FI92107C - Method and apparatus for determining real-time offset for angular velocity transducers - Google Patents

Description

92107

Offset real-time measurement method jaf hardware for angular velocity sensors

The invention relates to a real-time offset measurement method according to the preamble of claim 1.

5

The invention also relates to an apparatus for real-time offset determination, in particular in Strapdown angular velocity sensor apparatus.

The invention is used in connection with inertial navigation systems (Strapdown systems), inertial and angular velocity sensors (rate gyroscopes, rate transducers) and position determination (Vertical and Azimuth reference Unit).

The invention does not explicitly apply to Stabilized platforms (Gimballed systems). The principle of operation of these mounting units 15 is substantially different from that of the Strapdown units.

Angular velocity sensors are measuring devices that measure the rotational or angular velocity around a certain axis. Sensors suitable for measuring the rotation of a free body are most often based on the inertia of the mass. The most typical inertia-angle-20 speed sensors are gyroscopes, gas rate transducers, piezoelectric vibrating gyroscopes, and optical gyroscopes. Optical gyroscopes are not strictly based. to the slowness of the mass (because there is light rain in motion), but they are usually counted as inertial components.

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The most common use of inertia angular velocity sensors is to determine the position of a freely moving object (eg an airplane, ship or vehicle) in three-dimensional space. In this case, three angular velocity sensors are usually mounted at right angles to each other to measure the rotational speed of the body around each axis of rotation (x, y, z) (Strap-30 down unit). By integrating the total rotation, the position information is calculated at each moment.

The main sources of error in position determination are: - sensor offset error, 92107 2 - sensor gain error, - sensor nonlinearity and 5 - sensor installation direction error.

Of these, the offset error is by far the largest source of error. If the offset error is not compensated, an error accumulates in the position estimate, regardless of the movement of the object. In this case, the position information will soon be unusable.

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Offset errors are, of course, greatest in low-cost angular velocity sensors and decrease when switching to more expensive sensors.

Measuring and compensating for offset errors is problematic because the errors vary according to the 15 temperature conditions and also from one day to the next. Thus, offset errors cannot be accurately determined in advance, for example in laboratory conditions, but must be able to estimate errors in real time.

Previous techniques 20

A simple known method for determining the offsets of a strapdown positioning unit is ‘‘ land vehicles have to stop the vehicle at suitable intervals and measure the sensor readings ’* · averaging over a suitable time. In this case, however, the rotation of the earth and the position of the vehicle as well as the direction on the earth must be taken into account. The method is inherently unsuitable for flying or waterborne vehicles. Stopping the vehicle also interferes with normal operation.

Another known method is suitable for rotary gyroscopes and is based on modulating the rotational speed of the rotor at a known frequency. However, this method is not suitable for other types of angular velocity sensors, such as optical gyroscopes, oscillation gyroscopes, or gas jet sensors.

3 '92107

Other known methods are most often based on the comparison, averaging, or prediction procedures of a plurality of permanently mounted additional angular velocity sensors. However, these methods do not determine the values of the offsets, but only give an estimate of the magnitude of the offset errors.

The object of the present invention is to eliminate the shortcomings of the above-described technique and to provide a completely new type of real-time offset measurement method and apparatus for angular velocity sensors.

The invention is based on the fact that the measuring direction of at least one additional an Tur with respect to the fixed sensors is changed during operation. The movement is carried out, for example, by means of two stepper motors.

More specifically, the method according to the invention is characterized by what is stated in the characterizing part of claim 1.

The apparatus according to the invention, in turn, is characterized by what is stated in the characterizing part of claim 4.

The invention provides considerable advantages.

Step motors (or other actuating means) are not required to be particularly precise in terms of movement or positioning. The current position of the rotating sensor does not need to be accurately measured. Sensor installation directional errors or linear gain errors do not affect the offset measurement accuracy. The invention is suitable for all types of inertia sensors.

The offset is determined while the vehicle is moving. Offset measurement does not interfere with position measurement.

The invention will now be examined in more detail with the aid of embodiments 30 according to the accompanying figures.

Figure 1 shows a perspective view of one arrangement according to the invention.

4 92107

Figure 2 shows the direction vectors of the fixed sensors of the apparatus according to the invention.

Figure 3 shows the direction vectors of a mobile sensor according to the invention.

