EP3894786A1

EP3894786A1 - Method and device for positioning determination by means of inertial navigation, and calibration system

Info

Publication number: EP3894786A1
Application number: EP19836454.9A
Authority: EP
Inventors: Saso Spasovski
Original assignee: CHRONOS VISION GmbH
Current assignee: CHRONOS VISION GmbH
Priority date: 2018-12-11
Filing date: 2019-11-29
Publication date: 2021-10-20
Also published as: WO2020119841A1; DE112019006140A5; US20210364652A1

Abstract

In a method and with a device (100) for position determination by means of inertial navigation, a current position (103) is determined from a known starting position (104) and starting orientation by sensing accelerations and rotation rates. To do this, sensors (10) are used to sense accelerations and rotation rates, and the accelerations and rotation rates acting on the sensors (10) along or about three sensor axes are calculated. An evaluation device (13) is used to determine a position from the data of the individual sensors (10), and the vector components of the positions determined are then added in a weighted manner. The weightings are determined by calibration.

Description

Method and device for determining position by means of

Inertial navigation, and calibration system

The invention relates to a method for determining position by means of

Inertial navigation, from a known starting position and

Orientation is determined by measuring accelerations and rotation rates a current position. Furthermore, the invention relates to a device for determining position by means of inertial navigation with a plurality of sensors for measuring accelerations and rotation rates. The invention further relates to a calibration system for calibrating the device.

The determination of the current spatial position of an object is often realized via global or regional satellite-based positioning systems (GNSS), such as. B. GLONASS, Galileo, GPS, Beidou, IRNSS or QZSS, and corresponding receivers. However, the applicability of the technology in the area of navigation is limited to situations in which reception of the signals is guaranteed. Due to the relatively low transmission power and the resulting low field strength of the satellite signals

Shielding of any kind is a massive obstacle to the functioning of a GNSS.

In addition to this physically justified limitation, which can seriously disrupt satellite-based navigation, for example in buildings, under the water surface and in underground construction, electromagnetic interference transmitters pose a further danger when determining the position using GNSS. For example, so-called spoofers can manipulate the satellite signal while so-called jammers can partially or completely disturb or prevent the reception of the signal. In principle, inertial-based navigation systems, also called INS, are based on the measurement of linear accelerations and rotation rates along or around three pairs of linearly independent body axes. Based on the classic mechanics, knowing the initial spatial position, speed and alignment, the initial conditions, the alignment or orientation is initially obtained from the continuously measured yaw rates around the three axes via simple integration. Together with the linear acceleration, which is also continuously measured, adjusted for gravitational acceleration, the current speed after integration and the current spatial position of a moving body after further integration.

Despite the fact that no electromagnetic signals or optical marks are used, such systems have some serious disadvantages. Especially when using inexpensive MEMS-based

Inertial sensors have these disadvantages, so that navigation is only possible for a relatively short period of time with sufficient positional accuracy. One of the main problems of inertia-based sensors is the bias error. This also results in small amounts of this error

Movement drift, which is expressed, for example, in the fact that a movement is derived from the measured acceleration data of a body at rest, but this does not actually take place. Due to the double integration in the position calculation, the position error increases quadratically with time. This means that the position determination can become unusable within minutes.

Figures 1a and 1b show examples of the influence of a minor

Noise and bias errors of the data of an acceleration sensor on the calculated speed in the X direction (FIG. 1 a) and on the X coordinate of the current position (FIG. 1 b) without an actual movement taking place. In these figures, a straight, dashed line 1 shows the actual value, while a curved, continuous line 2 shows the value determined from the sensor data. The object of the invention is to increase the accuracy of the position determination in environments or situations in which reliable reception of electromagnetic signals including visible light is not possible or there is no corresponding technical infrastructure.

To achieve this object, the invention provides a method for

Position determination by means of inertial navigation, in which from a known starting position and starting orientation by detecting

Accelerations and rotation rates a current position is determined, comprising the steps: providing sensors for detecting accelerations and rotation rates; Calculating the accelerations and rotation rates acting on the sensors over a period of time along or around three sensor axes; a position is determined from the data of the individual sensors and the vector components of the determined positions are then added in a weighted manner, the weights being determined by calibration.

Advantageous embodiments of the invention are the subject of the dependent claims.

To determine the current position, a non-linear combination of the vector components of the positions of a plurality of sensors (10) is preferably formed, the vector components and in each case at least the second power thereof being added up separately and weighted.

For example, a number of sensor combinations, each of which fulfills at least one quality criterion, is selected for calibration from a large number of sensor combinations for each coordinate direction.

The quality criterion is advantageously met if the sum of the deviations of the coordinates of the positions of the individual sensors of the respective sensor combination from the actual value of the coordinate of the current position is below a defined limit value for each coordinate direction at the end of the calibration. The quality criterion is preferably met if the deviation of the center of gravity of the coordinates of the positions of the individual sensors of the respective sensor combination from the actual value of the coordinate of the current position is below a defined limit value for each coordinate direction at the end of the calibration.

For example, the quality criterion is met if for each

Coordinate direction the sum of the integrated over the calibration period

Deviations of the individual coordinates of the positions of the

Sensor combination belonging sensors from the actual value of the coordinate of the current position is below a defined limit.

A number of sensor combinations is advantageously selected, at least one at different times during the calibration

Meet quality criterion.

A predetermined minimum and / or maximum number of sensor combinations which meet the quality criterion is preferably selected.

For example, a spatial coordinate of the center of gravity is used to determine the weights for each of the selected sensor combinations

corresponding coordinates of the current positions of the individual sensors of the sensor combination are calculated.

A spatial coordinate of the is advantageous for determining the weights

Center of gravity of the center of gravity of the corresponding coordinates is calculated.

The deviations of the corresponding coordinates of the current positions of the individual sensors of the selected sensor combinations from the actual value of the corresponding coordinate of the current position are preferably used to determine the weights for each coordinate direction. For example, an over-determined system of equations is solved for determining the weights for each coordinate direction.

