DE102019211110A1 - DELAY CALIBRATION FOR DECAWAVE UWB - Google Patents

Abstract

Calibration value calculator for determining at least one calibration value for a position determination system. The calibration value calculator is designed to determine at least one calibration value that describes a delay at or in a station of the position determination system on the basis of a plurality of transit time measurements or distance measurements between different pairs of stations of the position determination system.

Description

Technical area

Embodiments according to the invention relate to a transceiver for use in a positioning system, a computer for determining a transit time, and a corresponding system and method.

Background of the invention

Positioning systems are playing an increasingly important role in everyday life. Satellite navigation, for example, has in part already replaced paper maps and enables the use of autonomous cars and aircraft. With the increasing demands on logistics and production, precise information about the position of means of transport is imperative. There are different measuring principles and methods, depending on the operating conditions for determining the position.

The most common measurement methods are based on an arrival time, which is referred to in English as TOA / "Time of Arrival" or on a time difference of arrival, which is referred to in English as TDOA / "Time Difference of Arrival". The difference between the two methods is that TOA receives the distance between two stations ("anchors") through the signal propagation time and TDOA through the time difference between the stations.

A two-way range measurement is a so-called TWR method, which is referred to in English as "Two Way Range", uses the TOA technique to obtain the distance between two stations. In contrast to a one-way range measurement, such as is used in satellite-based applications, the TWR gives a response signal to the incoming signal. Therefore it is not necessary that the transmitting stations are synchronous. In applications where it is necessary to obtain not only the distance but also the position of a target (also known as "tag") in relation to the other stations, also known as anchors, a TWR method is used less suitable due to the short update time. A triangulation used for position determination in a two-dimensional space (2D) requires at least three distance measurements.

In contrast to TOA, TDOA is more suitable for applications with many tags (“targets”). The stations do not respond in TDOA applications. "Multilateration" results from the difference in time stamps between the stations. Geometrically speaking, the TOA equations correspond to circles, whereas TDOA equations correspond to hyperboloids in a two-dimensional space. Similar to satellite navigation systems based on TOA, it is necessary to synchronize the clocks of the TDOA stations. The synchronization can be done by wire or with the help of an additional station. In addition to the measuring technology, the measuring devices are also important.

Determining the position in an interior generally poses a challenge for RF-based localization systems. Reflections can lead to interference in the main signal and cause a weakening, which is also known as “fading”. In contrast to narrowband signals, ultra wideband signals, which are also known as UWB signals, are less susceptible to interference. A so-called “Decawave” transceiver is based on ultra-broadband technology (UWB) and complies with the IEEE802.15.4-2011 standard. It supports e.g. six frequency bands with medium frequencies from 3.5 GHz to 6.5 GHz and data rates up to 6.8 Mb / s. The bandwidth can vary with the selected medium frequencies from 500 to 1000 MHz.

In contrast to TOA, TDOA is better suited for applications with many tags. In TDOA applications, the anchors do not respond. A so-called multilateration results from the difference in time stamps between the anchors. Geometrically, TOA circles of equations and TDOA hyperboloids are in a two-dimensional space. Similar to satellite navigation systems based on TOA, it is necessary that the clocks of the TDOA anchors are synchronized.

Positioning with “Decawave” transceivers is based on time stamps. These are set when a signal is sent or received. It is necessary to consider all delays. Some of these delays, such as the “antenna delay”, are dependent on the ambient temperature. As a result, it is often necessary to determine the delays again and again. Known Methods are based on measured distances between the stations to infer the delay. This means that external measuring equipment is required.

It is therefore desirable to arrive at a concept that does not require any additional measuring equipment to determine the distances between the stations and that enables self-calibration.

This is achieved through the subject matter of the independent claims of the present application.

Further embodiments according to the invention are defined by the subject matter of the dependent claims of the present application.

Summary of the invention

An embodiment according to this invention relates to a calibration value calculator for determining at least one calibration value A. , B. , S. , O _i , O _j for a position determination system, the calibration value calculator being designed to calculate at least one calibration value A. and or B. and or S. , which describes a delay at or in a station, e.g. a base station or a transponder of the position determination system, on the basis of a plurality of time stamp-based transit time measurements or distance measurements, ie TOA measurements and optionally using further measurements, such as transit time difference measurements ie TDOA To determine measurements between different pairs of stations of the position determination system whose positions are, for example, at least partially unknown.

das Stations-individuelle Kalibrierwerte, z.B. A, B, S, O_i , O_j und auch unbekannte Positionskoordinaten zumindest einer der Stationen, z.B. x_j , y_j , z_j , a_i , b_i , s_i aufweist, beispielsweise exakt oder numerisch, z.B. mit linearen oder nichtlinearen Lösungsverfahren oder Optimierungsverfahren durchzuführen.According to one embodiment, the calibration value calculator is designed to solve a sufficiently determined or overdetermined system of equations, for example in accordance with the equation $${\mathrm{S.}}_{\mathrm{I.}}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-a_i\right)}^2+{\left(y_j-b_i\right)}^2+{\left(z_j-c_i\right)}^2}-O_i-O_j-d_{i,j}\right]}^2}}$$

the station-specific calibration values, e.g. A, B, S, O _i , O _j and also unknown position coordinates of at least one of the stations, e.g. x _j , y _j , z _j , a _i , b _i , s _i has to be carried out, for example, exactly or numerically, for example with linear or non-linear solution methods or optimization methods.

einer unter Vernachlässigung der Kalibrierwerte bestimmten Distanz der zwei Stationen, z.B. d_i,j und Kalibrierwerten der zwei Stationen, z.B. O_l, O_j beschreiben.According to one embodiment, the calibration value calculator is designed to perform a solution to a sufficiently determined or overdetermined system of equations, with equations of the system of equations each having a relationship between a geometric distance between two stations, for example $$\sqrt{{\left(x_j-a_i\right)}^2+{\left(y_j-b_i\right)}^2+{\left(z_j-c_i\right)}^2}$$

a distance between the two stations determined by neglecting the calibration values, e.g. d _{i, j} and describe calibration values of the two stations, for example O _l , O _j .