Figures 4a-4d show an alternative arrangement according to the invention in different positions of the variable sensor.

Figure 5 shows a block diagram of the apparatus according to the invention.

Figure 6 shows an operating sequence according to the invention.

Figure 7 shows an alternative interleaved sequence of action according to the invention.

Figure 8 shows a data flow diagram according to the invention.

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The three angular velocity sensors measure the angular velocity vector of an object in detail in theory. When additional sensors are added to the system, additional measurements and redundancy equations are obtained, which can be used to calculate the gain and offset parameters of the sensors. However, each time one Add sensor is added to the system, one additional 20 gain and offset parameter Add is also displayed. Thus, adding fixed sensors from the equations cannot be solved.

According to Figure 1, the problem is avoided by measuring, in addition to the fixed sensors 1 to 3 fixedly attached to the measuring object 5, one (or more) movable angular velocity sensors 4 rotating the body 5 in several different positions relative to the fixed sensors 1-3. This gives Add dependence equations between sensor measurements, but does not present any new unknown parameters. Measurements made in different positions can therefore be interpreted as measurements made with several completely identical sensors. A first stepper motor 8 is connected to the frame 7, on the shaft of which a movable sensor 4 is connected. A second stepper motor 6 is attached to the measuring object 30, to the shaft of which the frame 7 is attached, so that the frame 7 can be rotated by a second stepper motor 6 *. around the axis. The axes of the motors 6 and 8 are perpendicular to each other. Frame 7 5; 92107 can thus be moved by means of the first stepper motor 6 and in turn by means of the second stepper motor 8 fixed to the frame 7 the movable sensor 4 can be set to the desired arbitrary position. The number of measuring directions is thus unlimited.

An alternative way of realizing the movement of the sensor 4 according to Figures 3 and 4a to 4d is to use two two-position rotating magnets 40 and 41 (or any rotating relay) with which a four-position orientation can be realized. When the axes of rotation of the rotating magnets 40 and 41 are oriented at an angle of 135 degrees to each other and the Z-axis rotation angle is 180 degrees and the oblique axis rotation angle is approximately 110 degrees, an arrangement according to Figs. 4a to 4d is obtained. 16-19.

The actuators are not required to be accurate in terms of rotational speed or rotational speed, as no measurements are made with the sensor 4 during the change of position. The actuators are also not required to have an accuracy in positioning the angle, since the method is not based on the exact orientation of the sensor, but the actual orientation of the sensor is estimated on the basis of the measurements. The only essential requirement is sufficient strength of the actuating member 6 and 8, or 40 and 41, since the rotating sensor 4 must not move relative to the body 5 during the measurement.

In the block diagram of the apparatus according to Fig. 5 and with reference to Fig. 1, the angular velocity sensors 1-3 are fixedly mounted on the frame 5, the sensor 4 being mounted rotatably by means of actuating means.

Some of the equipment, such as the fixed angular velocity sensors 1 to 3, the A / D converter unit 50, and the computer unit 51 are already part of the conventional Strapdown position measuring device. These parts do not need to be duplicated, but the offset measurement can be integrated into the ** Strapdown position measuring equipment as appropriate.

For the sake of simplicity, the angular velocity sensors 1 to 4 described in the diagram are so-called Angular velocity sensors for one sensitivity axis 30, ie, they measure angular velocity about one axis of rotation ''. However, the invention is also applicable to angular velocity sensors with two sensitivity axes, in which case two single-axis sensors can be replaced by one two-axis sensor.

6 92107 The limitation of operation with these sensors is the fixed orientation of the shaft pair relative to each other. The measuring axes of a pair of shafts are typically at right angles to each other, in which case one pair of sensors can replace the pair of sensors 1-2-2-3 or 3-1.

5 Strapdown position measuring equipment often includes more than three fixed angular velocity sensors, e.g. to increase fault tolerance. The method is applicable to an arbitrary number of fixed sensors simply by applying it to each group of three sensors in parallel. The diagram shows the minimum number required for offset determination.

10

Angular velocity sensors can be of the rotary rotor type gyroscopes, optical gyroscopes, oscillating gyroscopes, gas jet sensors or in general any sensors that measure angular velocity with respect to inertial space. In certain cases, the use of an angular velocity sensor requires additional controls, such as controlling the speed of 15 rotors with rotary gyroscopes. However, the quality of these controls varies from case to case and is not relevant to the method.