The weights of the sensors for each coordinate are advantageous

Coefficients of a linear combination of corresponding coordinates of the positions associated with the sensors are formed.

According to another aspect of the invention, an apparatus for

Position determination created by means of inertial navigation, comprising a large number of sensors for detecting accelerations and rotation rates along or around their respective sensor axes, and an evaluation device for calculating a current position from the detected accelerations and rotation rates, the evaluation device being designed in such a way that it consists of the Data of the individual sensors determined a position and the

Vector components of the determined positions are then added in a weighted manner, the weights being determined by calibrating the sensors.

The evaluation device is advantageously designed to carry out the method according to the invention.

The device preferably comprises means for thermally decoupling the sensors from the environment and / or thermocouples to compensate for temperature changes.

For example, the device comprises a device for mechanical damping of the sensors.

The device is preferably used in an aircraft, land vehicle or watercraft, which can be manned or unmanned, for example, and / or is designed as a portable navigation device for people and / or for use under water, such as in particular for diving operations.

According to a further aspect of the invention, a calibration system is created which comprises a device according to the invention and a calibration unit for Calibration of the device according to the invention comprises.

At least 25, preferably at least 36, and particularly preferably at least 42 or 100 sensors are advantageously used in the device and / or in the method.

More than 50, particularly preferably more than 100, are preferred

Sensor combinations determined. "Good sensor combinations" are

Sensor combinations that meet at least one quality criterion.

For example, the good sensor combinations each comprise more than 10 sensors, preferably between 12 and 36 sensors.

For example, the computing time for determining the weights in e.g. 100 sensors are in the range of a few minutes using a standard computer. With greater computer performance, the

Computing time can also be shorter.

The weights can also be determined, for example, using a PC, which is integrated directly into a charging station, for example. After the weights have been determined with the aid of the external PC, these are transferred to the device or to the navigation device and the system can be used, for example by a user.

The invention solves the above-mentioned problems in the prior art by dispensing with the evaluation of satellite signals. In general, no electromagnetic radiation is used as an information carrier. In order to

The invention differs fundamentally from localization technologies such as Wi-Fi-based location, beacons, time of flight using UWB, VLC, where light signals are used for navigation, and camera-based solutions such as stereo vision, triangulation, etc.

This property predestines the present invention for use in environments and situations in which reliable reception of EM Signals (including visible light) is possible or there is no corresponding technical infrastructure. This includes the localization of emergency and rescue workers, for example in the event of mining accidents, building fires, diving missions or navigation to the sea, on the ground or in air space in the event of disturbed or manipulated GPS reception.

The invention can be counted among the inertial-based navigation systems. For example, it can also be referred to or described as inertial navigation using the IMU matrix (IMU = inertial measurement unit).

For example, the invention uses a number of so-called inertial measurement units (IMU: Intertial Measurement Unit) manufactured in microsystem technology (English micro electro mechanical system - MEMS).

For example, a matrix of inertial measuring units is used.

If not explicitly excluded, then in the following

assumed that the sensors or IMU sensors each contain a digital three-axis acceleration sensor and a three-axis digital gyroscope or rotation rate sensor. However, it is not a necessary condition that acceleration sensors and gyroscopes are in the same housing. Some IMUs also contain a digital thermometer and a

triaxial digital magnetometer.

The invention is based on the following considerations:

For each of the three axes, each sensor supplies a stream of data that characterizes the linear acceleration and rotation rate. The simplest model uses a linear relationship for the relationship between sensor value and movement variables. For example, the following mapping or transformation rule applies to linear acceleration and the rotation rate along or around the X axis:

The parameters are sensor-specific a * and ox denote the actual acceleration and angular velocity or rotation rate along or around the sensor X-axis, a _{x, s} and oox.s the raw values sent by the sensor for the linear acceleration and rotation rate in or around the sensor X direction, sc _ax and sccox the scaling factors and biasax or bias _ffl x the values at

vanishing acceleration and yaw rate along or around the sensor X axis (a _x = 0, cox = 0) are sent by an IMU.

The parameters scax, sc «, x, biasax and biaso * in the figure above are determined via a calibration process, which, however, is not part of the present invention. To distinguish it from the calibration described below, this is called parameter calibration below.

In principle, each of the three sensor axes is z. B. parallel and then aligned antiparallel to the direction of gravitational acceleration. The meanwhile

recorded raw sensor values correspond to acceleration 1g or -1g or 9.81m / s ² and -9.81 m / s ² . To calibrate the parameters for the rotation rates around the respective axes, the sensors are rotated around the corresponding axis with at least two different but known angular velocities.

The drift described above is u. a. through the noise and through the

The fact causes that the scaling parameters and in particular the bias values are known only with limited accuracy even after parameter calibration and can vary slightly each time the IMU is switched on (turn-on to turn-on bias or turn-on instability).

Figures 2, 3a and 3b show a possible histogram or the

Distributions of the bias error (as raw sensor values) of the linear acceleration on the individual sensors of the matrix. The bias error of the linear acceleration and yaw rate along or around an axis can be defined as the deviation of the current bias value for this axis from the true value.

2 shows a histogram of the bias errors (in raw sensor values) of the linear acceleration for the X axis with 36 IMU sensors.

FIGS. 3a and 3b show a possible distribution of the bias error (in raw sensor values) of the linear acceleration for the X and Y axes in 36 IMU sensors. The graphic shows that the bias errors have different values for each sensor and for each axis.

The approach on which the invention is based for calculating the trajectory or trajectory and thus the current position differs from that of existing navigation systems with one or more IMUs. It is not the primary aim to minimize the noise of the sensor values by using an intelligent filter, or to identify the influence of other effects, parameters and sizes and to include them in a suitable way in order to obtain optimized properties with regard to the drift behavior, or in general one Prevent position errors or keep them small.

In the path followed in this invention, the current position determination is instead optimized by weighting the positions calculated with the aid of the individual sensors in such a way that, for. B. a linear combination of the X coordinates of the positions belonging to the individual sensors of the IMU matrix leads to a more precise X coordinate.