According to one embodiment, the calibration value calculator is designed to determine, in addition to determining station-specific calibration values, position coordinates of at least one station in the context of solving the system of equations.

According to one embodiment, the calibration value calculator is designed such that a coordinate system selected for the transit time measurements or distance measurements can be aligned such that the origin of the coordinate system coincides with the coordinates of a station and one of the coordinate axes is aligned with a further station.

According to one embodiment, the calibration value calculator is designed to determine the position of further stations in a coordinate system that is defined by at least three anchor stations.

According to one embodiment, the calibration value calculator is designed to calculate calibration values on the basis of transit time measurements or distance measurements between all pairs of stations.

According to one embodiment, the calibration value calculator is designed to calculate calibration values based on a first set of time stamp-based runtime measurements or distance measurements that are carried out in a first arrangement of the stations and at least a second set of time stamp-based runtime measurements or distance measurements that are carried out in a second arrangement of the stations. In the second arrangement of the stations, at least one position of a station is changed in relation to the first arrangement, a position of the stations relative to one another being changed in relation to the first arrangement.

According to one embodiment, the calibration value calculator is designed to determine calibration values based on time stamp-based transit time measurements or distance measurements with changed positions of at least one of the stations.

According to one embodiment, the calibration value calculator is designed to determine calibration values in a first approximation based on the assumption that calibration values of different stations are the same.

According to one embodiment, the calibration value calculator is designed to determine calibration values using time stamp-based transit time measurements or distance measurements and time stamp-based transit time difference measurements or distance difference measurements.

According to one embodiment, the calibration value calculator is designed to determine calibration values, an equation system being calculable according to the following formula $$\mathrm{S.}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=i+1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-x_i\right)}^2+{\left(y_j-y_i\right)}^2+{\left(z_j-z_i\right)}^2}-O_i-O_j-d_{i,j}\right]}^2}}$$

According to one embodiment, the calibration value calculator is designed to include parameters such as position coordinates x _j , y _j , z _j , a _j , b _j , c _i of the stations and calibration values O _i To determine O _{j of} the stations that describe the positions of a plurality of stations and calibration values of the plurality of stations, for example using an optimization method, in such a way that an objective function is at least approximately minimized. The objective function describes a sum of a plurality of quadratic errors between geometrical distances between two stations, which arise on the basis of position coordinates, on the one hand, and themselves through correction of measured distances d _{i, j} between the two stations with calibration values O _i , O _j resulting distances between the two stations d _{i, j} + O _i + O _j on the other hand.

According to one embodiment, one or more summands of the objective function are assigned to a first spatial arrangement of the stations. One or more summands of the objective function are assigned to a second spatial arrangement of the stations, in which a relative spatial arrangement of the stations to one another is changed in comparison to the first spatial arrangement, for example by the fact that the position of at least one of the stations is relative to one or has changed several other stations.

According to one embodiment, the calibration value calculator is designed to include at least one calibration value based on a transit time measurement / TOA between a first station A. and a third station S. to determine. The calculation is based on a runtime measurement / TOA between a second station B. and the third station S. and based on a transit time difference measurement / TDOA, in which a difference between the times of arrival of two signals transmitted in a time-coordinated manner by the first station and the second station is evaluated at the third station.

über einen zeitlichen Abstand zwischen einer Aussendung eines Signals durch die erste Station A und einer Aussendung eines Signals durch die zweite Station B bei der Laufzeitdifferenzmessung und unter Berücksichtigung einer Information über einen Abstand zwischen der ersten Station, oder einer Antenne der ersten Station, und der zweiten Station, oder einer Antenne der zweiten Station, zu bestimmen.According to one embodiment, the calibration value calculator is designed around the at least one calibration value, taking into account information $$K=T_{TO\mathrm{A.}}+\mathrm{\Delta }{T}_{1.2}^T+2\mathrm{B.}$$

over a time interval between a transmission of a signal by the first station A. and transmission of a signal by the second station B. for the transit time difference measurement and below Consideration of information about a distance between the first station, or an antenna of the first station, and the second station, or an antenna of the second station, to be determined.

• - um eine Information $\mathrm{\Delta }{T}_{}^{}$${}_{\mathrm{1,2}}^S$
  
  über eine Zeitdifferenz zwischen einem ersten Zeitpunkt, zu dem die dritte Station ein von der ersten Station ausgesendetes Signal empfängt, und einem zweiten Zeitpunkt, zu dem die dritte Station ein durch die zweite Station ausgesendetes Signal, das mit dem durch die erste Station ausgesendeten Signal koordiniert ausgesendet wird, empfängt, zu erhalten;
• - um eine Information $\mathrm{\Delta }{T}_{}^{}$${}_{\mathrm{1,2}}^A$
  
  über einen zeitlichen Abstand zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der ersten Station und der dritten Station zu erhalten;
• - um eine Information $\mathrm{\Delta }{T}_{}^{}$${}_{\mathrm{1,2}}^S$
  
  über einen zeitlichen Abstand zwischen einem Empfang des Anregungssignals und einer Aussendung des Antwortsignals bei der Laufzeitmessung zwischen der ersten Station und der dritten Station zu erhalten;
• - um eine Information $\mathrm{\Delta }{T}_{}^{}$${}_{\mathrm{1,2}}^B$
  
  über einen zeitlichen Abstand zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der zweiten Station und der dritten Station zu erhalten; und
• - um eine Information $\mathrm{\Delta }{T}_{}^{}$${}_{\mathrm{1,2}}^S$
  
  über einen zeitlichen Abstand zwischen einem Empfang des Anregungssignals und einer Aussendung des Antwortsignals bei der Laufzeitmessung zwischen der zweiten Station und der dritten Station zu erhalten; und
• - um basierend darauf einen der ersten Station zugeordneten Kalibrierwert A und einen der zweiten Station zugeordneten Kalibrierwert B oder eine lineare Kombination, z.B. A+B oder A-B des der ersten Station zugeordneten Kalibrierwerts und des der zweiten Station zugeordneten Kalibrierwerts zu erhalten.

