NO843479L - APPARATUS FOR AA MAKING A SIGNAL REPRESENTING THE ANGLE MOVEMENT SPEED OF A CONSTRUCTION - Google Patents

Description

The present invention relates to an apparatus for measuring inertia-specific force and angular velocity of a body in motion, by means of a plurality of accelerometers mounted on mutually perpendicular axes. The invention is particularly applicable to an apparatus and method as used in a high-precision, non-gyroscopic Inertial Measurement Unit (IMU) for an Inertial Navigation System (INS), as described in US Patent Application No. 357,714 as well as in an article by Shmuel J. Merhav entitled "A Nongyroscopic Intertial Measurement Unit", published in AIAA J. of Guidance and Control, May-June 1982, pages 227-

235, and is therefore described below in relation to such an application.

The above-mentioned patent application shows a method and

an apparatus for measuring the specific force vector and angular velocity vector of a body in motion by means of a plurality of periodically operated accelerometers. The described embodiment uses rotary accelerometers, which in a broad sense have been proposed as early as 1965, but which have not yet matured as a practical technology, as discussed in the aforementioned patent application. That patent application is specifically directed to a new method of processing the accelerometer output signals to derive the specific force vector F and its components of the angular velocity vector SL in such a way that the unwanted compo-

nents are depressed to a sufficiently low level to be compatible with INS precision requirements. Briefly, the angular velocity vector components of SL (ie, SL i , where i = x, y, z), are derived from each of the accelerometer outputs ("a"), by: (1) multiplying the accelerometer output; with the function sgncos U) t to generate the product signal a• sgncos 661, and (2) integrating the product signal over the cycle period'. Specifically, the force-vector components of F (ie Fj_

where i = x, y, z) is derived by integrating the respective accelerometer output signals ("a") over the cycle period.

The aforementioned patent application includes a discussion and a mathematical analysis of the dynamics involved, and shows that a number of important advantages can be achieved, making the described method and apparatus particularly applicable to non-gyroscopic Inertial Navigation Systems (INS). Reference is made to the above-mentioned patent application and the article by S.J. Merhav, mentioned above, for further details of the described technique for signal separation

desire and the benefits that can be obtained from this.

An object of the present invention is to produce a new apparatus for measuring the specific force and angular velocity of a body in motion, which makes it possible to achieve further important advantages, which will be explained in more detail below. Apparatus according to this application is particularly applicable to the technique of signal separation described in the above-mentioned patent application, and is therefore described below according to that technique, but it must be understood that the invention of this application, or features thereof, can also be used with advantage in other applications.

Briefly, the present invention provides an apparatus for measuring the specific force and angular velocity of a body in motion by means of a plurality of accelerometers, mounted on mutually perpendicular axes and periodically driven by a drive device in a mutually perpendicular plane, characterized in that each accelerometer is mounted for vibration movement, and is driven by the drive device along a vibration axis in its respective plane, instead of being rotated in the plane as in the embodiment of the invention described in the above-mentioned patent application. Several devices which constitute further features of the invention are described below to achieve the vibrating movement of the accelerometers.

In one of the described embodiments, the accelerometers are thus mounted spring-loaded on an elastically yielding device, so

as a diaphragm, so that the accelerometer is limited to movement only along the axis of vibration, while the drive device can be connected to a source of sinusoidal current to vibrate the accelerometer along the axis of vibration. Each reference axis of the moving body may be provided with two such vibrating units mounted in a coaxial, back-to-back relationship, the drive of one unit vibrating that unit synchronously, but in the opposite direction, with the drive of the other, as that one unit serves as a balancing mass to dynamically balance the other unit.

An apparatus constructed according to the foregoing features makes it possible to achieve a number of important advantages, particularly with application to non-gyroscopic Inertial Navigation Systems (INS). It thus makes it possible to operate the accelerometers periodically without rotating or sliding mechanical joints, thus avoiding the need for slip rings and other sliding electrical contacts. In addition, the described device produces an accelerometer unit that is inherently rigid along the sensitive axis, which allows vibrational motion and is impressed upon the accelerometers at amplitudes, frequencies and phase angles that can be very precisely controlled, and which renders the accelerometers essentially insensitive to external forces. , shock and vibration. A further advantage, particularly in the back-to-back arrangement,

is that it generates the necessary vibrational movement on

such a way that the dynamic forces are precisely balanced.

The foregoing advantages produce a much higher mean time between failures (MTBF) than gyro types of IMU, or non-gyro types of IMU with rotating accelerometers.

In another described embodiment, the accelerometers are mounted on a support part, rotatable around a rotation axis at right angles to the vibration axis, where the drive device swings its support part through a small angular movement around the rotation axis. The support part also includes a balance mass on the opposite side of the axis of rotation to balance the accelerometer mass. In this described embodiment, the driving device comprises an electric motor, driven by the sinusoidal current to perform a small angular oscillating movement (a few degrees) which is almost linear.

This design has the further advantage of essentially total immunity to external linear vibration and shock, simple construction, and high precision and low cost.

A third embodiment of the invention is described below, comprising a tuning fork, which embodiment also allows accurate balancing of the dynamic forces. The accelerometer thus comprises a mass mounted for vibrating movement on the first branch of the tuning fork, where the second branch of the tuning fork comprises a balancing mass which causes the two branches to vibrate at a predetermined natural frequency. In this described embodiment, the electric drive part is carried

on one part of the tuning fork, and the electrical recording part can be carried by the other branch. Such a device can comprise an electrical feedback loop from the recording part to the drive part, in order to provide an electromechanical oscillator whose oscillations are maintained by the feedback loop.

The tuning fork design provides, in addition to a balanced dynamic system due to the counter-moving masses, a number of additional advantages. When the power requirement to drive the drive part is only what is required to replace energy lost to friction, the device thus only requires a very small amount of power. Furthermore, as the device acts as a very sharply tuned oscillator, it will reject mechanical disturbances along the sensitive axis if it is not accurate at the resonant frequency. Furthermore, since the device operates at its natural frequency, it can be used to synchronize the multivibrator that controls the signal processor, thereby avoiding phase delays that could affect the accuracy of the angular velocity and specific force vectors derived from the accelerometer output signals.

