APPLICATION NOTE: APS011
Contents
1. and frequency offset the error in the accuracy of the range is large DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 7 of 21 author 5011 Sources of error in TWR schemes deca Wave 2 4 Symmetric double sided two way ranging SDS TWR with clock drift The error in ranging accuracy in the simple two way ranging scheme is large even with small frequency offsets An alternative scheme to minimize the error by introducing another message in the ranging transaction is shown in Figure 6 device A device B 16 T Areply 1 us Areply 10 us 14 Areply 100 us 12 troundA treplyB 10 8 TOF eee TOR 5 4 treplyA troundB 2 0 0 5 10 15 20 TOF j csl ees ppm time time Figure 6 Symmetric two way ranging Figure 7 Ranging error in SDS TWR scheme scheme The dominant error in the ranging accuracy of this scheme is given by 1 Error a4 ea eg Now we can see that the dependence on t ep yg has been eliminated the error is now dependent upon Which is the difference between t epiya As a result the error in the ranging accuracy is much smaller as plotted in Figure 7 DecaWave 2014 This document is confidential and contains in2. decaWave APPLICATION NOTE 5011 5011 APPLICATION NOTE SOURCES OF ERROR IN DW1000 BASED TWO WAY RANGING TWR SCHEMES Version 1 0 This document is subject to change without notice DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the author 5011 Sources of error TWR schemes Wave TABLE OF CONTENTS 1 INTRODUCTION I 4 1 1 QVERVIEW 4 1 2 ABOUT THISIDOCUNAEN Tess 4 2 RANGING ACCURACY IN THE PRESENCE OF CLOCK 5 2 1 INTRODUCTION Eden d Ee px 5 2 2 DW1000 OSCILLATOR AND QUARTZ CRYSTAL cssessscsesssscsesscecsesesssscsesssaesesesassesassesesaesesesaesesesaesesesacaesesaeseseaeonss 5 2 3 TWO WAY RANGING TWR WITH CLOCK DRIFT sees ennt nennen tnnt tenni te tnter tnter nnn 6 2 4 SYMMETRIC DOUBLE SIDED TWO WAY RANGING SDS TWR WITH CLOCK DRIFT ener 8 2 5 SYMMETRIC DOUBLE SIDED TWO WAY RANGING SDS TWR WITH FREQUENCY DRIFT 9 3 RANGING ACCURACY VS RECEIVED SIGNAL eene ne ee
3. 3993 6 x 10 for channel number 2 see Table 3 and using this formula Pp dBm P dBm G dB 20 log o c 20 logyo 4rrf R we find that Pg 14 3 2 20 log 0 299792458 20 log o 4 x 3 1415926 x 3993 6 x10 x 2 14 3 2 169 536 220 032 62 8 dBm Using this result in Table 2 rounding up to 63 dBm gives a correction of 18 7 cm for this measurement DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 14 of 21 author 5011 Sources of error TWR schemes deca Wave 4 CONCLUSION 4 1 Ranging accuracy in the presence of clock drift For a two way ranging scheme SDS TWR is the most practical However if an implementation executes a ranging exchange during crystal warm up to reduce power consumption then the additional error in the accuracy due to frequency drift needs to be minimized The guidelines for any ranging implementation to minimize this error are to e Make t 4and trepiyg as short as possible If say was 10 ms then any additional ranging error would be unlikely to exceed 2 cm e the difference between t epiy4 and trepiyg Arepry as small as possible 4 2 Hanging accuracy vs received signal power There is an error in the timestamp recorded by the DW1000 that is dependent on incident
4. 55 50 Received Signal Level dBm Figure 10 Diagram illustrating the effect of range bias on the reported distance For most applications this bias can be ignored however higher precision ranging applications must correct for this effect This can be achieved in software by applying a correction factor 3 2 DecaRanging Implementation DecaRanging ARM based source code which includes DW1000 driver code includes range bias adjustment software to allow for this effect This allows DecaWave s EVK1000 two way ranging demonstration kit to achieve its target accuracy The DecaRanging ARM based source code takes a simple approach to compensating for this range bias effect The reported range