According to one embodiment, the calibration value calculator is designed

• - for information $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}$
  
  on a time difference between a first point in time at which the third station receives a signal transmitted by the first station and a second point in time at which the third station receives a signal transmitted by the second station which coordinates with the signal transmitted by the first station sent out, received, received;
• - for information $\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}$
  
  about a time interval between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the first station and the third station;
• - for information $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}$
  
  about a time interval between receipt of the excitation signal and transmission of the response signal in the transit time measurement between the first station and the third station;
• - for information $\mathrm{\Delta }{T}_{1.2}^{\mathrm{B.}}$
  
  about a time interval between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the second station and the third station; and
• - for information $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}$
  
  about a time interval between receipt of the excitation signal and transmission of the response signal in the transit time measurement between the second station and the third station; and
• based thereon a calibration value assigned to the first station A. and a calibration value assigned to the second station B. or to obtain a linear combination, for example A + B or AB, of the calibration value assigned to the first station and the calibration value assigned to the second station.

According to one embodiment, the calibration value calculator is designed around the calibration value assigned to the first station A. and the calibration value assigned to the second station B. or the linear combination, for example A + B or AB, of the calibration value assigned to the first station and the calibration value assigned to the second station using information K which describes a time interval between the coordinated transmission of the signal transmitted by the first station and the signal transmitted in coordination therewith by the second station, and using information L (A, B) about a distance between the first station and the second station or antennas assigned between the first station and the second station.

zwischen einem Empfang des Anregungssignals und einer Aussendung des Antwortsignals bei der Laufzeitmessung zwischen der zweiten Station und der dritten Station, dem zeitlichen Abstand $\mathrm{\Delta }{T}_{\mathrm{1,2}}^A$

zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der ersten Station und der dritten Station und dem zeitlichen Abstand $\mathrm{\Delta }{T}_{\mathrm{1,2}}^B$

zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der zweiten Station und der dritten Station, beispielsweise unter Berücksichtigung von K beschreibt, und ferner einen beispielsweise linearen Zusammenhang zwischen den Kalibrierwerten A, B, dem zeitlichen Abstand $\mathrm{\Delta }{T}_{\mathrm{1,2}}^A$

zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der ersten Station und der dritten Station und dem zeitlichen Abstand $\mathrm{\Delta }{T}_{\mathrm{1,2}}^B$

zwischen einer Aussendung eines Anregungssignals und einem Empfang eines Antwortsignals bei einer Laufzeitmessung zwischen der zweiten Station und der dritten Station beschreibt, beispielsweise unter Berücksichtigung des Abstands L(A,B) und der Lichtgeschwindigkeit, zu bestimmen, um die Kalibrierwerte A, B zu erhalten oder um eine lineare Kombination der Kalibrierwerte A, B zu erhalten.According to one embodiment, the calibration value calculator is designed to provide a solution to a, for example, linear system of equations which, for example, has a linear relationship between the calibration values A. , B. , the time interval $\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}$

between receipt of the excitation signal and transmission of the response signal during the transit time measurement between the second station and the third station, the time interval $\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}$

between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the first station and the third station and the time interval $\mathrm{\Delta }{T}_{1.2}^{\mathrm{B.}}$

describes between sending an excitation signal and receiving a response signal during a transit time measurement between the second station and the third station, for example taking K into account, and also describes a linear relationship, for example, between the calibration values A. , B. , the time interval $\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}$

between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the first station and the third station and the time interval $\mathrm{\Delta }{T}_{1.2}^{\mathrm{B.}}$

between sending an excitation signal and receiving a response signal in a transit time measurement between the second station and the third station, for example taking into account the distance L (A, B) and the speed of light, to determine the calibration values A. , B. or to obtain a linear combination of the calibration values A. , B. to obtain.

According to one embodiment, an equation of the equation system defines a requirement that a transit time difference determined by the transit time difference measurement is equal to a difference between a transit time difference between the first station via the transit time measurement TOA A. and the third station S. certain transit time on the one hand and one by the transit time measurement TOA between the second station B. and the third station S. certain term on the other hand $$-\mathrm{A.}+\mathrm{B.}=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+K-0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{5.6}^{\mathrm{B.}}\right).$$

According to one embodiment, an equation of the equation system defines a requirement that a transit time determined by a transit time measurement between the first station and the second station corresponds to a predetermined value L (A, B), c ₀ (speed of light) $$-\mathrm{A.}-\mathrm{B.}=\frac{\mathrm{L.}\left(\mathrm{A.},\mathrm{B.}\right)}{c_0}-0.5\cdot \left(\mathrm{\Delta }{T}_{7.8}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{7.8}^{\mathrm{B.}}\right).$$

An embodiment according to this invention relates to a method for determining at least one calibration value A. , B. , S. , O _i , O _j for a position determination system, with at least one calibration value A. and or B. and or S. , which describes a delay at or in a station, e.g. a base station or a transponder of the position determination system, on the basis of a plurality of time stamp-based transit time measurements or distance measurements, ie TOA measurements and optionally using further measurements, such as transit time difference measurements ie TDOA Measurements between different pairs of stations of the position determination system whose positions are, for example, at least partially unknown, is determined.

An embodiment according to this invention relates to a computer program with a program code in order, when executed on a computer, to provide a method for determining at least one calibration value A. , B. , S. , O _{i To} execute O _j for a position determination system, with at least one calibration value A. and or B. and or S. , which describes a delay at or in a station, e.g. a base station or a transponder of the position determination system, on the basis of a plurality of time stamp-based transit time measurements or distance measurements, ie TOA measurements and optionally using further measurements, such as transit time difference measurements ie TDOA Measurements between different pairs of stations of the position determination system whose positions are, for example, at least partially unknown, is determined.