From the above it will be understood that "vibrating motion"

as supplied to the accelerometers can be not only rectilinear movement, as in the first of the above embodiments,

but can also be a substantially rectilinear motion (eg a small angular oscillating motion that is almost rectilinear)

such as in the second and third of the above embodiments of the invention. This will appear better from the following detailed description of each of the three designs. A further improvement of a speed and force sensor using vibrating accelerometers can be achieved by using paired accelerometers for each axis for which angular velocity information is desired. There are three devices with paired accelerometers described

here, which can produce a significant improvement in the accuracy of both speed and power signals. The first such device uses two accelerometers mounted together, with their input or force-sensing axes parallel to the axis around which they are vibrated. Another arrangement has both accelerometers mounted back to back, with their force-following axes opposite each other and at right angles to the axis around which they are vibrated. The third arrangement requires the accelerometers to be mounted back to back, with their force-sensing axes opposite each other and with the accelerometers vibrated in a linear direction at right angles to the force-sensing axis.

The paired devices described above make it possible

to further separate the force signals from the speed signals by summing and differentiating the output signals from the paired accelerometers before the signals are fed into a signal separation circuit.

Further features and advantages of the invention will become apparent

of the description below.

The invention is described by way of example only, with reference to the drawings, where:

Figure 1 is a diagram that will help in the explanation

of the principles of signal separation as described in the above-mentioned patent application and used in the preferred embodiment of the present invention as

described here;

Figure 2 is a block diagram illustrating one form of non-gyroscopic Inertia measurement system based on the principles of signal separation as described in the above patent application, and also included in the preferred embodiment of the present invention;

Figure 3 is a diagram similar to that shown in Figure

1, but modified so that it includes vibrating accelerometers according to the present invention, instead of rotating accelerometers which

shown in Figure 1;

Figure 4 illustrates one form of vibrating accelerometer unit

constructed according to the present invention;

Figure 5 is a diagram of a closed loop drive for an accelerometer unit constructed in accordance with the present invention;

figure 6 schematically illustrates the use of two vibrating accelerometers, each according to the construction which e.g. is illustrated in Figure 4, mounted in a back-to-back relationship to balance dynamic forces;

figure 7 illustrates another form of vibrating accelerometer unit constructed according to the present invention, based on the use of an electric torque motor which rotary drives the accelerometers, and a counterbalance mass, through a small angular oscillating motion; figure 8 illustrates a third form of vibrating accelerometer unit constructed according to the present invention, based on the use of a tuning fork for accurate balancing of the dynamic forces;

Fig. 9 is a block diagram illustrating an electromechanical oscillator device comprising a tuning fork type accelerometer assembly as illustrated in Fig. 8;

Figure 10 is a simplified perspective diagram of paired accelerometers with their force-sensitive axes parallel to

an angular vibration axis;

Figure 11 is a simplified perspective diagram of paired accelerometers arranged back to back, with their force-sensitive

axes at right angles to the angular-vibration axis;

Figure 12 is a simplified perspective diagram of paired accelerometers arranged back to back, with their force-sensitive

axes at right angles to the linear direction of vibration; figure 13 is a diagram similar to that of figure 3, used

to illustrate the operation of the paired accelerometer device of Figure 10 in a three-axis speed sensor-

Figure 14 is a diagram of a type similar to that of Figure

3, illustrating the operation of the paired accelerometer device of Figure 11 in a three-axis speed sensor;

Figure 15 is a diagram of a type similar to that of Figure

3, which illustrates the operation of the paired accelerometer device of Figure 12 in a three-axis speed-

and force sensor;

figure 16 is a side view of a mechanism for realizing it

paired accelerometer device of Figure 10;

figure 17 is a side view of a mechanism for realizing it

paired accelerometer device of Figure 11;

figure 18 is a side view of a mechanism for realizing it

paired accelerometer device in Figure 12, and

Figure 19 is a block diagram of a signal separation circuit

of the type shown in Figure 2, additionally comprising a pre-processor circuit for summing and differentiating the output signals from the accelerometers.

Before a description of the various embodiments of the invention as illustrated in Figures 3 to 8, it is believed that a preliminary discussion of the principles of signal separation and the overall system for measuring particular force and angular velocities in a body in movement, both as described in the above-mentioned patent application, to provide a better understanding of the present invention and its advantages, especially when the present invention is used in such measurement systems.

Referring to Figure 1, the general formula for total acceleration that can be measured by a point mass moving in a rotating system is:

where St is the angular velocity or velocity vector in the system, F is the specific force vector, and r is the instantaneous distance of the point mass from the center of rotation in the system. In particular, r = p + 1, where p is the moment vector distance from the point mass from the center of rotation, and 1 is the fixed distance from the center of rotation of the element to the center of rotation of the system. The index b indicates differentiation with respect to the axis of the rotating body. Formula (1) can now be rewritten as follows: by inserting

where i, 2,°9^ are unit vectors respectively in the directions x,

y and z, comprising the noise components nx, ny and nz, resolving a into ax, ay, and a2la px= py = pz= p and rearranging the expressions we get

Each of the noise signals n = £nx, ny, nz ' is assumed to consist of

three components as follows:

n = nc+ nv<+>no

where:

njj - low frequency noise

nv - periodic or random vehicle vibration noise

nr - random zero-medium high-frequency sensor

noise

In the rotating accelerometer system illustrated in the above-mentioned patent application, there is thus, in addition to the underlined, desired expressions in the formulas (3) - (5), a majority of unwanted expressions which potentially contribute to errors. These result primarily from the dynamic expressions containing p, q and r and their derivatives, and from sensor-noise components in n.

As further described in the above-mentioned patent application, is

an important feature of that invention is that it provides a means of separating Fx from q, Fy from r, and Fz from p, on

such a way that the unwanted expressions are suppressed to a sufficiently low level so that the effect of the cross-product expressions gp, gr and rp is essentially eliminated.

An important advantage of the use of vibrating accelerometers according to the present invention is that the orthogonal surface pressures, e.g. 2 6dpsin60t ^r + -~^- ) ^ formula (3) above (and the corresponding expression in formulas (4) and (5) above) falls out,

and thus further reduces this source of error in the rotating accelerometer device. That is, since these orthogonal expressions come from the rotary motion of the accelerometer,

is not present in the invention of this patent application,

which includes a vibrating movement of the accelerometers.

Figure 2 of the present application (which corresponds to figure

4 of the above-mentioned patent application) illustrates in block-diagram form a non-gyroscopic Inertia measuring unit (IMU) which realizes the above-described principles of signal separation in relation to a channel, namely that of the accelerometer Az . It must be understood that the other two channels, for the accelerometers Ax and Ay, are constructed in a similar way.

The unit illustrated in Figure 2 comprises three main subsystems, namely: a control pulse generator, generally designated 2; an electromechanical drive, generally designated 3, for rotating each of the accelerometers in the triad illustrated in Figure 1, and an electronic signal separation processor, generally designated 4.