from the TWR operation is used as an index to a table of range DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 10 of 21 author 5011 Sources of error in TWR schemes Wave adjustment figures which are used to adjust the reported range to allow for the effect This adjusted figure is then reported as the result of the TWR operation Table 1 gives a sample of such a table where the measured TWR distance is related to the correction factor for a given PRF These tables can be investigated in the DecaRanging source code Table 1 Sample range bias correction table from DecaRanging TWR software fo
5. information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 18 of 21 author 5011 Sources of error in TWR schemes deca Wave If we assume that t epiya trepiy ANd trepiyg then trounda 2TOF trepty Arepty trounap 2TOF trepty So the error becomes ATOF 2TOF trepiy Arepty trepty ea 2TOF trepty trepty Which reduces to 2 1 1 zT 0F e T Areply Ca 7 3 SDS TWR with frequency drift The true TOF is the same as for the SDS TWR scheme 4TOF LroundA treplyA trounaB treplyB However now we have frequency drift in device A represented by e and so the estimated TOF based on the round trip time measurements becomes trounaa 1 EE treptya 1 eap trounaB m treplyp 1 Again the difference between the true TOF and estimated TOF gives the error for the ranging transaction 4TOF 4TOF trounaa 1 m trepiya 1 eap E tress ZH trounaA m trepiya troundB trepiyB 4TOF trounaa a trepiya ean trounar trepiyB en If we assume that trepiy ANd trepiyg then trounda 2TOF trepiy Arepiy trounag 2TOF trepiy Then the error becomes ATOF 2TOF tre
6. ARM UP 9 FIGURE 9 RANGING ERROR OF SDS TWR SCHEME WITH FREQUENCY DRIFT IN DEVICE A eesseeeeeeeeeeenennnen nnne eene 9 FIGURE 10 DIAGRAM ILLUSTRATING THE EFFECT OF RANGE BIAS ON THE REPORTED 10 FIGURE 11 RANGE BIAS ERROR FOR A GIVEN RECEIVED SIGNAL LEVEL e eere enne nennen enne nnne sss sst 12 DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 3 of 21 author 5011 Sources of error in TWR schemes deca Wave 1 INTRODUCTION 1 1 Overview DecaWave s DW1000 a multi channel transceiver based on Ultra Wideband radio communications allows very accurate time stamping of messages as they leave from and arrive at the transceiver This allows the construction of a number of different system topologies in the area of real time location systems and proximity measurement devices The simplest of such topologies is where two nodes communicate between themselves exchange messages and based on transmit and receive timestamps of those messages they can calculate the round trip time of the signal between the two nodes and hence the time of flight and therefore the distance between the two nodes A complete description of DecaWave s two way ranging protocol is descri
7. N TABLE FROM DECARANGING TWR SOFTWARE FOR CHANNEL 2 11 TABLE 2 RELATIONSHIP BETWEEN RSL AND RANGE BIAS CORRECTION 13 TABLE 3 CALIBRATION DISTANCE FOR CHANNELS AND PREF ssssseseeeseeeeeeeeeeeeeer nennen nsns nnne 45 TABLE OF REFERENCES ss E TABLE 5 RANGE BIAS CORRECTION FACTORS VS RECEIVED SIGNAL LEVEL FOR 900M HZ CHANNELS DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 2 of 21 author 5011 Sources of error TWR schemes deca Wave LIST OF FIGURES FIGURE 1 CLOCK DRIFT DUE TO FREQUENCY ERROR IN DEVICE AND DEVICE 5 FIGURE 2 RTXO FREQUENCY CHANGE AT TURN ON eene FIGURE 3 EVB1000 CRYSTAL OSCILLATOR START UP IN THE FREQUENCY DOMAIN FIGURE 4 TWO WAY RANGING SCHEME FIGURE 5 RANGING ERROR IN TWR SCHEME uoo FIGURE 6 SYMMETRIC TWO WAY RANGING SCHEME esee nenne sisi isst 8 FIGURE 7 RANGING ERROR IN SDS TWR SCHEME sess nennen enne nnn 8 FIGURE 8 FREQUENCY DRIFT IN DEVICE A DURING QUARTZ CRYSTAL W