Figure list

• 1 zeigt eine schematische Darstellung einer Hardware-Verzögerung bei einer Zweiwege-Reichweitenmessung gemäß einer TOA-Ausführungsform der Erfindung;
• 2 zeigt eine schematische Darstellung einer Hardware-Verzögerung bei einer Zweiwege-Reichweitenmessung gemäß einer TDOA-Ausführungsform der Erfindung;
• 3 zeigt eine schematische Darstellung einer Konfiguration mit drei Stationen mit je einer Hardware-Verzögerung A, B, S;
• 4 zeigt eine schematische Darstellung einer TOA-Messung zwischen den Stationen A und S;
• 5 zeigt eine schematische Darstellung einer TOA-Messung zwischen den Stationen B und S;
• 6 zeigt eine schematische Darstellung einer Information K, die einen zeitlichen Abstand zwischen der koordinierten Aussendung des durch die erste Station ausgesendeten Signals und des durch die zweite Station damit koordiniert ausgesendeten Signals beschreibt;
• 7 zeigt eine schematische Darstellung einer TOA-Messung zwischen den Stationen A und B;
• 8 zeigt eine schematische Darstellung einer Konfiguration mit drei BasisStationen B_i und drei Transponder T_j; und
• 9 zeigt in einer schematischen Darstellung ein Beispiel eines erfindungsgemäßen Kalibrierwertberechners.

The drawings are not necessarily to scale, but typically emphasis is placed on illustrating the principles of the invention. In the following description, various embodiments of the invention are described with reference to the following drawings, in which:

• 1 shows a schematic representation of a hardware delay in a two-way range measurement according to a TOA embodiment of the invention;
• 2 shows a schematic representation of a hardware delay in a two-way range measurement according to a TDOA embodiment of the invention;
• 3 shows a schematic representation of a configuration with three stations, each with a hardware delay A. , B. , S. ;
• 4th shows a schematic representation of a TOA measurement between the stations A. and S. ;
• 5 shows a schematic representation of a TOA measurement between the stations B. and S. ;
• 6 shows a schematic representation of information K which describes a time interval between the coordinated transmission of the signal transmitted by the first station and the signal transmitted in coordination therewith by the second station;
• 7th shows a schematic representation of a TOA measurement between the stations A. and B. ;
• 8th shows a schematic representation of a configuration with three base stations B _i and three transponders T _j ; and
• 9 shows in a schematic representation an example of a calibration value calculator according to the invention.

Detailed description of the embodiments

Identical or equivalent elements or elements with identical or equivalent functionality are denoted in the following description by identical or equivalent reference numbers, even if they appear in different numbers.

In the following description, numerous details are set forth in order to enable a more complete explanation of the embodiments of the present invention. However, it will be apparent to one skilled in the art that embodiments of the present invention can be practiced without these specific details. In other instances, known structures and devices are not shown in detail but are shown in block diagrams in order to avoid obscuring the embodiments of the present invention. In addition, features of the various embodiments described herein can be combined with one another, unless expressly stated otherwise.

Zeitstempel an der Referenzstation

Zeitstempel am Transponder (tag)

Zeitstempel an der Station S

Zeitstempel an der Station A

Zeitstempel an der Station B

ΔT_n,m

Differenz zwischen zwei Zeitstempeln Tm - Tn

C_n,m

Driftfehler der Uhr berechnet aus den Zeitstempeln

E_l

Zeitstempelfehler durch die Signalleistung

A, B, S

Hardware-Verzögerung

K

Zeitverzögerung

c_o

Lichtgeschwindigkeit

D

Anzahl der Dimensionen

N

Anzahl der Basisstationen B_i;

M

Anzahl der Transponder T_j

d_i,j

Abstandsmessungen zwischen B_i; und T_j

x_j, y_j, z_j}

Positionen der Transponder T_j, 1<=j<=M

a_i, b_i, c_i

Positionen der Basisstationen B_i, 1<=i<=N

O_i

Hardware-Verzögerung (Offset) der Ankerstation

O_T

Hardware-Verzögerung (Offset) der Transponder

T

Anzahl der Transponder

The following notations can be used:

Time stamp at the reference station

Time stamp on the transponder (tag)

Time stamp at station S

Time stamp at station A

Time stamp at station B

ΔT _{n, m}

Difference between two time stamps Tm - Tn

C _{n, m}

Clock drift error calculated from the time stamps

E _l

Timestamp error due to signal power

SECTION

Hardware delay

K

Time Delay

c _o

Speed of Light

D.

Number of dimensions

N

Number of base stations B _i ;

M.

Number of transponders T _j

d _{i, j}

Distance measurements between B _i ; and T _j

x _j , y _j , z _j }

Positions of the transponders T _j , 1 <= j <= M

a _i , b _i , c _i

Positions of the base stations B _i , 1 <= i <= N

O _i

Hardware delay (offset) of the anchor station

O _T

Hardware delay (offset) of the transponder

T

Number of transponders

gesetzt werden.As already mentioned, position determination with the Decawave transceivers is based on time stamps. These are set when a signal is sent or received. It is necessary to consider all delays. 1 shows a schematic representation of a hardware delay between a reference station and a transponder / tag in a TWR / two-way range measurement according to a TOA embodiment of the invention. A and B are the delays / offsets caused by the hardware delay: A in the reference station and B in the transponder, with corresponding time stamps $T_{\mathrm{I.}}^{\mathrm{R.}}\text{and}{T}_{\mathrm{I.}}^T$

be set.