The control pulse generator 2 is driven by a free-running multivibrator 21 with a high-precision reference frequency 4f (f = l/T). The multivibrator controls a square wave generator 22 which generates square waves with a frequency f. These square waves are used as synchronization pulses.

They are supplied to a reset and integrate control pulse generator 23 and to a sampling pulse generator 24, which generators are used to control the operation of the processor 4, which will be described more specifically below.

The synchronization pulses from the square wave generator 22

is also supplied to a drive signal generator 31 inside the electromechanical drive system 3. The output pulses from the generator 31 drive the accelerometers in the unit 32, so that the accelerometers are rotated around their respective axes at a predetermined frequency ( ) which is equal to 2iyf. When the body to which the accelerometer unit 4 is attached is subjected to a specific force Fzog and an angular velocity p, it generates a resultant output signal of az.

The accelerometer output signal az is fed to the processor 4 to extract the specific force vector Fz and the angular velocity vector p in such a way as to substantially suppress the unwanted components of the signal azi according to the formulas (3) - (5) and ( 6) - (8) as discussed above. IN

in this case we are talking about the components Fzog p, so that-

it is formula (5) that is interesting.

The processor 4 thus comprises a multiplier or sign-changing circuit 41 for multiplying the produced values az with the zero-mean function "sgncosWt", and giving the output signal azsgncos b) t. The latter signal is fed to an integrating circuit 42 which integrates the product signal over the cycle period T. The integrating circuit 42 is reset at the end of the period T by the control pulse generator 23, but before it is reset it sends out its contents to the sample-and-hold circuit 43, which is controlled by the sampling pulse generator 24. As described above, this causes processing of the accelerometer output signal azat the content of the sample-and-hold circuit 43 corresponds to the angular velocity component "p".

The accelerometer output signal is also fed

the second channel inside the processor 4, comprising another integrating circuit 44 which integrates the signal over the period T. The integrating circuit 44 is also reset at the end

of the period T by the control pulse generator 23, but just before it is reset it sends out its content to another sample-and-hold circuit 45, controlled by the sampling pulse generator 24. It will be understood from the previous discussion that the content of the sample-and-hold circuit 44 will correspond to the specific force vector Fz.

One can refer to the above-mentioned patent application for a further description of the overall system and the advantages produced by the principles of signal separation on which the system is based. It must be understood that the same advantages will apply to the present invention, when it is realized in such a measurement system in addition to the further advantages that can be achieved with the present invention, as described in more detail below.

Briefly, the present invention uses vibrating accelerometers to generate the accelerometer output signals from which the components of the specific force vector F and the components of the angular velocity vector Si are derived. , while substantially suppressing the unwanted components of such signals. This is illustrated in Figure 3, which is similar to the diagram in Figure 1, but which includes vibrating accelerometers instead of rotating accelerometers. Figure 3 thus illustrates a triad of accelerometers Ax, Ay, A arranged to vibrate at an amplitude "p" and a frequency "Oi" in (x, y), (y, z) and

The (x, z) planes, with the sensitive input axes as shown, on

line with the x, y, z directions.

Specific vibrating accelerometer mechanisms as illustrated in Figures 4 to 9 shall be described below. These figures illustrate only one channel, namely that of the accelerometer Az , where the accelerometer-sensitive axis for the specific force vector is the Z-axis, and the vibration axis is the Y-axis, the sensitive axis for the angular velocity vector is the X-axis. The accelerometer A2 thus vibrates along the Y axis, measuring the specific Inertia force and the angular velocity of the moving body

in relation to the axes Z and X. It will be understood that the other two channels, i.e. for the accelerometers Ax and Av, are similarly constructed and provide corresponding measurements for their respective axes. Preferably, the vibration frequency (( A ) of the accelerometers

in all the described embodiments 30-60 Hz, and the displacement during the vibrating movement is typically in the range from 0.25-3 mm.

As indicated above, one of the main benefits of its use is

of vibrating accelerometers instead of rotating accelerometers, that the orthogonal expressions in formulas (3) - (5) (e.g. 2ti)psin£Jt ^r<+>2~£j"^ ^ f°rinelen 3) do not exist, and therefore allows a very large improvement in overall effectiveness.Many other advantages are more specifically described below.

The accelerometer assembly illustrated in Figure 4, generally designated 50, comprises an outer cylindrical housing 52 which encloses an accelerometer 54 containing an accelerometer sample mass 56. The accelerometer assembly 54 is supported by a mounting plate 58, resiliently mounted inside the housing 52 by means of a elastic membrane 60, which limits the movement of the accelerometer unit 54 only to the Y-axis which is the vibration axis and perpendicular to the Z-axis, which is sensitive to the specific force vector in the accelerometer unit, as mentioned above.

The drive means to vibrate the accelerometer unit

54 along the Y-axis comprises a permanent magnet 62 of cylindrical construction, fixed inside the housing 52 at one end thereof and designed with a cylindrical air opening 64, coaxial with the Y-axis for vibration of the accelerometer unit. The drive device further comprises a driver coil 66, carried on a cylindrical coil form 68 fixed on the accelerometer mounting plate 58 inside the cylindrical air opening 64 and coaxial with the vibration axis Y. The driver coil 66 is adapted to receive sinusoidal driver current to generate a force which causes the accelerometer- the unit 54, including the sample mass 56 and the mounting plate 58, moves in a sine function along the Y-axis as limited by the spring force in the membrane 8. The accelerometer unit illustrated in figure 4 further comprises a recording device placed inside the housing 52 and connected to the accelerometer unit 54 and its mass 56 to measure the rate of displacement along the Y-axis of vibration. Such a recording device can comprise another permanent magnet 70 (or an iron-free field coil) and a recording coil 72 which works together with this on the other end of the housing 52. Permanent magnet 70 is also of cylindrical design, but with much smaller dimensions than the driver magnet 62, and is also designed with a cylindrical air opening 74, and the pickup coil 72 is also carried by a cylindrical coil form 76, attached to the accelerometer unit 54 so that the pickup coil 72 is located inside the air opening 74 and is coaxial with the Y axis for vibration of the accelerometer unit.

The accelerometer unit illustrated in Figure 4 further comprises a first group of external terminals 77 connected by electrical wires (not shown) to the driver coil 66 for feeding the driver current and the pick-up coil 76 which measures the movement of the accelerometer 54, and a second group of external terminals 78 connected with electrical wiring (not shown) to internal terminals 79 carried by the accelerometer unit 54 to feed the power supply voltage and output signals to and from the accelerometer unit 54 .

