
circuit 29 is connected to the output 51 of the second processing circuit 
28 and the latter is in turn connected to a second input 52 of the second 
integrator 43. This input 52 is connected through a resistor 53 to the 
summation point 54. If inter alia, the amplifier 55 of the comparison 
circuit 29 has sufficient amplification, it may be assumed that the direct 
voltage and very low-frequency components at the input 48 are equal to the 
same quantities at the input 49. Consequently, the output 47 supplies a 
signal which is equal to the static angle measured by the levelling 
instrument 12. It will be appreciated that the output 50 constitutes with 
the resistor 53 a source which takes up the current which is equal to a 
direct voltage at the output 36 and the input 42 divided by the resistance 
value of the resistor 46. It is very advantageous to include the capacitor 
27 of the low-pass filter 25 in the comparison circuit 29. One side of the 
capacitor is then not connected to ground, but is connected instead to the 
output 50, as is indicated by the capacitor 56. The amplifier 55 is then 
an operational amplifier whose amplification is very large, as is known. 
The direct voltage at the input 48 and hence the average static signal is 
now very close to the desired angular signal at the output 47. In this 
integrator circuit, which serves at the same time as a voltage comparator, 
the advantage is obtained that alternating components which are indeed 
desirable in the angular signal at the output 47 are supplied with 
amplification substantially equal to unity to the input 52, after which 
they are further subjected to the attenuation of the RC time constant of 
the resistor 53 and the capacitor 45 and thus supply a negligible negative 
feedback signal. In the circuit first described, this negative feedback 
signal is A times larger because the amplifier 55 amplifies A times, for 
example 100 or 1000 times. 
This fact should be taken into account in the dimensioning of the RC 
time-constant and the frequency ranges.