A general equation for TOA position estimation with clock drift correction c _{n, m} and signal power correction E _l as follows: $$T_{TO\mathrm{A.}}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}-\mathrm{\Delta }{T}_{1.2}^T-\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}}}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+\mathrm{E.}1\right)\right)-{\mathrm{E.}}_2-{\mathrm{E.}}_1\right)-\mathrm{A.}-\mathrm{B.}$$

In one embodiment, the clock drift and the signal power can be neglected. This results in the following equation: $$T_{TO\mathrm{A.}}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{R.}}-\mathrm{\Delta }{T}_{1.2}^T\right)-\mathrm{A.}-\mathrm{B.}$$

In 2 is the influence of an antenna delay on the TDOA measurement between the reference station and one of the stations N as well as between the day and the station N shown.

wobei $$K=T_{TOA}+\mathrm{\Delta }{T}_{\mathrm{1,2}}^T+\left(\frac{C_{\mathrm{1,3}}^{RT}}{\mathrm{\Delta }{T}_{\mathrm{1,3}}^T}\cdot \left(\mathrm{\Delta }{T}_{\mathrm{1,2}}^T+E_1\right)\right)+E_1+2B$$

With consideration of clock drift correction c _{n, m} and signal power correction E _l the following general equations for a TDOA position estimation result: $$T_{T\mathrm{D.}O{\mathrm{A.}}_k}=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{S.}}}{\mathrm{\Delta }{T}_{1.3}^{\mathrm{S.}}}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+{\mathrm{E.}}_3-{\mathrm{E.}}_{\mathrm{4th}}\right)\right)-{\mathrm{E.}}_{\mathrm{4th}}-{\mathrm{E.}}_3+K$$

in which $$K=T_{TO\mathrm{A.}}+\mathrm{\Delta }{T}_{1.2}^T+\left(\frac{{\mathrm{C.}}_{1.3}^{\mathrm{R.}T}}{\mathrm{\Delta }{T}_{1.3}^T}\cdot \left(\mathrm{\Delta }{T}_{1.2}^T+{\mathrm{E.}}_1\right)\right)+{\mathrm{E.}}_1+2\mathrm{B.}$$

wobei in diesem Fall $$K=T_{TOA}+\mathrm{\Delta }{T}_{\mathrm{1,2}}^T+2B$$

In a similar way to the above-mentioned exemplary embodiment, the following simplified equation results when clock drift and the signal power error are neglected: $$T_{T\mathrm{D.}O{\mathrm{A.}}_K}=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+K$$

being in this case $$K=T_{TO\mathrm{A.}}+\mathrm{\Delta }{T}_{1.2}^T+2\mathrm{B.}$$

To estimate the antenna delay, a TDOA measurement for the station with the antenna delay is carried out in a first step S. determined. The station A. is in this embodiment as a reference station and the station B. used as a tag, as in 3 shown. It should be noted that the antenna delay in this case has no influence on the TDOA measurement, because the delay that affects the time stamp is the same for both signals. The delay therefore has no influence on the TDOA measurement. As a result, a delay-free measurement for the difference distances can be implemented using TDOA, which is used to infer the offsets using TOA. Therefore the following equation results: $$T_{T\mathrm{D.}O{\mathrm{A.}}_K}=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+K$$

In a second step, a TOA measurement is made between the station A. and S. performed as in 4th shown. This results in the following equation: $$T_{TO{\mathrm{A.}}_{\mathrm{A.}}{}_{\mathrm{S.}}}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}\right)-\mathrm{A.}-\mathrm{S.}$$

The same consideration can be given for the stations B. and S. can be applied. This results in the following equations: $$T_{TO{\mathrm{A.}}_{\mathrm{B.}}{}_{\mathrm{S.}}}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{B.}}-\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}\right)-\mathrm{B.}-\mathrm{S.}$$

etwa gleich $\mathrm{\Delta }{T}_{\mathrm{5,6}}^S$

ist.Because the processing time is almost constant, it can therefore be assumed that $\mathrm{\Delta }{T}_{3.4}^{\mathrm{S.}}$

about the same $\mathrm{\Delta }{T}_{5.6}^{\mathrm{S.}}$

is.

The difference between the two previous equations for TOA measurements leads accordingly to the following equation for a TDOA measurement: $$T_{T\mathrm{D.}O\mathrm{A.}}=0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{1.2}^{\mathrm{C.}}-\mathrm{\Delta }{T}_{1.2}^{\mathrm{B.}}\mathrm{+\; \Delta }{T}_{1.2}^{\mathrm{C.}}\right)-\mathrm{A.}+\mathrm{B.}$$

An equation can then be calculated that results from the difference between two TOA measurements and the TDOA measurement: $$T_{T\mathrm{D.}O\mathrm{A.}K}=T_{TO{\mathrm{A.}}_{\mathrm{A.}\mathrm{S.}}}-T_{TO{\mathrm{A.}}_{\mathrm{B.}\mathrm{S.}}}$$

The corresponding result can be formulated as follows: $$\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+K=0.5\cdot \left(\mathrm{\Delta }{T}_{3.4}^{\mathrm{B.}}-\mathrm{\Delta }{T}_{5.6}^{\mathrm{B.}}\right)-\mathrm{A.}+\mathrm{B.}$$

The parameter K can be determined when the broadcast time of the stations A. and B. is known. This is possible when the wards A. and B. be operated with the same time, as exemplified in 6 shown. K here corresponds to the difference in the transmission times of the stations A. and B. .

With the known parameter K corresponds to the difference between the offset A. and B. the following equation: $$-\mathrm{A.}+\mathrm{B.}=\mathrm{\Delta }{T}_{1.2}^{\mathrm{S.}}+K-0.5\cdot \left(\mathrm{\Delta }{T}_{1.2}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{5.6}^{\mathrm{B.}}\right)$$

With the known distance L (A; B) between the station A. and the station B. corresponds to the sum of the offsets A. and B. as follows: $$-\mathrm{A.}-\mathrm{B.}=\frac{\mathrm{L.}\left(\mathrm{A.},\mathrm{B.}\right)}{c_0}-0.5\cdot \left(\mathrm{\Delta }{T}_{7.8}^{\mathrm{A.}}-\mathrm{\Delta }{T}_{7.8}^{\mathrm{B.}}\right)$$

An estimate of antenna delay based on TOA and a moving transponder is described below. The terms used are summarized in the following table:

List of reference symbols

N

Number of base stations Bi

M.