The basic idea is to first consider each IMU of the arrangement separately and to calculate the associated trajectory or the current position using customary and known methods from the continuously measured sensor data and, for example, read out with a microcontroller using a suitable computing architecture. Usually, when using N sensors z. B. due to the noise and the sensor-specific bias error mentioned above

Results in general N different trajectories and thus also N current positions in space, which can differ, in part very strongly, from the actual trajectory and current position of the room (see FIG. 4).

FIG. 4 shows the calculated current positions 41 of the individual sensors of an arrangement of 36 IMU sensors (crosses) after a calibration period of 10 minutes (the Z coordinate has been omitted); the system was at rest during calibration. It can be seen very clearly that after 10 minutes the deviation of the calculated values from the

Sensor data, which are shown as crosses 41, from the rest position 42 (x = 0, y = 0) located in the center of the graphic up to approximately 2 or 3 km and more.

The idea of the invention is based on the fact that instead of the path coordinates individually calculated for each sensor, the components of the linear acceleration and the rotation rate of the individual sensors can also be suitably weighted, in order thereby to have one continuously for each point in time

to generate representative, individual substitute values for the components of the acceleration and yaw rate, with the help of which the current orientation and

Room position can be calculated.

The arrangement as a matrix is not relevant. For example, the sensors can be arranged in a single row or completely arbitrarily, as long as the positions are known and the three sensor axes of all IMUs are each parallel. This also has advantages in the

Parameter calibration, since all sensors can then be calibrated at the same time in order to determine the respective sensor-specific scaling factors and bias values.

With an increasing number N of sensors, the probability increases that the calculation of an average trajectory or the formation of the center of gravity of all N current position results in a more precise result when calculating the actual trajectory or the actual position in space.

The mentioned center of gravity t represents the vector sum of all current positions originating from the individual sensors | n = 1 .. N] divided by N and can be viewed mathematically as a linear combination of the N current positions with the identical coefficients 1 / N:

Despite an improvement in accuracy, the error exceeds, i.e. the

Deviation of the calculated from the averaging from the actual current position, an amount after a short time that makes this procedure unsuitable for navigation (see FIG. 5).

FIG. 5 shows the error 51 of the calculated X coordinate for all sensors of the IMU arrangement after 10 minutes. The arithmetic mean of the deviations is approx. 200 m.

However, the probability that the focus of the current positions of only a subset of the sensors leads to a more accurate result also increases. If, for example, the individual results of the sensors drift systematically in different directions, from a sufficiently large number of sensors it is likely that the drift of an individual sensor will be compensated for by the drift of another individual sensor. However, focusing as a special case of a linear combination with identical coefficients is not the only way to combine the sensor results. The main idea of this invention follows a more general approach and consists in carrying out a weighted addition of the individual coordinates or their powers of all current IMU position vectors component by component for the current position determination. Simulation calculations have confirmed that this approach usually leads to more precise results than a traditional focus. With very high

The weights or contributions of the individual IMUs for the three spatial coordinates will be different, so that for each of the coordinates X, Y, Z of the current position a separate set of N weights or also

Weight vector is to be used, i.e. wx— (wx _lt ..., wx _N ) (4) wy = (wy ₁ , ..., wy _N ^' )

wz = (wz _lt ..., wz _N )

For example, it is very likely that the weight of the IMU sensor Sj deviates from the weight for the Y and Z coordinates when determining the X coordinate of the current position: wxi wyi wzi.

It is also quite conceivable that these weight vectors do not represent time constants and depend, for example, on the temperature, so that different weight vectors for different coordinates for each coordinate

Periods and temperatures must be used.

In principle, the temperature of the IMUs could be kept relatively constant to a certain degree and with a certain effort (thermal insulation, heating and cooling elements, early switching on, etc.). Alternatively, the calibration process described below can also be carried out for different temperatures. For these reasons, the temperature influence is not considered further at first. In the simplest case, the weight vectors for each coordinate, ie wx, wy and wz, are constant over time and are not or no longer temperature-dependent (see above).

The approach for calculating the coordinates of the current position is then:

(the operator ° denotes the Hadamard product) or in components:

X (t) = wx _x Xi (t + wx ₂ Xz (t) + ··· + wx _N X _N t) (6)

or more compact with the help of the dot product:

Z (t) = (wz, Z (t) with

Z (t): = (Zi (t), -.Z _w (t)) (8) and the weight vectors:

wx = (wx _lt ..., WX _N )

wy = (wy _lt ..., wy _N )

wz = (wz _lt ..., wz _N )

The formulation using a scalar product shows the basic idea of the approach particularly clearly, that the individual coordinates of the current position are separated from the corresponding coordinates of the individual sensors

Weighting emerge.

But it is also conceivable that a non-linear combination is more accurate

Deliver results as the linear variant. As an example for the X coordinate and with 2 as the highest power for the current X coordinates of the individual IMUs, the following results:

+ wx _N2 X _N ² (t)

The associated weight vector then has twice the number of components: wx = (wx _ll wx ₁ 2, ..., wx _N1 , wx _N2 ) (10)

As mentioned at the beginning, the previous considerations can also apply to the

Components of linear accelerations and yaw rates are applied. The approaches to calculating the components of the current linear

Acceleration and the rotation rates along or around the sensor axes are then (the time dependency is omitted for simplification): a _x = waxy a _xl + wax ₂ a _{x 2} + · + wax _N a _XN (11) a _Y = way- _L a _Y1 + way ₂ a _{Y 2} H - l · way _N a _YN a _z = waz _x a _zi + waz ₂ a _Z2 + - I- waz _N a _ZN

and

w _c = wgx _x w _CL + wgx ₂ w _C2 + - + wgx _N ü) _XN ü _Y = wgy iw _g1 + wgy ₂ w _U2 + ··· + wgy _N w _UN w _g = wgz- _L w _zi + wgz ₂ w _Z2 + ··· + wgz _N w _ZN with the weight vectors

wax = (wax _l ..., wax _N ) (12) way = (way _l ..., way _N ) waz = (waz _lt ..., waz _N )

and

wgx = (wgx _l ..., wgx _N ) wgy = (wgy _l ..., wgy _N ) wgz = {wgz ^ _^ wgz ^.