One can thus see that the sinusoidal driver current

(I = Imsin&)t) fed into the driver coil 66 exerts a force proportional to it and which causes the accelerometer assembly 54, including its mass 56 and mounting plate 58, to vibrate as a sine function along the Y axis as limited by the elastic membrane 60 in the same way as the excitation of a loudspeaker. The pickup coil 72, moving with the accelerometer unit 54, induces a voltage proportional to the speed of the sinusoidal movement of the accelerometer unit 64, the measured speed of movement along the Y-axis of vibration (namely y) being output via the terminals 77. If the motion due to I = Imsin«Jt is y = ymsin((Jt + j>) = p sin ( 0J t +

where ^ is a phase shift due to the dynamic delay of the moving unit, the corresponding velocity is y = p U) cos ( u) t + § ) . The signal emitted by the pickup coil 72 constitutes the measured speed (y) of the moving unit, comprising the accelerometer unit 54.

Figure 5 illustrates how this measured speed (y),

sent out at the pickup coil 72, is also used to effect a closed-loop controlled movement of the accelerometer unit 54 by controlling the supply of driver current to the driver coil 66.

The control signal generator 80, synchronized by the input pulses 81, thus generates the signal V = Vm cosfjt, which is fed via the line 82 to a differential power amplifier 84. The output of the amplifier 84 is connected at the line

86 with the driver coil 66 in the accelerometer unit illustrated in Figure 4, thereby driving the unit by means of a current I = Im sin(W t + ). The latter current produces the power

F = Fm sin( U) t + f), which causes the movement (indicated by the output arrow 88) y = p Wcos( b) t + $ ) . The latter movement is received by the pickup coil 72 in Figure 4, and is fed via line 90 into another input terminal of the differential power amplifier 84. The small difference between the signals on line 90 and the signal V = Vm cos&Jt is amplified and creates the drive signal I = Imsin (C0 t + ^ ) .

The arrangement in Figure 5 is a negative feedback loop with a total loop gain L which is determined by the gain in the amplifier 84 and the recording 82. For those familiar with this technique it is clear that by arranging L >>1, one is assured that y will closely follow V = Vm cos t, and that a possible force disturbance F^, shown schematically via the dotted line 92, will excite a disturbance in the velocity y given by Yd— Fd/L- Da L»l, y ^be depressed to a negligible

low level, thus forcing the accelerometer unit 54 and the mass 56 in Figure 4 to act in practice as a rigid body in relation to disturbing forces along the Y axis.

It is thus seen that the closed loop driver system in figure

5 provides a well regulated and controlled sinusoidal linear velocity along the Y axis. The amplifier 84 is so constructed in terms of frequency response that the closed-loop transfer function in Figure 5, denoted by H(W) 4 y ( )/Vj_ ( 6J ), is

flat up to a bandwidth "b", so that b>>u , and the phase shift

^ ="£H( tø ) at the driver frequency tø , is practically zero. In high-gain, feedback driver systems, it generates the required motion with negligible nonlinearity and phase distortion.

Two aspects of great importance will now be demonstrated:

(1) large bandwidth and small phase distortion of the closed-loop system; and (2) immunity to nonlinear distortion due to the speed pickup coil 72. (1) With respect to aspect (1) above, the open-loop transfer function of the electrodynamic drive is given by:

F = BU * Blu/Rc; where ;B = magnetic induction; 1 = length of driver coil; ;Rc= the resistance of the driver coil; ;J a u/Rc; and;u = input voltage at the coil terminals. ;If now;m = mass of the moving unit; ;b = the damping coefficient; and c = the spring constant of the membrane, ;is: ; ; If we assume that e.g. A cf 100, it is clear that AKH is of the order of IO<5>r IO<6>. Thus AKH» 2 G)n zeta,; and the ratio y JS — Vj_ holds over a very wide bandwidth so that the phase distortion 4 can be made negligibly small for excitation frequencies of 30-60 Hz. ;1 (2) When it concerns aspect (2) above, since y Sl ^ Vj_ we can write y = hV-j where h = ^n. Let a possible non-linearity be expressed as follows: ;y hQV± + hiV^;For V i = V^mcos 4/t we have:; ; It is clear that the operation of sgncos in the signal separation processor and the integration over the cycle period T causes the contributions due to -^°92 to drop. The speed recording sensor 72 is thus not critical for the requirements for linearity. It will be understood that when the invention is applied to a fixed type Inertia control system, the accelerometer unit 50, as illustrated in Figure 4, comprising a closed loop driver as illustrated in Figure 5, will be used for each of the three axes, with the outer housing 52 of the accelerometer unit mounted on the vessel (ie the body in motion). In a stable gimbal mounted platform type of Inerti control system, the outer housing 52 of the accelerometer unit 50 for each axis would be applied to the inner gimbal suspension of the platform. ;In either application, the vibrating motion of the accelerometer unit can cause reactive forces acting on the support for the outer housing 52. To avoid these unwanted unbalance forces, two vibrating units, as shown at 50a and 50b in Figure 6, can be mounted back to back, with a unit comprising an accelerometer as described above vibrating synchronously with, but in the opposite direction to, the other unit vibrating a counterbalance mass, so that dynamic balance of the accelerometer unit is obtained. Figure 7 illustrates another type of vibrating accelerometer device, namely one in which the accelerometer is rotated by an electric torque motor through a small angular oscillating motion (eg a few degrees) which makes the vibrating motion nearly rectilinear. The sensitive axis of the accelerometer is parallel to the axis of rotation. A suitable balance mass is provided to dynamically balance the accelerometer during its oscillating motion, so that no external forces are transmitted to the body on which the device is mounted. The accelerometer unit illustrated in Figure 7, where it is generally designated 100, thus comprises an outer cylindrical housing 102 rotatably mounted on a shaft 104 via rotary bearings 106 and 108. Attached to the shaft 104 is a disc or plate 110 , which serves as a support member to support an accelerometer unit 112 with a sample mass 114. The disk 110 also carries a counterbalance mass 116 on the opposite side of the disk. The disk 110 is driven through a small angular oscillating motion by of an electric torque motor, comprising a stator 118 attached to the housing 102 and a rotor 120 attached to the shaft 104. A take-up rotor 122 is attached to the opposite end of the shaft 104, and is placed inside a take-up stator 124 attached to the housing 102. The electrical connections may be the same as illustrated in Figure 5, where the differential power amplifier 84 feeds the driver current to the conductors of the torque motor's stator 118 to drive its rotor 120, and thus the accelerometer 112 and counterbalance ma ssen 116 attached to the motor-rotor 120, through a small angular swinging movement with an amplitude " ". This will cause the displacement y «f ry , where "r" is the radius from the axis of rotation 130 of the shaft 104 to the center of gravity of the accelerometer test mass 114. If "y = YmsinftJt, then y = ruyracos Wt, pointing into the plane of the paper. It will It will be understood that the oscillating motion of the accelerometer 112 into and out of the plane of the paper is substantially linear along an axis perpendicular to the sensitive Z axis of the accelerometer. As an example, "r" may be about 3 cm; -the movement may be a few degrees; and the amplitude of the displacement of the accelerometer may be 0.25-3 mm. ;The recording 122 attached to the shaft 104 senses the angular velocity;tymcos t • As in the case of the recording 72 in Figure 5,;the output of the recording 122 in Figure 7 be connected as a feedback into the differential amplifier 84, to which the drive voltage Vj_ = Vmcos o0t is fed via line 82. The angular velocity y in the device in Figure 7 is caused to closely follow the drive voltage V -j_ = Vmcoswt.; This device illustrated in Figure 7 has a number of advantages over that described above with reference to Figures 4-6, including simpler mechanical parts, higher precision of motion realization, and essentially total immunity to linear accelerations in all axes. ;Figure 8 illustrates a third type of vibrating accelerometer device, namely one that uses a tuning fork, which can be arranged for each sensitive axis of the moving body to produce dynamic balance of the forces, as well as important advantages to be described below. Figure 9 illustrates one way of connecting the vibrating accelerometer assembly of Figure 8 to form an electromagnetic oscillator to maintain oscillations in the tuning fork accelerometer assembly with only a small amount of input power sufficient to replace the energy lost to friction. Reference is first made to figure 8. The vibrating accelerometer unit, generally denoted by 200, comprises an outer cylindrical housing 202 in which is mounted a tuning fork 204, comprising a pair of branches 204a and 204b. The branches extend parallel to the sensitive axis of the respective accelerometer unit, which is the Z-axis in Figure 8, and thus perpendicular to the vibration axis of the accelerometer unit, which is the Y-axis in Figure 8. The tuning fork 204 is mounted inside the housing 202 by means of a mounting post 206, attached to an intermediate link 204c on the tuning fork. The housing 202 further comprises another post 207 in line with the post 206, but separated from this, and also from the intermediate link 204c of the tuning fork 204. The post 208 is used to mount, on one side, a permanent magnet 210 which works together with a drive coil 212, and on the other hand a permanent magnet 214; which works together with a recording coil 216. The two permanent magnets 210 and 214 are of cylindrical design, and comprise cylindrical air spaces in which are placed their respective driver coil 212 and recording coil 216, and each of the coils are carried on cylindrical coil forms 218 and 220 attached to the inner surfaces of the two branches 204b and 204a. On the outer surface of the branch 204b of the tuning fork, an accelerometer unit 224 with a mass 226 is attached by means of a fastening device 222. In a similar way, another mass 228 is attached on the outer surface of the branch 204a of the tuning fork for to provide a counterbalance for the accelerometer unit 224 and its mass 226. ;The electrical connections to the driver coil 212 and the pickup coil 216, as well as to the accelerometer unit 224, are provided at terminals 230 and 232 which extend outside the housing 202, and the terminals 234 inside the housing and connected to the accelerometer unit 224. ;It must be understood that the tuning fork 204 of Figure 8 vibrates;at its natural frequency, thereby causing the accelerometer unit 224 and its mass 226 on the branch 204b to move synchronously with, but in the opposite direction to, the counterbalance mass 228 on the branch 204a. No net force is thus exerted against the housing 202, and therefore not on any support to which the vibrating accelerometer unit 200 is attached. As described above with reference to Figures 4-6, this support would have been the movable body itself in a fixed embodiment, and the internal suspension of a platform in a stable gimbal platform application. The device illustrated in Figure 8 thus produces a high degree of dynamic balance. Due to friction and damping, the oscillations of the tuning fork 204 would decrease to zero in a relatively short time. In order to maintain the oscillations for a longer time, the vibrating accelerometer unit 200 illustrated in Figure 8 can be connected so that it forms an electromechanical oscillator, as illustrated in Figure 9. As shown in Figure 9, the signal over the receiving coil 216 is thus fed to an amplifier 240, whose output signal is connected to the input of the driver coil 212. The amplifier 240 is of such a polarity that it amplifies a first displacement of the branches 204a, 204b of the tuning fork 204. The system thus acts as an electromechanical oscillator with a frequency determined of the natural frequency of the tuning fork. This natural frequency can be used to precisely synchronize the frequency of the freewheeling multivibrator 21 of Figure 2. The amplifier 240 is preferably of a non-linear type, which includes a saturation device so that it forces the overall electromechanical oscillator to stabilize at a certain amplitude. Thus, it can be seen that the tuning fork accelerometer assembly illustrated in Figures 8 and 9 produces a balancing dynamic system due to the counter-moving masses, requiring only a small amount of power to drive the coil 212, just to replace the energy lost to friction. The device, which is a sharply tuned oscillator, rejects mechanical disturbances in the axis of vibration (the Y-axis in Figure 8) if it is not exactly at the resonant frequency. Furthermore, the structure is inherently rigid in the sensitive axis of the accelerometer, namely the Z-axis. Furthermore, since the unit operates at the natural frequency and synchronizes the multivibrator 21 in the control pulse generator 2 in Figure 2, there is no phase shift between cos £»>t and sgncos Wt. The accelerometer unit is also very simple, and can be constructed ;at low cost.;The advantages that can be obtained by using the vibrating accelerometer as described above enable the construction of IMUs ;which theoretically have a much higher mean time between failures (MTBF); than both the gyroscope type and the rotary accelerometer type of IMU. While the invention has been described with respect to several preferred embodiments, it must be understood that these are presented by way of example only. There are thus many other possible devices for generating the vibrating movement, e.g. using mechanical devices such as cams or joints to convert rotary motion such as from an electric motor (preferably synchronous motor) into vibrating motion. Many other variations, modifications and applications of the invention will be apparent. Significant improvements in signal strength for both the force and velocity channels can be achieved along with a reduction in signal noise when a pair of accelerometers, instead of a single accelerometer as shown in Figure 3, is used for each axis of rotation. Simplified illustrations of three devices with paired accelerometers are shown in Figures 10-12. A significant advantage of using accelerometers arranged in pairs, as shown in Figures 10-12, is that noise present in both the force and velocity channels in Figure 2 is increased only by the square root of 2, while the effective force and speed signals are doubled. ;This produces an effective increase in the signal-to-noise ratio;at the square root of 2. In addition, common acceleration disturbances in the velocity channel due to external forces that may result from vessel and mechanical sources are essentially canceled in this type of device. ;The first device with paired accelerometers is illustrated in Figure 10, where a pair of accelerometers 300 and 302 are mounted on an angle-rotating base 304 which vibrates about the Z-axis 306 as indicated by arrows 308. The force-sensing axes ;Az and Az of the accelerometers 300 and 302 are aligned so that they are parallel to the Z-axis 306 about which the support 304 vibrates. Since the device in Figure 10 comprises a pair of accelerometers with their force-sensing axes a| and a| parallel to the vibration axis 306, this device will hereafter be referred to as the PAPVA device. ;Another device with paired accelerometers is shown;in Figure 11, where two accelerometers 310 and 312 are mounted on;a support device 314 which vibrates angularly about the Z-axis indicated at 318, as suggested by arrows 316. In this device, the accelerometers 310 and 312 attached to the support device 314 in a back-to-back device, so that the force-sensing axes Ax and Ax are parallel, but in opposite directions, and are normal to the vibration axis 318. This device will hereafter be called The PANVA device to denote a pair of accelerometers subjected to angular motion with their force-sensing axes normal to the axis of vibration or angular motion. The third device is illustrated in Figure 12, where a pair of accelerometers 320 and 322 are arranged back to back with their force-sensing axes A^ and Ay placed in parallel but in opposite directions. In this device, the accelerometers 320 and 322 are caused to vibrate in a linear direction along the X-axis, as indicated by arrows 324 and 326. For convenience, this device will hereafter be called PLNVA due to the fact that it is a device with paired accelerometers which are caused to vibrate in a linear fashion along an axis of vibration normal to the force-following axis. Figures 13-15 correspond to the PAPVA, PANVA and PLNVA devices in Figures 10-12, and provide a concept illustration of how the paired accelerometers can be arranged in triads. ;In Figures 13-15, the accelerometers are designated by their force-sensing axes A^, A^, A^, Ay, a| and a| and produce force and angular velocity sensing along and around the orthogonal axes X, Y and Z. The devices shown in Figures 13-15 are suitable for use in an Inerti reference system which can further be used in an Inerti navigation system. ;In the PAPVA mechanism as shown in Figures 10 and 13, six accelerometers are required, namely A^, Ax, Ay, Ay, Azog a| The accelerometer pairs are vibrated at a constant angular frequency60 and with a constant angular amplitude. The principles of force and angular velocity signal separation are essentially the same as illustrated in Figure 2. The accelerometer outputs contain the same basic information for angular rotationA and force F, although the actual signal content is somewhat different. In developing equations that describe the signal content of the accelerometers in Figure 13, the instantaneous distance of each accelerometer from the vessel's center of rotation is given by: ; ; and defines;6= 6MSut (7);= u 6 ..Cut (8);M ;while assuming: {<<l;Sin 6 * 6 = 6MS wt (9)