The position measuring apparatus usually also includes sensors other than angular velocity sensors, generally e.g. three accelerometers 20 mounted at right angles to each other. In some cases, the angular velocity sensor and the acceleration sensor are even integrated into one sensor (eccentric rotary gyroscope). However, the amount and quality of other sensing varies greatly and is not relevant to the method. For the sake of simplicity, the diagram shows only the configuration necessary for the determination of the offset.

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In the diagram, the movement of the rotating sensor is implemented by two stepping motors, which are controlled by the stepping motor controller 52 according to the instructions of the computer 51. An alternative way to perform the movement is to use e.g. two two-position rotating magnets or a rotating relay.

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According to Fig. 6, the following operating sequence is implemented: • «92107 τ 61. The rotating sensor 4 is set to its first position. Positioning accuracy does not affect the estimation result, but certain nominal trends are advantageous for the accuracy of the method.

5 62. Sensors 1 to 4 perform simultaneous measurements (sampling) at a frequency, the upper limit of which is determined by the bandwidth of the angular velocity sensors. A typical measurement frequency is 50 Hz. A sufficient measurement period at each fixed position of the sensor 4 is e.g. 1000-10000 readings as the body 5 moves, depending on the desired accuracy and the noise of the sensors. The measurement time is then typically 20 to 200 s. If the body 5 is completely stationary within the measurement accuracy of six, the required movement can be left to wait. Motion can also be artificially generated using maneuvers or external equipment.

63. On the basis of the measurement law, coefficients are determined that describe the interdependence between the measurements. The odds are saved.

15 64. The rotating sensor 4 is moved to the next position. The measurement of the rotating sensor 4 is interrupted or left inoperative during changes in the position of the sensor. However, sensors 1-3 perform a continuous measurement due to the determination of the position of the body 5.

20 65. Steps 62-64 are repeated until the desired number or positions of at least four rotating sensors 4 have been used.

• · 66. Based on the stored coefficients, the offsets of the sensors are determined. In order to monitor the offsets in real time, the sequence described above is repeated non-stop. Move to paragraph 25 61.

An alternative, interleaved sequence of action is shown in Figure 7.

When at least 1 measuring time has been performed for each nominal orientation of the sensor 4, the evaluation of the offsets 30 can be performed in a sliding manner in accordance with this alternative sequence. From here on, the offset estimation is performed in connection with the position of each sensor 4, so that the last measurement result (coefficients) 8 92107 corresponding to each nominal position is taken into account.

According to Fig. 8, the successive measurement results y1) to y4 (j) of the angular velocity sensors 1 to 4 are stored in the computer memory until a sufficient number of measurements with the constant orientation of the sensor 4 have been performed. Measurements of angular velocity sensors 1-3 are also used for position determination.

From the stored measurement time, the dependence between the sensor measurements is calculated, which can be modeled, for example, as the coefficients of the linear dependence equation Ις ,, - ΐς ^, as well as <* n. 10 The odds are stored in the computer's memory. Instead of a linear dependence, a higher degree polynomial can also be used, in which case the nonlinearity of the sensors can also be modeled.

When the coefficients have been calculated sufficiently corresponding to the different orientations of the rotating sensor 4 (at least 15 to four), the offset values a ^ a are solved from the stored coefficients. * Estimates of successive offsets can be smoothed by different filtering methods.

The estimates of the offsets are fed to a position measurement block, where they can be used in real time to compensate the measurements of sensors 1 to 3.

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The following is a theoretical review of the invention based on the above figures: • ·

The angular velocity of a rotating body can be represented by the vector ω (ΐ), ωχ (t) 'ω (t) = «y (t), (1) ωζ (0 25 whose direction defines the axis of rotation and the length | ω (0 | about the axis of rotation of the angular velocity in the correct coordinate system.

The angular velocity Uj (t) of the part about any p-, axis of rotation is obtained as a point product 9 · 92107 ω1 (C) ω (t) (2) bil-1 · <3)

An inertial angular velocity sensor (eg a gyroscope) with an axis of sensitivity oriented in the direction p, indicates the angular velocity cj; (t). In a traditional strapdown navigation system, the angular velocity is measured in at least three linearly independent directions P: 'ω ^ ΟΙ Γωχ (0' ω2 (t) -p uy {t) (4) ω3 (C) J w2 (t) det P * 0, (5 ) where P is a quadrilateral-5 rice formed by three linearly independent unit vectors describing the position of the sensors.