Number of transponders T _j

d _{i; j}

Distance measurements between Bi and T _j

x _j ; y _j ; z _j

Positions of the transponder T _j <j <M

a _i ; b _i ; c _i

Positions of the base stations B _i <i <N

D.

Number of dimensions

The embodiment from 4th shows three base stations B _i and three transponders Tj, each located at an unknown position. The distances d _{i; j} between the base stations B _i and the transponders T _j are known in the present exemplary embodiment. The distances between the individual base stations B _i are, however, unknown. The aim of self-calibration is to get the relative coordinates between all base stations and the unknown offsets O.

wobei $$D\cdot \left(N+M\right)+N+M\le N\cdot M$$

The offset (O) can be a constant value that can be assigned to each base station. A system of equations for a TOA self-calibration is shown below. This system of equations can be solved for the unknown positions and offsets using linear and non-linear solution methods, with so-called optimization algorithms. In addition to determining the offset, the unknown positions (x, y, z) of the base stations are also estimated. A corresponding objective function is: $${\mathrm{S.}}_{\mathrm{I.}}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-a_i\right)}^2+{\left(y_j-b_i\right)}^2+{\left(z_j-c_i\right)}^2}-O_i-O_j-d_{i,j}\right]}^2}}$$

in which $$\mathrm{D.}\cdot \left(N+\mathrm{M.}\right)+N+\mathrm{M.}\le N\cdot \mathrm{M.}$$

wobei N die Anzahl der Basisstationen ist. Die geometrische Konstellation ist Translations- und Rotationsfrei. Dementsprechend sollten beispielsweise Ankerpunkte gesetzt werden. Dabei kann das Koordinatensystem in eine Basisstation gelegt werden, die mit einer Koordinatenachse auf eine andere Basisstation ausgerichtet ist. Als Beispiel soll das Koordinatensystem in Basisstation 1 zentriert und die Y-Achse auf Basisstation 2 ausgerichtet werden.The number of distance measurements corresponds to $$N\ast \left(N-1\right)/2$$

where N is the number of base stations. The geometric constellation is free of translation and rotation. Anchor points, for example, should be set accordingly. The coordinate system can be placed in a base station which is aligned with another base station with a coordinate axis. As an example, the coordinate system should be centered in base station 1 and the Y-axis aligned on base station 2.

This results in a planar view $$x_1={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="DE102019211110A1\_0048.png,DE102019211110A1\_0049.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=x_2=0$$

In the three-dimensional case it would be $$x_1={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="DE102019211110A1\_0048.png,DE102019211110A1\_0049.png"\; state="\{\{state\}\}">y</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="DE102019211110A1\_0048.png,DE102019211110A1\_0049.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=x_2={\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="DE102019211110A1\_0048.png,DE102019211110A1\_0053.png"\; state="\{\{state\}\}">z</figure-callout>}}_2={\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="DE102019211110A1\_0051.png"\; state="\{\{state\}\}">z</figure-callout>}}_3=0$$

As a rule, it is not possible to carry out a stationary 2D self-calibration with 4 base stations (6 measurements, 9 unknowns). Such a self-calibration assumes, for example; that all offsets are the same (6 measurements, 5 unknowns) or the position of one base station or all base stations changes.

Changing the position of a station would increase the number of unknowns by the coordinates of the new position, but would require more measurements. As a result, self-calibration would already be possible with four base stations: here, for example, with 13 unknowns, two position changes with 15 measurements would be required.

wobei $$D\cdot \left(N+M\right)+N+1\le N\cdot M$$

If the one transponder is used at different positions, the following objective function results: $${\mathrm{S.}}_{\mathrm{I.}}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-a_i\right)}^2+{\left(y_j-b_i\right)}^2+{\left(z_j-c_i\right)}^2}-O_i-O_T-d_{i,j}\right]}^2}}$$

in which $$\mathrm{D.}\cdot \left(N+\mathrm{M.}\right)+N+1\le N\cdot \mathrm{M.}$$

In examples, the calibration value calculator can be in hardware using analog and / or digital circuits, in software, through the execution of instructions by one or more universal or specialty processors, or as a combination of hardware and software. For example, embodiments may be implemented in the environment of a computer system or other processing system. A computer system may have one or more processors connected to a communication infrastructure such as a bus or network. The computer system may include main memory such as random access memory (RAM) and secondary memory such as a hard disk drive or removable storage drive. The secondary memory can enable computer programs or other machine-readable instructions to be loaded into the computer system. The computer system can also have a communication interface to enable machine-readable instructions and data to be exchanged between the computer system and external devices. The communication can take place electronically, electromagnetically, optically or via other signals that can be handled by the communication interface. Communication can be wired or wireless.

9 shows schematically an example of a calibration value calculator as disclosed herein, which has a memory 22 and a computing device 24. The computing device 24 receives an input signal 20 which specifies transit time measurements and / or distance measurements and, based thereon, generates an output signal 26 which specifies the calibration value. In examples, computing device 24 may be implemented by any suitable circuit structure, such as microprocessor circuits, ASIC circuits, CMOS circuits, and the like. In examples, the computing device can be implemented as a combination of hardware structures and machine-readable instructions. For example, the processing circuit can have a processor and memory devices that store machine-readable instructions that provide the functionalities described and lead to the implementation of methods described herein when they are executed by the processor. In examples, memory 22 may be implemented by any suitable storage device, such as EPROM, EEPROM, Flash EEPROM, FRAM (ferroelectric RAM), MRAM (magnetoresistive RAM), or phase change RAM. The memory 22 is coupled to the computing device 24 or can be integrated into the computing device 24 as part of the computing device 24.

Further embodiments are defined by the appended claims. Each embodiment, as defined by the claims, can be supplemented by details (features and functionalities) as described above.