Cos 6 1-1/2 £M.<2>S<2>ujt (10)

and defines:

L 5M<=>P/2

By inserting equations (6) - (10) into equation (1) and solving, the following accelerometer output equations are obtained:

Before entering the signal processor in Figure 19, the accelerometer signals are preprocessed as sums and differences as shown in Figure 19 according to the following matrix equation: Assuming again that F. and il are essentially constant in the interval T , all time derivatives in equations (11) - (16) disappear. By inserting into equation (17) and solving, we get:

Two advantages have thus been achieved through the paired mechanization, all specific force components have been removed from the acceleration signals in equations (18) - (20), and all angular velocity components have been removed from the signals in equation (21).

This provides a significant improvement in the decoupling of F from .fl.. Common mode noise expression due to vessel noise is also removed from the SL channel, as can be seen from equations (18) - (20).

To obtain estimates of p, q, and r as defined by Eqs

(22) below

put q and f in equations (18) - (20) into equation (22). and to obtain an estimate for Fx, Fy and Fz as defined by equation (23) below,

Set Fx. Fy and Fzi equation (21) into equation (23). The corresponding results are:

p, q and f are thus precisely determined, except for a constant known scale factor, and fx. Fy and £z are the same as determined previously.

One can see from the equations above that the output signals

which is achieved in many respects is equivalent to the mechanization using a single accelerometer. The effect of vessel noise in the /X channel is also almost canceled due to the common mode rejection achieved through the accelerometer pairing,

as indicated by equation (24). Gradients in vessel noise along L, however, keep some noise in Si. the channel. As L will normally be a few centimetres, vessel noise will thus not occur

completely cancelled. Through possible residual angular vibration in the drive shaft. residual, synchronous and uncontrolled noise can be retained and arise as an unknown bias in the St channel. The mechanization in figure 13 is also in principle dynamically balanced.

As illustrated in Figure 14, six accelerometers become A^.

Ax, Ay. A^ Az, and a| used in the PANVA mechanization. Again, the accelerometers are vibrated at an angular frequency 0& and angular amplitude p. The accelerometer outputs contain St and F information as before, but with different dynamic expressions in addition. As with the PAPVA mechanization in Figure 13, the basic principles are

for signal separation unchanged. This mechanization also has the advantage of essentially perfect vessel noise rejection.

According to the arrangement shown in Figure 14, the instantaneous distances of each accelerometer from the vessel's center of rotation are:

As the accelerometer input axes in this mechanization change direction in relation to the body's axes, the felt components are • modulated. The input axes vary, e.g. according to 3 :

£cos i.i,0.j,Sin £ .kj .

If one names the total acceleration that would be felt along the axes of the body in the case of ideal parallel motion by ax, ay and a|. the real accelerations sensed by the angular-vibrating accelerometers will be given by:

With equations (7) - (10) and insertion of the equations

(26) and (27) in equation (1) and solving, the real accelerometer pair output for a^ and ax can be represented by:

Similar equations for a<y>, ay, a| and a| results from this insertion.

Since the PANVA mechanization of Figures 11 and 14 is back-to-back, the pre-processing operation of Figure 19 for the PANVA device is represented by the following matrix equation: Inserting Equations (28) and (29) together with similar equations for a<y> , a<y>, a| and a| in equation (30), and assuming that F and A are constant throughout the period T, it results in:

with similar equations for a£ and a§ and equation (32) below f FF

for axx and similar equations for ayy and azz.

Inserting the equations for the angular velocity components of the accelerations, such as equation (31), and the equations for the force components of the acceleration, such as equation (32) into equations (22) and (23) results in:

Inserting equation (36) below into equation (1) and solving gives the following equations for ax and ax:

with similar equations for ay, ay, a| and a| which also results from this insertion.

Inserting the equations (36) and (37) together with the equations for ay, ay, a\ and a| in equation (30), and assuming that F and il are constant throughout the period T, gives:

Here, as before, p, q, r, Fx, Fy and Fzved are found by inserting equations (38) - (43) into equations (22) and (23). The results will be:

f

In this mechanization, therefore, all common-mode vessel noise components are essentially eliminated as in the PANVA mechanization.