The angular velocity vector oj (t) can be calculated from the measurements o>, (t), ω2 (0 and ω3 (ί) by inverting the matrix P. Normally P is chosen as the unit matrix I, the sensors being arranged orthogonally parallel to the rotation main axes.

10

The angular velocity vector is integrated using, for example, Quaternio's representation to produce location information. Measurement integration errors accumulate in the location estimate. Thus, the offsets of the sensor measurements are not desirable because the offset error integrates and this causes the position angle independent of the actual angular velocity of the object to be corrected.

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The properties of angular velocity sensors can be described by serial developments yx (t) = β1 + 2) 1ω1 (t) + c ^ i (t). . . (6) y2 (t) = az + jb2 <o2 (t) + c2g> 2 (t). . . (7) y3 (t) = a3 + £ 3 <»> 3 (t) + c3 (03 (t)..., (8) where y; (t) is displayed by the sensor, coefficients a, offset errors, coefficients b ( are linear ___________. 1-- 92107 10 gain factors and coefficients c, ... describe nonlinearity errors.

The solution according to the invention uses a fourth redundant angular velocity sensor with offset error factors a; the determination of. The redundant sensor has similar properties to the other 5 sensors and can also be described by the receiver development: y4 (t) = ai + biu> A {t) + c4 <»> 4 (t). . . . (9)

The simultaneous real angular velocities of the four angular velocity sensors have the following dependence: ωχ (t) Γωχ (t) 'ω4 (t) = p4 P'1 ω2 (fc) = [P4i P42 P43] ω2 (c) / (10) ω3 (t ) J | ω3 (ί :) where the unit row vector p4 is the direction of the redundant sensor. Normally, the nonlinearity error coefficients c ,, ... are small compared to offset and gain errors. We break the beneficiary developments of formulas (6) ... (9): yi (C) = ai + bi (0i (t) (11) and place the reduced expressions in formula (10): y4 (c) = i> 4 ([Ep Eli Sm <12> ([bl b2 J [jTj (t) J bl b2 b3)> 1 (t) 1 = [^ ^ 2 ^ 3] y2U) -k ^ -k ^ -k ^ + ai (13)

[y3 (t) J

Vi (t) '^ k ^ kj] y2 (t) + «. (H) [y3 (t) Thus a linear dependence is obtained between the measured angular velocities, from which the coefficients k, - k3 and a can be determined, for example, by applying a linear regression to the measured values y4 (t). Assuming that the values y; (t) are not constant within the resolution of the A / D transform 92107 ti, linear regression gives non-biased estimates for kt · k3 and a with the accuracy of fractions of the measurement noise σ. One very suitable method in this case, where all measurements include noise, is the Total Least Squares method, which is based on the singular value decomposition [Golub & Van Loan].

5

Consider what happens when the direction of a redundant sensor is changed with respect to sensors 1-3. As a result, the coefficients p4I to p43 in formula (10) change, but the gain and offset coefficients remain the same, assuming that the measurement period is short compared to the rate of change of the offsets.

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Perform four estimates for the coefficients k, - k3 and a using four different orientations (n = 1 .. .4) for the redundancy. When the trends are properly selected, a group of four linearly independent equations is obtained, with four unknown offset coefficients d ^: ~ ku ~ ki2 11 r-ra »1 ®l in addition to the known coefficients Ις, - and an (n = 1 .. .4) "^ 21 ~ k22 ~ k23 1 a2 _ a2” ^ 31 ”- ^ 32 ~ k33 1 a3 a3 15 [- ^ 1 ~ ki2 - *« 3 lj La'JL “4j: · from which the offset coefficients can be solved by inverting a square matrix. Note that according to the algorithm, the directions P and p4 of the angular velocity sensors 1 to 4 do not need to be known and thus installation errors do not cause errors in this solution model. enables easy implementation and accurate determination of offsets, but the actual gain of the sensors .. bj does not need to know that the accuracy of the offset estimate is not affected by the gain errors.