Although some aspects have been described in connection with a device, it goes without saying that these aspects also represent a description of the corresponding method, so that a block or a component of a device is also to be understood as a corresponding method step or as a feature of a method step. Analogously, aspects that have been described in connection with or as a method step also represent a description of a corresponding block or details or features of a corresponding device. Some or all of the method steps can be carried out by a hardware apparatus (or using a hardware Apparatus), such as a microprocessor, a programmable computer or an electronic circuit. In some embodiments, some or more of the most important process steps can be performed by such apparatus.

A signal encoded according to the invention, such as an audio signal or a video signal or a transport stream signal, can be stored on a digital storage medium or can be transmitted on a transmission medium such as a wireless transmission medium or a wired transmission medium, e.g. the Internet

The encoded audio signal according to the invention can be stored on a digital storage medium or can be transmitted on a transmission medium such as a wireless transmission medium or a wired transmission medium such as the Internet.

Depending on the specific implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be carried out using a digital storage medium, for example a floppy disk, a DVD, a Blu-ray disc, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, a hard disk or any other magnetic or optical memory, on which electronically readable control signals are stored, which can interact with a programmable computer system in such a way that the respective method is carried out becomes. Therefore, the digital storage medium can be computer readable.

Some exemplary embodiments according to the invention thus include a data carrier which has electronically readable control signals which are able to interact with a programmable computer system in such a way that one of the methods described herein is carried out.

In general, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being effective to carry out one of the methods when the computer program product runs on a computer.

The program code can for example also be stored on a machine-readable carrier.

Other exemplary embodiments include the computer program for performing one of the methods described herein, the computer program being stored on a machine-readable carrier.

In other words, an exemplary embodiment of the method according to the invention is thus a computer program which has a program code for carrying out one of the methods described here when the computer program runs on a computer.

A further exemplary embodiment of the method according to the invention is thus a data carrier (or a digital storage medium or a computer-readable medium) on which the computer program for performing one of the methods described herein is recorded. The data carrier, the digital storage medium or the computer-readable medium are typically tangible and / or non-perishable or non-temporary.

A further exemplary embodiment of the method according to the invention is thus a data stream or a sequence of signals which represents or represents the computer program for performing one of the methods described herein. The data stream or the sequence of signals can, for example, be configured to be transferred via a data communication connection, for example via the Internet.

Another exemplary embodiment comprises a processing device, for example a computer or a programmable logic component, which is configured or adapted to carry out one of the methods described herein.

Another exemplary embodiment comprises a computer on which the computer program for performing one of the methods described herein is installed.

A further exemplary embodiment according to the invention comprises a device or a system which is designed to transmit a computer program for performing at least one of the methods described herein to a receiver. The transmission can take place electronically or optically, for example. The receiver can be, for example, a computer, a mobile device, a storage device or a similar device. The device or the system can for example comprise a file server for transmitting the computer program to the recipient.

In some exemplary embodiments, a programmable logic component (for example a field-programmable gate array, an FPGA) can be used to carry out some or all of the functionalities of the methods described herein. In some exemplary embodiments, a field-programmable gate array can interact with a microprocessor in order to carry out one of the methods described herein. In general, in some exemplary embodiments, the methods are performed by any hardware device. This can be universally applicable hardware such as a computer processor (CPU) or hardware specific to the method such as an ASIC.

The devices described herein can be implemented, for example, using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

The devices described herein, or any components of the devices described herein, can be implemented at least partially in hardware and / or in software (computer program).

The methods described herein can be implemented, for example, using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

The methods described herein, or any components of the methods described herein, can be carried out at least in part by hardware and / or by software.

The above-described embodiments are merely illustrative of the principles of the present invention. It is to be understood that modifications and variations of the arrangements and details described herein will be apparent to other skilled persons. It is therefore intended that the invention be limited only by the scope of protection of the following patent claims and not by the specific details presented herein with reference to the description and explanation of the exemplary embodiments.

Although certain combinations of features are recited in the patent claims and / or disclosed in the description, it is not intended that these features restrict the disclosure of possible implementations. In fact, many of these features can be combined in ways that are not specifically set out in the claims and / or disclosed in the description.

Although each of the dependent claims below may only depend on one or some claims directly, the disclosure of possible implementations includes each dependent claim in combination with all other claims in the set of claims.

Claims (23)

A calibration value calculator for determining at least one calibration value for a position determination system, wherein the calibration value calculator is designed to determine at least one calibration value that describes a delay at or in a station of the position determination system on the basis of a plurality of transit time measurements or distance measurements between different pairs of stations of the position determination system. Calibration value calculator according to Claim 1 , wherein the calibration value calculator is designed to perform a solution to a system of equations which has station-specific calibration values and also unknown position coordinates of at least one of the stations. Calibration value calculator according to Claim 2 , wherein equations of the system of equations each describe a relationship between a geometric distance between two stations, a distance of the two stations determined while neglecting the calibration values, and calibration values of the two stations. Calibration value calculator according to Claim 2 or 3 , wherein the calibration value calculator is designed to help determine position coordinates of at least one station in the context of solving the system of equations. Calibration value calculator according to one of the Claims 1 to 4th , wherein a coordinate system selected for the transit time measurements or distance measurements can be aligned such that the origin of the coordinate system coincides with the coordinates of a station and one of the coordinate axes is aligned with a further station. Calibration value calculator according to one of the Claims 1 to 5 , wherein the calibration value calculator is designed to determine the position of further stations in a coordinate system that is defined by at least three anchor stations. Calibration value calculator according to one of the Claims 1 to 6 , wherein the calibration value calculator is designed to calculate calibration values on the basis of transit time measurements or distance measurements between all pairs of stations. Calibration value calculator according to one of the Claims 1 to 7th , wherein the calibration value calculator is designed to calculate calibration values based on - a first set of time stamp-based transit time measurements or distance measurements that are carried out in a first arrangement of the stations, and - at least a second set of time stamp-based transit time measurements or distance measurements that be carried out in a second arrangement of the stations, wherein in the second arrangement of the stations at least one position of a station is changed in relation to the first arrangement. Calibration value calculator according to one of the Claims 1 to 8th , wherein the calibration value calculator is designed to determine calibration values based on time stamp-based transit time measurements or distance measurements with changed positions of at least one of the stations. Calibration value calculator according to one of the Claims 1 to 9 , wherein the calibration value calculator is designed to determine calibration values based on the assumption that calibration values of different stations are the same. Calibration value calculator according to one of the Claims 1 to 10 , the calibration value calculator being designed to determine calibration values using transit time measurements or distance measurements and transit time difference measurements or distance difference measurements. Calibration value calculator according to one of the Claims 1 to 11 , the calibration value calculator being designed to determine calibration values, an equation system being calculable according to the following formula $$\mathrm{S.}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=i+1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-x_i\right)}^2+{\left(y_j-y_i\right)}^2+{\left(z_j-z_i\right)}^2}-O_i-O_j-d_{i,j}\right]}^2}}$$