The small periodic deviation of two from exact collinearity with the input axes varies according to S ui t. Possible noise on

due to f artøys acceleration is thus eliminated by the Sgn(C Wt) operation of the processor in Figure 19. Centripetal force due to periodic excitation does not exist in the PANVA mechanization.

Figures 16 to 18 illustrate devices for realizing the PAPVA mechanization in Figure 10, the PANVA mechanization in Figure 11, and the PLNVA mechanization in Figure 12. The device for the mechanization of the PAPVA mechanism is shown in Figure 16, and comprises a housing 330 with a pair of input/output plugs 332 and 334. Attached to the housing 330 by means of a pair of bearings or flexible connections 336 and 338 is a shaft 340. The paired accelerometers 300 and 302 are mounted on the accelerometer support frame or member 304 which in turn is attached to the shaft 340 to rotate with it. Rotary vibration of the shaft 340 is provided by a motor comprising a rotor 342 connected to the shaft 340 and a stator 344 attached to the housing 330. Signals which provide either position or velocity information for a feedback signal to a drive servo which would control the amplitude X of the shaft's vibration 340 can be obtained by the recording device, denoted generally by 346.

An apparatus for realizing the PANVA mechanization is arranged in Figure 17, where the accelerometers 310 and 312 are mounted on the support device 314 which in turn is attached to an axle 348. The axle 348 is rotatably attached inside the housing 350 by means of a pair of bearings or flexible connections 352 and 354. Angular vibration of the shaft 340, and therefore the accelerometers

310 and 312 are provided by an electric motor comprising a rotor 356 attached to the shaft 348 and a stator 358 attached to the housing 350. Signals for the movement of the accelerometers 310 and 312 can be obtained by the recording device indicated generally at 360 to produce a negative feedback for a drive servo which controls the amplitude $ of the vibration of the shaft 348.

A device for realizing the PLNVA mechanization on

Figure 12 is illustrated in Figure 18. In this particular embodiment, linear translation of the accelerometers 320 and 322

along the axes 324 and 326, as shown in figure 12, arranged at

a mechanism comprising a support frame 362 holding the accelerometers 320 and 322, which is attached to a housing 364 by means of a pair of flexible connections 366 and 368. A connection element 370 abuts the lower part of the accelerometer support the frame 362, and is fixed to a shaft 372. The shaft 372 is rotatably fixed inside the housing 364 by means of a pair of bearings or flexible connections 374 and 376. An electric motor, comprising a rotor 378 fixed to the shaft 372, and a stator 380 attached to the housing 364 will cause the shaft 372 to rotate or vibrate back and forth through a limited angular rotation. As the shaft 372 rotates back and forth through a small angle, the connecting member 370 will cause the accelerometers 320 and 322 to move in directions that are substantially at right angles to the force-sensitive axes A^ and Ay. As a result, substantially linear movement of the accelerometers 320 and 322 in a direction at right angles to their force-sensitive axes can be achieved using the mechanism of Figure 18. Signals representing angular position or velocity of the shaft, for use by a drive servo may be obtained by means of the pickup device indicated generally at 382.

The preferred embodiment of a signal processor for separating the force signals F from the angular velocity signals XI. for the paired accelerometer mechanization of Figures 10 to 13,

is illustrated in figure 19. The basic operation of the processor circuit shown in figure 19 is the same as the signal separation circuit in figure 2. The control pulse generator 2 is e.g. the same as shown in Figure 2, with a line 384 connecting the square wave generator 22 as shown in Figure 2 to the drive signal generator 31. Similarly, the output of the reset and integrate control pulse generator 23 is sent over line 386 from the control pulse generator in Figure 2, and the output of the sample and pulse generator 24 is sent on a line 388. Since the paired accelerometer mechanisms make use of two accelerometers, two accelerometer units 390 and 392 are shown in Figure 19, corresponding to the accelerometers 300 and 302 in Figure 10 and the accelerometers 310 and 312 in Figure 11 and the accelerometers 320 and 322 in Figure 12. The accelerometer output signals az and az are sent from the accelerometer units 390 and 392 on a pair of lines 394 and 396.

The signal separation is performed in the circuit of Figure 19, generally in the same manner as the circuit of Figure 2 except that the force channel generating the signal Fz on a line 398 and the angular velocity channel generating the signal p. on a line 400

is represented in Figure 19 as two separate circuits. As shown in Figure 19, a power channel circuit 402 comprises the integrator circuit 44 and the sample-and-hold circuit 45 in the electronic signal separation processor 4 of Figure 2, while the signals on lines 386 and 388 are supplied to the integrator circuit 44 and the sample-and -hold circuit 45 as shown in Figure 2. Similarly, angular rate circuit 404 includes an integrating circuit 42 and a sample-and-hold circuit 43 in Figure 2, as well as sign change-

or the multiplier circuit 41. The signals on lines 386 and 388 are fed to the integrator circuit 42 and the sample-and-hold circuit 43, as well as the pulse signal on line 384 in the same manner as shown in Figure 2.

One of the key advantages of the paired accelerometer mechanisms is their ability to use sum and difference techniques to separate the signals that primarily relate to translational motion from the signals that primarily relate to angular motion. In order to cancel linear specific force signals coming out of paired accelerometers, it is necessary that the force-sensitive axes are as closely parallel as possible, and also

that the effective centers of mass are as close to each other as possible.

The extent to which the force-sensitive axes of the accelerometers are in the same or opposite directions is a matter of convenience in the construction of mounting devices for the accelerometers.

In both cases, separation is made possible by constructing the mechanisms that generate the vibrational motion so that the driven speed factors are equal and opposite at all times when measured with reference to the housing.

A processor circuit for designing the sum and difference functions is illustrated in dotted line 406 in Figure 19. Pre-separation or pre-processing circuit 406 comprises two summing points 408 and 410. The particular pre-processing circuit 406 shown in

figure 9 is used for mechanizations where the force-sensitive axis is in the same direction, such as in the PAPVA mechanization shown in figure 10 and as such realizes the logic in equation (17). Here the summation point 408 works so that it generates a signal to the power channel 402 that represents the sum of

the accelerometer signals on lines 394 and 396. Likewise, the summing point 410 produces a signal to the angular velocity channel 404 that represents the difference between the accelerometer signals on lines 394 and 396. It is assumed that the non-rotating specific force signals will remain in the substantially equal on lines 394 and 396, so that the sum of the signals on line 412 will give twice the sensitivity to specific force as measured by the accelerometer along the force-sensitive axes. Likewise, difference signals on line 414 will be substantially free of components representing specific power. On the other hand, a pure rotational movement will generate two sinusoidal Coriolis accelerations along the force-sensitive axes of the accelerometers,

with a phase difference of 180°. This phase difference occurs because the coriolis accelerations are vector products of angular velocity and relative velocity, and in this case the angular velocity is common, while the relative velocities are 180° out of phase. Accordingly, the output of summing point 408 on line 412 is substantially free of components representing angular rotation. For the same reason, the output of the summing point 410 on line 414 will generate a signal to the angular velocity channel 404 with twice the angular velocity sensitivity.