8. ach oscillator has a fixed frequency error e with respect to the nominal oscillator frequency The frequency errors or offset on each device will give rise to a clock drift relative to the nominal frequency as shown in Figure 1 count 4 f 1 ea f clock drift 1 measured at t t1 10 11 time Figure 1 Clock drift due to frequency error in device A and device B A frequency drift is when the frequency error on any device is not fixed but changes over time 2 2 DW 1000 oscillator and quartz crystal In a DW1000 based design the combination of a quartz crystal and the circuitry within the DW1000 is classified as a room temperature crystal oscillator RTXO An example of an RTXO warm up at oscillator turn on is shown in Figure 2 taken from 3 There are frequency jumps of 0 5 ppm before the RTXO stabilizes DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 5 of 21 author 5011 Sources of error in TWR schemes deca Wave 0 5 ppm time min Figure 2 RTXO frequency change at turn on DecaWave s EVB1000 evaluation board two of which are included in our EVK1000 evaluation kit uses such an RTXO Measurements of the frequency of the crystal oscillator on the EVB1000 were taken during crystal warm up an
9. bed in other documents available from DecaWave This Application Note focuses on the sources of error in the reported timestamps and what corrections mitigation strategies the system designer can employ to report as accurate a result as possible 1 2 About this document This document deals with two fundamental sources of error e Errors related to clock drift in the two nodes e Errors related to incident signal level at a node These are dealt with in individual sections Other application notes are available from DecaWave and you should contact your local representative or info decawave com for more information DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 4 of 21 author 5011 Sources of error TWR schemes deca Wave 2 RANGING ACCURACY IN THE PRESENCE OF CLOCK DRIFT 2 1 Introduction In the case of tag to anchor two way ranging there are a number of sources of error due to clock drift and frequency drift In order to have a robust ranging solution these errors either need to be eliminated or controlled Some parameters in the ranging scheme can exacerbate the ranging error if not chosen correctly If we consider two ranging capable devices device A and device B each device has a DW1000 with a free running crystal oscillator and a microprocessor We assume that e
10. d are plotted in Figure 3 This shows a similar effect of frequency jumps before it reaches stability 0 2 F Af f ppm eg 38 2 1 1 1 1 1 0 200 400 600 800 1000 1200 1400 time ms Figure 3 EVB1000 crystal oscillator start up in the frequency domain 2 3 Two way ranging TWR with clock drift Consider the ranging scheme shown in Figure 4 the start of the ranging transaction begins by device A sending a message to device B Now device B waits a known amount of time and sends a response back to device A DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 6 of 21 author 5011 Sources of error in TWR schemes Wave device A device B 350 T treplyB 10 us treplyB 100 us 300 treplyB 1000 us 250 troundA treplyB E m 5 150 jer 4 100 50 0 0 5 10 15 20 JY JY time time Figure 4 Two way ranging scheme Figure 5 Ranging error in TWR scheme The dominant error in the ranging accuracy of this scheme is given by 1 Error 5 trepiya Ca eg We can see that there is a strong dependence on in this equation A plot of this error is shown in Figure 5 For practical values of