For example, a _{Xn \} = a _Xn (t) and w _Ch : = co _Xn (t) denote the current linear acceleration and yaw rate along or around the X axis of the sensor Sn, which are calculated using the parameters biasax.n, scax .n, bias _ffi x, n and sc _m x, n (from the parameter _calibration ) are derived from the associated sensor data (see formulas (1) and (2)).

If the weight vectors have been determined in a calibration process, then exactly one substitute value for the linear acceleration and one substitute value for the rotation rate can be determined from the raw data of all N sensors for each IMU axis and at any time. This makes it possible to like the sensor matrix to treat a single IMU. The orientation and spatial position of the system can then be determined by customary and known methods which are not part of this invention.

In principle, the acceleration vector measured by an IMU in its own reference system ("body frame") is transformed into the world coordinate system ("earth frame"), after firstly the current orientation with regard to an initial orientation using the three-axis gyroscope of the IMU through simple integration the angular velocity or rate of rotation is determined (see formula (14)) and secondly the acceleration due to gravity from the above

Acceleration vector was subtracted. A double integration of the

Acceleration in the world coordinate system gives the position in relation to a known starting position.

Instead of the angular velocity or rate of rotation, alternatively the

Orientation angles around the three world axes are developed according to the corresponding angles of the individual IMUs:

<Px s wgx ₁ f _{c 1} + wgx ₂ f _{c 2} + ··· + wgx _N f _CN (13) yg = ^w 9Vi <PY, 1 + wgy ₂ f _{U 2} + - + wgy _N f _UN f _g = wgz _Y f _{z 1} + wgz ₂ f _{z 2} + ··· + wgz _N f _ZN

For example, it applies to the sensor Si that the current angular position about the Y axis of the world coordinate system can be calculated using an initial angular position f _{U ί} (t ₀ ) and the following formula:

It is the integral of a staircase function, the steps w _{U ί} {ί _h ) of the raw data sent by the gyroscope of the IMU Si up to time t for the sensor Y-axis are given, but they can also be added with the help of

associated scaling factor and bias or offset value from the

Parameter calibration were transformed into rotation rates. The in the

Time intervals appearing as factors result from the reciprocal of the readout rate and do not necessarily have to be identical. The shorter the time intervals, the more precisely the integral of the yaw rate and thus the angle around the Y axis is approximated using the above expression.

Exemplary embodiments of the invention are described below with reference to

attached drawings explained in more detail. It shows:

Flgs. 1a, b is a diagram of an example of the influence of a small one

Noise and bias error in the data of one

Acceleration sensor to the calculated X coordinate of speed and position;

2 shows an exemplary histogram of the bias errors of the linear ones

Acceleration for the X axis with 36 IMU sensors;

Figs. 3a, b a possible distribution of the bias error of the linear

Acceleration for the X and Y axes with 36 IMU sensors;

Fig. 4 shows an example of the calculated current positions of individual

Sensors of an arrangement of 36 IMU sensors after a calibration period of 10 minutes;

5 shows an example of the errors of a calculated X coordinate for all

IMU array sensors after 10 minutes;

Figs. 6a, b a device for position determination according to a preferred

Embodiment of the invention as a schematic representation; 7 shows a histogram of the accumulated deviations per

Sensor subset with a large number of sensor subsets (> 10 ⁵ );

Fig. 8 shows an example of good subsets or sensor combinations

Calculation of the X and Y coordinates of the current position;

Fig. 9 shows an example of an actual and a means

Weight vectors calculated flat trajectory for an arrangement of 25 IMU sensors;

Figs. 10a, b show the development over time of the X and Y errors of the calculated trajectory shown in FIG. 9;

11 shows an example of the detection of a movement of a person according to FIG. 12

Minutes according to the method according to the invention;

12 is a block diagram of an embodiment of the

The inventive method as a schematic representation;

13 shows a block diagram in which a calibration according to a

Embodiment of the invention is shown schematically; and

14 shows a calibration system 200 according to a preferred embodiment of the invention as a schematic illustration.

Figures 1 to 5 serve to illustrate the general

Basic considerations for the invention. They have already been explained above.

FIGS. 6 a and b show the basic structure of a device 100 for position determination according to a preferred embodiment as

schematic representation. The front A and the back B are shown. Figure 6b shows an arrangement for displaying and transmitting the data. A large number of sensors 10, which are designed as inertial measuring units (IMUs), form a sensor arrangement 20, which is arranged on a support unit 11 designed as a circuit board. The sensors 10 are used to measure

Accelerations and rotation rates along or around the sensor body axes and are arranged on the front A of the circuit board 11. In this example, the sensor or IMU arrangement consists of 25 sensors.

Furthermore, an evaluation device 13 in the form of several processors or microcontrollers (MCU) 13a, 13b is provided, which are arranged on the rear side B of the circuit board 11. The main task of the processors or MCUs 13a, 13b is to read out the IMU data and calculate the position. The MCU 13b is used for weighting the individual results and for carrying out further calculation steps, as well as for displaying the result on a display 16 and / or for sending to a receiving station via a transmitter or receiver 17 using an MCU 13c (see also FIG. 6b ).

The evaluation device 13 is designed such that it calculates a position value for each coordinate axis and for each point in time from the sensor data of the plurality of sensors 10, positions for each IMU separately, for example, from the sensor data of the plurality of sensors 10 after conversion into accelerations and rotation rates are calculated and then added weighted component by component. The weight for each sensor 10 and for each

Coordinate is determined by calibration.

Due to the small size of the IMU sensors 10 (approx. 4 mm x 4 mm x 1 mm), the system has a very compact design. The area of the board 11 with the

Sensor arrangement 20, which in this example consists of 25 sensors 10, is 35 mm × 35 mm.

On the back side B of the board 11 are further ² l C-multiplexer or arranged ^I2C switches fourteenth The device 100 shown here is designed such that a plurality of IMUs or

Sensors 10 can be read by an MCU 13a. The IMUs each have an l ² C interface so that they can be addressed directly by an MCU or, if necessary, via an l ² C multiplexer.