Calibration value calculator according to one of the Claims 1 to 12th , wherein the calibration value calculator is designed to determine parameters describing the positions of a plurality of stations and calibration values of the plurality of stations so that an objective function is at least approximately minimized, the objective function being a sum of a plurality of square errors between them based on Geometric distances resulting from position coordinates between two stations on the one hand and distances between the two stations resulting from the correction of measured distances between the two stations with calibration values on the other hand. Calibration value calculator according to one of the Claims 1 to 13 , wherein one or more summands of the objective function are assigned to a first spatial arrangement of the stations, and wherein one or more summands of the objective function are assigned to a second spatial arrangement of the stations, in which a relative spatial arrangement of the stations to one another in comparison to the first spatial arrangement is changed. Calibration value calculator according to one of the Claims 1 to 14th , wherein the calibration value calculator is designed to calculate at least one calibration value based on a transit time measurement between a first station and a third station, based on a transit time measurement between a second station and the third station, and based on a transit time difference measurement in which a difference between arrival times of two is evaluated by the first station and the second station coordinated signals sent out at the third station. Calibration value calculator according to one of the Claims 1 to 15th , wherein the calibration value calculator is designed to calculate the at least one calibration value taking into account information about a time interval between transmission of a signal by the first station and transmission of a signal by the second station in the transit time difference measurement and taking into account information about a distance between the first station, or an antenna of the first station, and the second station, or an antenna of the second station. Calibration value calculator according to one of the Claims 1 to 16 , wherein the calibration value computer is designed to receive information about a time difference between a first point in time at which the third station receives a signal transmitted by the first station and a second point in time at which the third station receives a signal transmitted by the second station sent out coordinated with the signal sent out by the first station, receives, receives; in order to obtain information about a time interval between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the first station and the third station; in order to obtain information about a time interval between receipt of the excitation signal and transmission of the response signal during the transit time measurement between the first station and the third station; in order to obtain information about a time interval between the transmission of an excitation signal and the reception of a response signal during a transit time measurement between the second station and the third station; and to obtain information about a time interval between receipt of the excitation signal and transmission of the response signal during the transit time measurement between the second station and the third station; and based thereon to obtain a calibration value assigned to the first station and a calibration value assigned to the second station or a linear combination of the calibration value assigned to the first station and the calibration value assigned to the second station. Calibration value calculator according to one of the Claims 1 to 17th , wherein the calibration value calculator is designed to calculate the calibration value A assigned to the first station and the calibration value B assigned to the second station or the linear combination of the calibration value assigned to the first station and the calibration value assigned to the second station - using information K which has a temporal Describes the distance between the coordinated transmission of the signal transmitted by the first station and the signal transmitted in coordination with it by the second station, and - using information L (A, B) about a distance between the first station and the second station or between the first station and the second station assigned antennas. Calibration value calculator according to one of the Claims 1 to 18th , wherein the calibration value calculator is designed to provide a solution to a system of equations that shows a relationship between the calibration values A, B, the time interval between receipt of the excitation signal and transmission of the response signal during the transit time measurement between the second station and the third station, the time interval Describes the distance between the transmission of an excitation signal and the reception of a response signal during a transit time measurement between the first station and the third station and the time interval between the transmission of an excitation signal and the receipt of a response signal during a transit time measurement between the second station and the third station, and Furthermore, a relationship between the calibration values A, B, the time interval between the transmission of an excitation signal and the reception of a response signal in the case of a transit time measurement between the first station and the third station, and the temporal A The distance between the transmission of an excitation signal and the reception of a response signal during a transit time measurement between the second station and the third station describes to determine in order to obtain the calibration values A, B or to obtain a linear combination of the calibration values A, B. Calibration value calculator according to one of the Claims 1 to 19th , An equation of the system of equations defines a requirement that a transit time difference determined by the transit time difference measurement is equal to a difference between a transit time determined by the transit time measurement between the first station A and the third station S on the one hand and one determined by the transit time measurement between the second station B and the third Station S certain transit time on the other hand. Calibration value calculator according to one of the Claims 1 to 20th , wherein an equation of the system of equations defines a requirement that a transit time determined by a transit time measurement between the first station and the second station corresponds to a predetermined value. $$\mathrm{S.}:={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=i+1}^{\mathrm{M.}}{\left[\sqrt{{\left(x_j-x_i\right)}^2+{\left(y_j-y_i\right)}^2+{\left(z_j-z_i\right)}^2}-O_i-O_j-d_{i,j}\right]}^2}}$$

Method for determining at least one calibration value A, B, S, Oi, Oj for a position determination system, wherein at least one calibration value A and / or B and / or S, which causes a delay at or in a station, e.g. a base station or a transponder of the Position determination system describes, on the basis of a plurality of time stamp-based transit time measurements or distance measurements, ie TOA measurements and optionally using further measurements, such as transit time difference measurements i.e. TDOA measurements between different pairs of stations of the position determination system whose positions are, for example, at least partially unknown, is determined. Computer program with a program code for carrying out a method according to Claim 22 on a computer.

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