11. e to the frequency drift the error in the ranging accuracy is dependent upon this error is plotted in Figure 9 The deceptive problem with this ranging error is that it will be slightly different on each oscillator start up and from crystal to crystal In essence this can be considered as a random frequency offset therefore its effect needs to be minimized DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 9 of 21 author 5011 Sources of error in TWR schemes Wave 3 RANGING ACCURACY VS RECEIVED SIGNAL LEVEL 3 1 Introduction Ideally there should be no relationship between the reported timestamp of a received signal and the received signal level In practice a bias which varies with received signal level RSL can be observed in the reported time stamp compared with the correct value and this leads to a bias in the calculated time of flight based on those time stamps This is illustrated in Figure 10 below where the red line labelled Ideal indicates the ideal result constant and the blue line labelled Actual indicates the actual measured result which varies with received signal level 500 MHz Bandwidth 10 dE D 1 Oo 0 9 e D rod 5 Qc 10 95 90 85 80 75 70 65 60
12. formation which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 8 of 21 author 5011 Sources of error in TWR schemes deca Wave 2 5 Symmetric double sided two way ranging SDS TWR with frequency drift For lowest power operation battery powered devices remain in the SLEEP mode with the crystal oscillator off so to perform a ranging transaction the device is switched on the transaction is completed and the device is switched off again In this case the ranging transaction is performed while one of the devices is transitioning through the crystal warm up phase This means there is a frequency drift on one of the devices during the ranging transaction The frequency error on device B remains constant We assume that the cumulative error of the frequency drift on device A can be approximated as two separate frequency errors as shown in Figure 8 16 T count treply 1 ms treply 10 ms 14 treply 100 ms 7 f 1 eB Ranging error cm frequency drift S 0 0 005 0 01 0 015 0 02 10 time ppm Figure 8 Frequency drift in device A during Figure 9 Ranging error of SDS TWR scheme quartz crystal warm up with frequency drift in device A The dominant error in the ranging accuracy with frequency drift is now given by 1 Error a treriya ea eap Now du
13. hysical distance being measured Reported distance the distance reported by the un corrected TWR operation Range Bias Correction the adjustment figure in cm taken from Table 2 500 MHz Bandwidth 15 16 MHz 64 MHz PRF 10r 5 _ Range Bias cm 0L 5 10 _ 1 5 20 95 90 85 80 75 70 65 60 Received Signal Level dBm Figure 11 Range bias error for a given received signal level DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 12 of 21 author 5011 Sources of error in TWR schemes a decaWave Table 2 Relationship between RSL and range bias correction factor RSL PRF 16 MHz PRF 64 MHz 500 MHz 500 MHz Gow cm cm 61 19 8 11 0 63 18 7 10 5 65 17 9 10 0 67 16 3 9 3 69 14 3 8 2 71 12 7 6 9 73 10 9 5 1 75 8 4 2 7 77 5 9 0 0 79 3 1 2 1 81 0 0 3 5 83 3 6 4 2 85 6 5 4 9 87 8 4 6 2 89 9 7 7 1 91 10 6 7 6 93 11 0 8 1 Figure 11 and Table 2 use an antenna delay calibration see 2 for an explanation of this that places the zero point of the range bias i e where the actual and ideal curves in Figure 10 intersect at 81 dBm for a PRF of 16 MHz and 77 dBm for a PRF of 64 MHz In this way the zero point is towards the
14. ight channel the signal power of the unobstructed first path as it arrives at the receiver can be calculated based on the distance reported by the chip using Friis path loss formula Pg dBm Pr dBm G dB 20 logio c 20 log o 4rrf Rt Where e Pr is the received signal level e Pris the transmitted power In a properly calibrated system the DW1000 transmits 41 3 dBm MHz into 500 MHz bandwidth channel corresponding to a total power Pr of 14 3 dBm DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 11 of 21 author 5011 Sources of error TWR schemes deca Wave e Gincludes the antenna gains of the transmitting and receiving antennas as well as any other gain from external amplifiers and or PCB losses e cis the speed of light 299792458 m s e f is the centre frequency of the channel used expressed in Hertz e Ris the reported distance in meters returned from the TWR operation Knowing your system parameters such as antenna gain G etc it is possible to calculate P the received signal level RSL Using this RSL in Table 2 the range bias correction can be determined The reported distance can then be corrected such that Actual distance Reported distance Range Bias Correction Where Actual distance the p