In the event that the l ² C address of the IMUs cannot be changed, the l ² C multiplexers 14 offer the possibility of reading out all the associated IMUs separately. Each microcontroller 13 can thereby select an on addressing, for example, of 8 IMUs, which are connected via separate channels using a multiplexer l ² C-.

In one possible variant, each IMU is assigned exactly one microcontroller.

The circuit board 11 thus forms an IMU matrix circuit board with a suitable computer architecture 13, 14 for reading out the IMU data via I ² C multiplexers, for calculating the position via weight vectors by means of the processor or the MCU 13b, for transmission a display 16 and to a PC during a calibration. The calculated position data or the sensor data or other relevant information can also be sent to a receiver.

A method for determining the position is explained below by way of example, which is preferably carried out with the device described above.

In order to determine the weights or the weight vectors for each coordinate direction X, Y, Z for a more precise position calculation, there are several possibilities, as described below.

For the sake of simplicity, the calibration method presented below only refers to the X coordinate and has proven to be useful in computer simulations.

The basic idea is based on the random selection of Q subsets or subsets from the set of sensors 10 {5 ₁ ..., S _N } with at least K and at most M elements:

{5 ₁ ..., S _N ] A Ti good subset], which makes this set a subset of the power set P ({S _lt ..., S _N }).

Furthermore, it should be good subsets, ie the subsets or sensor combinations Ti are characterized in that, for. B. the accumulated deviation Xerror, ie the sum of the deviations of the X positions of the individual sensors 10 of the subset from the actual value of the current position C (ΪE), at the end of the calibration period T _calib = [0; t _E ] is low. A more precise definition of the term good subsets is given below.

FIG. 7 shows a possible histogram of the accumulated deviations Xerror per sensor subset with a large number (> 10 ⁵ ) of subsets of the sensor arrangement 20

In general, therefore, only a relatively small part of the possible ones

Sensor combination the specified property on (xerror low). A possible definition for a good subset is:

where the summation over the | Ti | Extends elements of the sensors 10 belonging to the subset or their X coordinate errors and C ti, h the X position of the nth sensor belonging to the subset Ti at the end of the calibration period Tcaii _b = [0; t _E ]. A similar criterion for selecting good subsets is the following

Condition:

(ü) Ti is a good subset for the calculation of the X coordinate (17)

<=>

It requests that the centroid or mean of the X positions of the sensors 10 of the subset from the actual value of the X coordinate at the end of the

Calibration period tE must not deviate too much.

The focus of the X-coordinate XTI such a good part quantity as the sum of the current X-positions of the individual sensors associated with the parts Cti amount _h divided by the number of elements of the subset

can already be a useful approximation for the current X position.

Figure 8 shows an example of good subsets for calculating the X and Y coordinates of the current position. The horizontally striped IMUs or sensors 10a represent a good subset or good sensor combination for calculating the X coordinate of the current position; the vertically striped sensors 10b form a good subset for the Y coordinate. A sensor can also belong to the two good subsets.

When the calibration is carried out in practice, the sensor data of all IMUs or sensors 10 are stored for a certain period of time T _calib = [0; t _E ] continuously recorded at a sufficiently high rate (e.g. tE = 10 min at 100 Hz), while a defined system movement with exactly known trajectory is also recorded known starting and ending point as well as known starting and ending orientation is carried out. However, it is also conceivable that the

Sensor arrangement with known orientation is not moved during data recording.

If the IMU matrix consists of e.g. B. N = 25 sensors 10 and should be the maximum

Thickness of the subsets to be examined {Ti} z. B. M = max ((| Ti |}) = 16 and the minimum number of sensors 10 per subset K = min ({| Til}) = 6, then there are many such subsets:

With N = 36 sensors 10, billions of such subsets already exist, so that only a relatively small part of them can be checked for the above quality criterion in an acceptable time.

The aim of the calibration is to identify such good subsets and to use them to determine the weight vectors. It is not only a search for the subset whose associated current X coordinate as the center of gravity of the current X coordinates of the sensors 10 belonging to this subset best matches the actual X coordinate of the system, but a certain, predetermined number Q of such good subsets (e.g. a few hundred with 25 IMU sensors). In the simulations carried out, the value of Limit was typically between 10 m and 100 m. The smaller this value is, the fewer sensor combinations can meet the criterion.

Due to the limited capacity in terms of memory and computing power, the calibration is preferably carried out using a PC or another suitable external platform. Figures 6a and 6b described above show a possible structure of the system. The clock rates of the microcontrollers (MCU) used are typically between 20 and 200 MHz and are thus more than an order of magnitude slower than modern PCs. It is therefore advantageous to transfer the IMU data to a PC during calibration in order to search for good sensor combinations and to calculate the weight. The weight vectors are then transferred from the PC to the system and are available for position determination.

The two specified criteria can be determined by other quality criteria or

Conditions are replaced or supplemented. For example, it is possible that not only the sum of the deviations from the current X position at the end of the recording tE is considered, but instead that the criteria are met at different times tk of the calibration period

Another condition can be, for example, that the length of the trajectories averaged over the subsets must match the actual length as closely as possible.

An even stricter criterion for a good sensor combination can also require that the sum of the deviations from the true value over the entire measuring time of the calibration must be as small as possible, which is equivalent to the requirement that the averaged trajectory of the subset agrees well with the actual trajectory is.

When calibrating, it is advantageous not to move the sensor matrix, since in this case too the actual position and orientation are known at all times.

For example, if you specify how many sensors 10 are good

Sensor combination may exist and must exist at least, then there is a way to determine good subsets by selecting a series of sensor combinations or subsets by random generator and checking for compliance with a quality criterion with a suitable computer system until a predetermined minimum number is found. Strictly speaking, the use of the term subset or subset in a mathematical sense is incorrect when sensors 10 may also appear multiple times per sensor combination, e.g. T34 = {S4, S9, S9, S9, S12, S19, S21}, which is algorithmic however, the numbers given for the number of possible subsets may again be increased significantly.