From the point of view of linear regression, it is optimal for the method to select the direction 25 of the sensors 1 .. 3 such that P * I. In this case, the correlation between the measurements is minimized and the susceptibility of the measurement matrix to interference is minimized [Golub & Van Loan]. Figure 2 shows one example of the orientation of sensors 1 to 3.

921 07 12

When P * I, the sensitivity of the equation (15) is minimized by selecting the approximate directions of the fourth sensor from the center of the regular quadrilateral to the angles of the quadrilateral. Such a symmetrical arrangement, the direction vectors p4 “of which are shown in Fig. 3, is obtained, for example, as follows:

Pi = (16) y / 3

Pi = -p [1 -1 1] (17) v / 3

Pi = -p [1 1 “I] (18) \ / 3

Pi = ["I" I "I] · (19) y / 3 5 The minimum is flat, so the sensitivity increases only slightly by selecting e.g.

P41 = [ioo] (20) P42 = [0 1 0] (21) P43 = [0 0 1] (22) P4 * -p [-1 -1 "I], (23) which may be easier to implement. It is also possible to measure more than four data sets (n> 4) and thus obtain an over-defined set of equations, then the offset coefficients are solved by the general pseudo-inverse method that finds the most suitable coefficients.

Pi = [1 Ο Ο] (24) ρΙ = [Ο 1 Ο] (25) ρ \ = [001] (26)

Pt = [- 100] (27)

Pi = [0-10] (28) pt = [00-1]. (29)

Using more than four data sets achieves a reduction in the statistical oscillation of the offset estimates. The actual direct advantage is not achieved with such a method, as the same result can also be obtained with other mathematical post-processing methods of successive estimates.

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When the number of fixed sensors is greater than three, the method can be applied separately to each group of three sensors.

If there is more than one movable sensor, the method is applied separately. 10 for each movable sensor.

[Golub & Van Loan]

Gene H. Golub and Charles F. Van Loan "Matrix Computations" 15 North Oxford Academic

Claims (11)

92107 A method for measuring the position of a body (5) by means of a "Strapdown" method in a real-time offset measurement method, wherein at least three angular velocity sensors (1, 2, 3) fixedly mounted on the body (1) measure the angle of the body (5) 2, 3) angular velocity information, characterized in that 5 - at least one additional movable angular velocity sensor (4) is used. and 10 - the offsets of the sensors (1, 2, 3, 4) are determined by comparing the simultaneous measurement results of the sensors (1, 2, 3, 4). Method according to Claim 1, characterized in that a linear dependence (Equation 14) is fitted between the measurements of the sensors (1, 2, 15 3, 4) at each different position of the sensor and the offset values are determined from the linear group of equations thus obtained. A method according to claim 1, characterized in that the additional: angular velocity sensor (4) is moved to positions parallel to the vectors extending from the center of the regular quadrilateral 20 to the quadrilateral angles (formulas 16 to 19). Method according to Claim 1, characterized in that the additional angular velocity sensor (4) is moved to positions in which four are parallel to the fixed sensors (1-3) and one deviates from them. 25 Method according to Claim 1, characterized in that the additional angular velocity sensor (4) is moved to positions which are parallel and opposite (formulas 24 to 29) to the fixed sensors (1 to 3). 92107 A method according to claim 1, characterized in that when the number of fixed sensors is greater than three, the method is applied separately to each group of three fixed sensors. A method according to claim 1, characterized in that when the number of movable sensors is greater than one, the method is applied separately to each movable sensor. An apparatus for real-time determination of an offset for angular velocity sensors measuring the position of a body (5), which apparatus comprises at least three angular velocity sensors (1, 2, 3) fixedly mounted on the body (5), characterized in that the apparatus comprises - 4), and 15 - movement means (6, 8) arranged between the body (5) and the additional sensor (4) for the additional angular velocity sensor. (4) to move to at least four different measuring positions. Apparatus according to Claim 8, characterized in that the actuating elements (6, ";;; '8) are stepper motors. Apparatus according to Claim 8, characterized in that the actuating elements (40, 41) are rotating magnets or rotating relays. 25 Apparatus according to claim 8, characterized in that the movable sensor .. (4) is attached to a first actuating member (8), which in turn is attached to a frame (7) movable by means of a second actuating member (6) connected to the measuring object (6). 5). 92107