In such mechanisms as PANVA in Figure 11 and PLNVA in Figure 12, where the force-sensitive axes have the opposite sense, the same principles apply, except that the signs of the signals are reversed. In the preprocessing circuit 406 for the PANVA and PLNVA mechanisms, summing point 408 would subtract the acceleration signals on lines 394 and 396, and summing point 410 would add the signals on lines 394 and 396 according to the conditions expressed in equation (30). Consequently, the sum signals from the summation point 410 will contain only angular velocity information, while the difference signals from the summation point 408 will contain only specific force information. It can therefore be seen that the pre-processing circuit 406 has the effect of separating specific force signals from angular velocity signals before the signals are fed to the force channel 402 and the angular velocity channel 404.

A further advantage of the circuit arrangement shown in figure 19

is that the difference and difference techniques provided by the preprocessing circuit 406 can be used to facilitate scaling of the signals fed to the force channel 402 and the angular velocity channel 404. Scaling is illustrated by means of a pair of scaling

amplifiers 416 and 418. The scaling amplifiers 416 and 418

can be used to scale the level of signals applied to the force channel 402 and the angular velocity channel 404 regardless of the amount of output signals from the accelerometers. This is particularly important when one takes into account that the amplitudes of the signals representing specific force Fz can be up to 100 times greater than the signal amplitudes relating to the angular velocity J\ . The value of the amplifiers' gain constants Kp and K^ can thus be adjusted to the expected signal amplitudes on lines 412 and 414 to allow maximum resolution of the signals without exceeding the ranges of circuits 402 and 404.

Similarly, the gains Kp and Kj^ for inertial navigation systems can be switched to increase the sensitivity, and therefore improve the resolution during the navigation systems adjustment process. During a mission, it may be necessary to temporarily reduce the sensitivity of either the force-sensitive or the speed-sensitive channel to avoid exceeding the ranges of circuits 402 and 404 during transient maneuvering of the vessel containing the navigation system.

Note: F2 and p are chosen as an illustration of one of the component pairs of F and JL. The same considerations apply to Fx and q and Fy and r.

Since one of the most important applications of the velocity signal SL generated by the accelerometer systems discussed above is in inertial navigation systems, the effect of noise and error signals

in the navigation system a significant issue. As it turns out, the accelerometer noise present in the output of the angular velocity channel 404 is an important factor in the accuracy of an inertial navigation system that uses accelerometers to determine angular velocity. The effect of accelerometer noise for a given accelerometer level of noise is inversely proportional to the vibration amplitude. One has e.g. found, using a QA-2000 accelerometer, commercially available from Sundstrand Data Control, Inc., that the position error is about

two nautical miles for a vibration amplitude of approximately 1.25

etc.

Claims (16)

1. Apparatus for generating a signal representing the angular velocity motion of a structure consisting of: a first accelerometer comprising means for generating a first output signal representing acceleration along a first force-sensing axis; another accelerometer comprising means for generating an output signal representing acceleration along another force-sensing axis; an alignment device for aligning the first accelerometer relative to the second accelerometer so that the first force-sensing axis is substantially parallel to said second force-sensing axis; characterized by a vibration device operatively connected to the structure, and means for vibrating the first and second accelerometers relative to the structure at a frequency W and in a direction substantially perpendicular to the first and second accelerometers force-sensing axis; and a signal processing device sensitive to the first and second output signals to generate a velocity signal representing the angular velocity movement of the structure about an axis perpendicular to the plane of said force-sensing axis and said direction of vibration. 2. Apparatus according to claim 1, characterized in that the vibration is an angle. 3. Apparatus according to claim 1, characterized in that the vibration is essentially linear. 4. Apparatus according to claim 1, characterized in that the vibration device is effective for vibrating the first and the second accelerometer so that the translational components of the vibration are essentially equal and opposite. 5. Apparatus according to claim 2, characterized in that the first and the second accelerometer are aligned by the aforementioned device, so that the first and the second force-sensing axis are parallel to the axis of angular vibration. 6. Apparatus according to claim 5, characterized in that the first and the second force-sensing axis are substantially equidistant from the angular vibration axes. 7. Apparatus according to claim 2, characterized in that the first and second accelerometers are arranged by the aforementioned device, so that the first and second force-sensing axes are opposite and essentially coaxial with each other. 8. Apparatus according to claim 7, characterized in that the axis of angular vibration is perpendicular to the first and the second force-sensing axis, and placed between the first and the second accelerometer. 9. Apparatus according to claim 2, characterized in that the vibration angle is approximately 50 milliradians peak to peak. 10. Apparatus according to claim 3, characterized in that the first and the second accelerometer are arranged by the aforementioned device, so that the first and the second force-sensing axis are opposite and are substantially coaxial with each other. 11. Apparatus according to claim 10, characterized in that the vibration amplitude is approximately 2 millimeters peak to peak. 12. Apparatus according to claim 1, characterized in that it comprises a pre-processing device, operatively connected between the first and the second accelerometer and the said signal processing device to supply the sum of the first and the second output signal to the said signal processing device. 13. Apparatus according to claim 12, characterized in that the pre-processing device additionally adds the difference between the first and the second output signal to the signal processing device. 14. Apparatus according to claim 1, characterized in that the signal processing device comprises a force channel device which is sensitive to the first and the second output signal to generate a force signal representing the acceleration of the apparatus along the force-sensitive axis and a velocity channel means sensitive to the first and second output signals to generate a velocity signal. 15. Apparatus according to claim 14, characterized in that it comprises a pre-separation device, operatively connected between the first and the second accelerometer and the said signal processing device to combine the first and the second output signal into a first combination signal to be sent into the power channel device and to combine the first and second output signals into another combined signal to be sent into the speed channel device. 16. Apparatus according to claim 15, characterized in that the first and the second force-sensing axis are aligned in the same direction, and where the first combination signal is a function of the sum of the first and the second output signal and that the second combination signal is a function of the difference between the first and the second output signal.