So far, simulation calculations without and with the restriction of simple use per sensor combination have not yet been carried out

Difference in the position accuracy achieved. However, it is possible to influence the calculation time when looking for good subsets.

If Q of such good subsets have been identified, the X coordinate of the center of gravity of the current positions XTI is first calculated for each of these subsets (i = 1 ... Q), this being defined as above (formula (18)).

The X coordinate of the center of gravity of these centers of gravity is then calculated (the time dependency is omitted below):

The following example is intended to illustrate this. Only 2 good subsets or sensor combinations Ti and T2 (i.e. Q = 2) are used. For example, let Ti = {S2, S3, S6, S11, S12, S19} and T2 = {Si, S3, S6, S11, SH, S17, S21}. The following then applies: | Ti | = 6 and | T2 | = 7. The associated priorities are:

where Xi denotes the X coordinate of the current positions belonging to the sensor Si. The focus of these priorities is: s «0.071 X + 0.083 X ₂ + 0.155 X ₃ + 0.155 X ₆ + 0.155 X ₁ +

0.083 X ₁₂ + 0.071 X _1A + 0.071 X ₁₇ + 0.083 X ₁₉ + 0.071 X ₂₁

This expression can be expressed in the following form:

and thus represents a linear combination of the current X coordinates of the

Individual sensors and can be used as an approximation for the X coordinate of the current position X _curr . The coefficients form the one sought

Weight vector for the X coordinate direction. As the example shows, individual components of a weight vector can also be 0 (e.g. wx ₄ = wx ₅ = wx ₇ = wx _a = wx ₉ = wx ₁₀ = 0, since the associated values X4, X5, X7, Cb, X9, X10 are not used when calculating the center of gravity).

This simple example already demonstrates that the more frequently sensors occur in good subsets, the greater their weights (S3, S6, S11 occur in both good subsets; accordingly, their weight is greater than that of the other sensors). It can also be seen that the weights also depend on the number of elements in a good subset. For example

the weights of the sensors S _x e T ₂ and S ₂ e 7 (wx ₁ =

0.071; wx ₂ = 0.083) due to the fact that the good subsets, of which they are an element, have different thicknesses: \ T \ = 6 \ T ₂ \ - 7. The more powerful the good subsets in which the sensors occur, the lower the weights of the sensors contained in the

Linear combination (see formula 23).

The more good sensor combinations there are, the more balanced it becomes

Weighting, so that in the limit case the weight vector converges:

which amounts to a classic averaging.

A typical example of weight factors for the calculation of the current X coordinate with an arrangement of 36 IMUs is: wx = (0.034, 0.013, 0.022, 0.025, 0.022, 0.032,

0.036, 0.036, 0.023, 0.026, 0.021, 0.036,

0.030, 0.039, 0.044, 0.027, 0.028, 0.025,

0.029, 0.030, 0.017, 0.028, 0.037, 0.019,

0.023, 0.030, 0.031, 0.027, 0.010, 0.029,

0.035, 0.031, 0.035, 0.017, 0.024, 0.030)

It should be recalled that the type of

Weight determination is not the only possibility and can only be seen as an example. As an alternative, for Formula 22 to approximate the current position, you can weight the focal points XTI of the good subsets by the thickness of the associated good subsets:

Or you can also use the above-mentioned deviations A _{T. X} = x _err0r to _weight the focal points XTI _according to the good subsets:

X _s = d ₁ X _Tl + d ₂ X _j2 + H dqX _TQ (24) where the coefficients di are inversely proportional to the deviations D _{t. c} = x _err o _r , i.e. di ~ V x _err o _r · This expresses that the coefficients di are larger the smaller the accumulated deviations or the errors of the mean values D _{t. c} = x _err o _{r of} the associated sensor combinations Ti. This expression can again be represented as a linear combination of the X coordinates of the current positions originating from the N IMUs of the matrix:

X _s = wx ₁ X ₁ + WX2X2 + ··· + wx _N X _N and can also be a good approximation for the current X position coordinate: Xs (t) »Xtrue (t).

Finally, we would like to point out the possibility that a weight vector wx = wx ^ ..., wx _N ) for the calculation of the actual or current X coordinate can also be derived from the solution of the following system of equations. On the left are values of the actual X position of the system at various times during the calibration process, the number W of which must exceed the number N of IMU sensors (W> N). This is an overdetermined system of equations in N unknowns {wxi, ..., WXN} that can be treated numerically with different approaches to determine the best weight vector wx = (wx _l ..., wx _N ): ( t _x ) = wx ₁ X ₁ (t _x ) + WZ _{2 2} (£ _I ) + "· + wx _N X _N {t) (25) (t ₂ ) = wx ^ iti + wx ₂ X ₂ (t ₂ ) + + wx _N X _N (t ₂ )

Xitw ^" ) - ^wx lXl (. Tw) + ^wx 2Xl fw) ^'" TT ^WX NXN ^ W with W> NA ti 6 T _calib , T _calib = [0; t _E ]. If powers of the current X coordinates of the individual sensors are also permitted when developing the current X coordinate, then the following system of equations in 2N unknowns (wxn,

WX12,. . . , WXN1, WXN2}:

with 2W> 2N L t _t e T _calib , T _calib = [0; t _ß ].

Since the weight vector wx = (wx ^ wx ^, ..., WX _N1 , WX _N2 ) (27) now has twice as many components, the number of measurements during the calibration process is therefore the number of equations for one

System overdetermination increase accordingly.

For example, it is advantageous to use adapted weight vectors for determining the current position for different time segments l _k = [t _{k> a} , - t _kb \. This results in the following development for each time period (again only for the X coordinate): N (28)

X (t) => wXi, i _k Xi (t), tel _k

i = 1 with the associated weight vectors

WX, _k = (WX _1Jkl ..., WX _NJk ). (29)

In order to be able to calculate position coordinates for each point in time, the union of the time segments must cover the period of interest T:

As already mentioned above, for the sake of simplicity, the previous explanations apply only to the X coordinate of the current position. With the remaining spatial coordinates, Y and Z, is in the determination of the associated

To proceed weight vectors in an analogous manner.

In general, the weight vectors calculated using different methods do not necessarily have to be identical.

Figures 9, 10a and b and 11 show results of

Simulation calculations for a one-hour or 12-minute level movement.

FIG. 9 shows an example of an actual flat trajectory 81 (shown continuously) and a plane calculated using the weight vector

Path curve 82 (shown in dashed lines) for an arrangement of 25 IMU sensors 10.

FIGS. 10a and 10b show the development over time of the X and Y errors of the calculated trajectory shown in FIG. 9. Figure 11 shows an example of the movement of a person who the

Device 100 wears after 12 minutes; the crosses show the positions 101 determined with the aid of the individual sensors 10 of the IMU matrix; the asterisk shows the position 102 determined by a weight vector according to the invention and coincides well with the actual position 103, which is represented as a circle. The starting position 104 is shown as a double circle.

In principle, all of the above considerations also apply in the event that a

Weighting of the linear accelerations and rotation rates or rotation angles of the individual sensors 10 is carried out in order to calculate the current orientation and position with the aid of the calculated substitute values.

The role of the coordinates of the individual sensors 10 take over

Components of linear acceleration and angular velocity or angle of rotation along or around the corresponding axes. In this case too, the sensor data of all IMUs are calibrated for a certain one

Calibration time is continuously read out at a sufficiently high rate (e.g. 15 min at 200 Hz), while a defined system movement is carried out with exactly known starting conditions, known path curve and known chronological course of acceleration and angular velocity or orientation, so that for each point in time ( after transforming the

Sensor raw data) values for the linear acceleration and the rotation rate are available for each sensor 10 and for each sensor axis.

From good sensor combinations or subsets for the X axis to

Calculation of the yaw rate, the angle of rotation and the linear acceleration can, for. B. The following are required:

<Limit or.

Ti is a good subset for the calculation of the angle of rotation (31) around the (world) X axis => Terror <Limit _f

and

Ti is a good subset for the calculation of the linear (32)

Similar definitions apply to the Y and Z axes. w _{c t. n} (t _E ) and a _{XT n} (t _E ) denote the rotation rate by or the linear acceleration along the sensor X axis of the nth sensor of the part quantity T and yc _, t ^^ e) the angle of rotation of the nth Sensor of the part quantity T around the world X axis at the end of the

Calibration period T _approx .

It is also possible to request the criteria mentioned for good sensor combinations at different times during the calibration, not only at the end of the calibration period tE. For example, let Z = (0, t, t ₂ , ..., t _E ) decompose the calibration period T _caüb = [0; t _E \, then, for example, for a good subset of sensors it may be required to meet the above criteria for all times of the decomposition (if necessary with the exception of t = 0).

As already mentioned above, other criteria are also possible. The different methods for deriving the weight vectors from a number of good subsets or by solving an over-determined one

System of equations have already been described above.

In addition to the method described above, a is shown in FIG

Block diagram of the method is shown schematically. Inscribed

Step A: Provision of the sensors;

Step B: detection of accelerations and rotation rates;

Step C: determine the positions that result from the data of each sensor;

Step D: Weighted addition of the vector components of the positions determined.

The individual steps of the method are described in detail above, which is referred to here.

FIG. 13 additionally shows a block diagram in which a calibration according to one exemplary embodiment is shown schematically. Inscribed

Step K1: detection of positions which are determined by a plurality of sensors at a known position;

Step K2: Check a variety of different sensor combinations for that

Fulfill at least one quality criterion;

Step K3: Selection of those sensor combinations that have at least one

Fulfill quality criterion;

Step K4: Determine the weights for the selected ones

Sensor combinations; Step K5: Provision of the weights for the weighted addition when carrying out the method for determining the position.

The individual steps of the calibration are described in detail above, which is referred to here.

FIG. 14 additionally shows a calibration system 200 according to a preferred embodiment of the invention, which comprises a calibration unit 110 for calibrating the device 100, as described above. The calibration unit 110 comprises units for carrying out those described in detail above

Calibration.

If there is a change in the

Weight vectors e.g. due to temperature changes

Scaling or bias values of the individual sensors can be calculated,

for example, due to a fluctuating ambient temperature or an increasing operating temperature, is according to one embodiment the

Invention a thermal decoupling of the system from the environment and / or the use of thermocouples for temperature compensation

provided, which is a helpful measure for error reduction.

An operational temperature gradient can be according to a

Embodiment can be reduced by early switching on before calibration and before use.

The system or the device 100 or at least the IMU sensors 10 can also be permanent by a corresponding energy supply

stay on, which is less than 20mW / IMU

(MPU6050) usually does not represent too great a restriction.

The calibration, as described above, should advantageously only be carried out after a certain operating time or operating time, since then a constant bias error can be assumed and it is also advantageous if this takes place promptly before the actual use, without that the system is switched off in the meantime, which also solves the "turn-on to turn-on problem" already mentioned.

A user can also operate two systems, one of which is calibrated while the other is in use.

Another way to increase accuracy is to use the

To carry out calibration over a long period of time, for example over a few hours, and to divide it into time segments for which a separate weight vector is determined for each coordinate.

If an assignment immediately follows the calibration and the system is not switched off in the meantime, a current one can be used

Weight vector for each coordinate are extrapolated from the associated weight vectors of the previous sections of the calibration by a fit.

In contrast to position determination, for which there is no possibility of a comparison with other manipulation-proof and insensitive to interference

Systems exist, when determining the alignment of the system under certain circumstances and to a certain extent it is advantageous to check the calculated alignment for consistency using a magnetometer and to correct it if necessary.

In particular if the earth's magnetic field is not deformed in an unknown manner by obstacles, the actual alignment of the system with respect to the orientation of the magnetic lines of the earth's magnetic field can be measured and used to correct the calculated direction of movement or orientation.

Under certain conditions, the position error resulting from the processing of the acceleration data can also be reduced.

For example, an external sensor system or generally external information can be used to determine whether an actual movement takes place relative to the earth's surface. It may also be possible to determine the amount to estimate the speed. For example, a coupling of the system or device 100 to e.g. B. a drive shaft or the wheels of a land vehicle provide information about whether and how fast the system is moving or when it is at rest.

This information, together with, for example, the knowledge of the maximum possible speed, can be used to calculate the acceleration data after a simple integration of the acceleration data

Adjust system speed and thus reduce the error in the calculation of the current or current position.

If the system or device 100 is used by people who move about, according to an advantageous further embodiment of the invention, e.g. B. detected steps via heuristic considerations of the sensor data. If there are no steps, the speed will most likely be zero. This corrects the calculated speed and reduces drift or the error in the position calculation.

According to a further special embodiment of the invention

Measurement data of physical variables such as water or air pressure are used to calculate the depth or height above the ground in order to further reduce errors, at least for the Z and height coordinates.

Can rapid linear or rotary system movements or

Accelerations due to e.g. B. the inertia are excluded, the sensor raw values of all sensors are advantageously via an adapted low-pass filtering or a history fit of

high-frequency components exempt. This reduces the influence of noise or vibrations. If, on the other hand, a drift-like movement is not to be expected, high-pass filtering is advantageously carried out in order to minimize drift.

The present invention can also advantageously be used in combination with other localization technologies. For example, is the reception of the GPS signal is only possible sporadically due to the environment, then the received GPS coordinates can be used to correct the position calculated continuously with the IMU matrix.

Reference symbol list:

1 actual value

2 value determined from sensor data

10 Inertial measuring unit / sensor

10a sensors of a good sensor combination (X direction)

10b sensors of a good sensor combination (Y direction)

11 carrying unit / circuit board

13 evaluation unit

13a, 13b, 13c processors / MCUs

14 l ² C multiplexer

16 display

17 transmitters or receivers

20 sensor arrangement

41 current sensor position

42 rest position

51 Calculated X coordinate error

81 actual flat trajectory

82 calculated plane trajectory

101 positions determined with sensors

102 position determined via weight vector

103 actual position

104 Starting position

110 calibration unit

200 calibration system

A front

B back

Claims

Expectations:

1. Method for determining position using inertial navigation, in which a current position (103) is determined from a known starting position (104) and starting orientation by detecting accelerations and rotation rates, comprising the steps:

Providing sensors (10) for detecting accelerations and rotation rates;

Calculating the accelerations and rotation rates acting on the sensors (10) over a period of time along or around three sensor axes; characterized in that

a position is determined from the data of the individual sensors (10) and the vector components of the determined positions are then added in a weighted manner, the weights being determined by calibration.

2. The method according to claim 1, characterized in that a non-linear combination of the to determine the current position

Vector components of the positions of a plurality of sensors (10) is formed, the vector components and in each case at least the second power thereof being added up separately and weighted.

3. The method according to claim 1 or 2, characterized in that for calibration from a variety of sensor combinations for each

Coordinate direction a number of sensor combinations is selected, each of which meets at least one quality criterion.

4. The method according to claim 3, characterized in that to meet the quality criterion for each coordinate direction

4.1. at the end of the calibration, the sum of the deviations of the coordinates of the positions of the individual sensors (10) of the respective sensor combination from the actual value of the

Coordinate of the current position below a defined one

Limit is; and or

4.2. at the end of the calibration, the deviation of the center of gravity of the coordinates of the positions of the individual sensors (10) of the respective sensor combination from the actual value of the

Coordinate of the current position below a defined one

Limit.

5. The method according to claim 3 or 4, characterized in that to meet the quality criterion for each coordinate direction, the sum of the deviations of the individual coordinates of the positions of the sensors belonging to the sensor combination (10) from the actual value of the coordinate of the current position below the integrated coordinates over the calibration period of a defined limit.

6. The method according to any one of claims 3 to 5, characterized in that a number of sensor combinations is selected which meet at least one quality criterion at different times during the calibration.

7. The method according to any one of claims 3 to 6, characterized in that a predetermined minimum and / or maximum number of

Sensor combinations that meet the quality criterion is selected.

8. The method according to any one of claims 3 to 7, characterized in that for determining the weights

8.1. one for each of the selected sensor combinations

Spatial coordinate of the center of gravity of the corresponding coordinates of the current positions of the individual sensors (10) of the Sensor combination is calculated, and / or

8.2. a spatial coordinate of the center of gravity of the centers of gravity of the corresponding coordinates is calculated, and / or

8.3. the deviations of the corresponding coordinates of the current positions of the individual sensors (10) of the selected sensor combinations from the actual value of the corresponding coordinate of the current position are used for each coordinate direction, and / or

8.4. an over-determined system of equations is solved for each coordinate direction.

9. The method according to any one of claims 3 to 8, characterized in that the weights of the sensors (10) for each coordinate from coefficients of a linear combination of corresponding coordinates of the positions associated with the sensors (10) are formed.

10. Device for determining position by means of inertial navigation,

full

a plurality of sensors (10) for detecting accelerations and rotation rates along or about their respective sensor axis, and

an evaluation device (13) for calculating a current position from the detected accelerations and rotation rates,

characterized in that

the evaluation device (13) is designed such that it determines a position from the data of the individual sensors (10) and the

Vector components of the positions determined are then added in a weighted manner, the weights being determined by calibrating the sensors (10).

11. The device according to claim 10, characterized in that the

Evaluation device for performing the method according to one of the Claims 1 to 9 is designed.

12. The apparatus of claim 10 or 11, characterized by means for thermally decoupling the sensors (10) from the environment and / or by thermocouples to compensate for temperature changes.

13. Device according to one of claims 10 to 12, characterized by a device for mechanical damping of the sensors (10)

14. Device according to one of claims 10 to 13, characterized in that it or in a space, air, land or water vehicle

Missile is used and / or is designed as a portable navigation device for people and / or for use under water.

15. Calibration system comprising a device according to one of claims 10 to 14 and a calibration unit for calibrating the device according to one of claims 3 to 9.