15. middle of the range bias variation This is to ensure we have the minimum error for applications that do not correct for range bias You may choose to calibrate the antenna delay such that the zero point of the range bias moves towards higher or lower signal levels depending on your application and whether you need accuracy at very short ranges or not Table 3 below lists the corresponding calibration distances used for the different channels and different PRFs Table 3 Calibration distance for channels and PRF Channel Number f MHz B PRF MHz Mobi al 2 3993 6 499 2 16 12 9 2 3993 6 499 2 64 8 1 3 4492 8 499 2 16 11 5 3 4492 8 499 2 64 7 2 4 3993 6 900 16 64 8 7 5 6489 6 499 2 16 7 9 DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 13 of 21 author 5011 Sources of error in TWR schemes a decaWave Channel Number fe MHz agrees PRF MHz 5 6489 6 499 2 64 5 0 7 6489 6 499 2 16 64 53 Also included in Appendix B is the corresponding figure and table for the two 900 MHz channels included in the DW 1000 3 41 Example Calculation For a system with the following parameters 1 dB in the TWR case we must allow for two antenna gains so 2 dB 14 3 dBm R 2m f
16. ne nnne nennen nsns sets asso senten 10 34 INTRODUCTION 10 3 2 DECARANGING IMPLEMENTATION cscsscscsesscscsssscscsessssceesssssscseseesssassesssasscsssasaesesaesssesauassesauacaesacecsecaeseeaeeees 10 3 3 DESIGN SPECIFIC DETAIS i nunu ndan thoi gma eave eed Da id bien RE DR TREES 3 4 FRIIS PATH LOSS FORMULA AND RANGE BIAS CORRECTION VALUE s 3 4 1 Exarmnpl Calc lati M e anaia A CONCLUSION M M 15 4 1 RANGING ACCURACY IN THE PRESENCE OF CLOCK DRIFT isses nnne 15 4 2 RANGING ACCURACY VS RECEIVED SIGNAL POWER s cesceccesecseeceeseeseceessecasscessceaecaeeeaeseesaeecaeeaeceesaesenesaeeateassaees 15 5 REFERENCES cicisescscccsssastevinsceccicccsavaccsessecsacscssvecsstesccscnsaascesccsceceseasavecsscsnacsassacacesestssceuesssescscuanecaressaacesssse 16 5 1 MISTING 16 6 ABOUT DECAWAVE 17 7 APPENDIX A DERIVING THE ERROR IN RANGING ACCURACY DUE TO 18 7 1 TWR WITH CLOCK 7 2 SDS TWR WITH CLOCK DRIFT 7 3 SDS TWR WITH FREQUENCY DRIFT 8 APPENDIX B RANGE BIAS FIGURES FOR 900 MHZ 20 LIST OF TABLES TABLE 1 SAMPLE RANGE BIAS CORRECTIO
17. ntial and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 16 of 21 author 5011 Sources of error TWR schemes deca Wave 6 ABOUT DECAWAVE DecaWave is a pioneering fabless semiconductor company whose flagship product the DW1000 is a complete single chip CMOS Ultra Wideband IC based on the IEEE 802 15 4 2011 UWB standard This device is the first in a family of parts that will operate at data rates of 110 kbps 850 kbps and 6 8 Mbps The resulting silicon has a wide range of standards based applications for both Real Time Location Systems RTLS and Ultra Low Power Wireless Transceivers in areas as diverse as manufacturing healthcare lighting security transport inventory amp supply chain management Further Information For further information on this or any other DecaWave product contact a sales representative as follows DecaWave Ltd Adelaide Chambers Peter Street Dublin 8 t 353 1 6975030 e sales decawave com w www decawave com DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 17 of 21 author 5011 Sources of error TWR schemes deca Wave 7 APPENDIX A DERIVING THE ERROR IN RANGING ACCURACY DUE TO DRIFT 7 1 TWR with clock drift With
18. pty Arepty Ca trepty Cap 2TOF trepty Arepty ep Which reduces to a 1 1 1 TOF TOF TOF e a Arepiy A Tos a treply a DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 19 of 21 author 5011 Sources of error in TWR schemes ad decaWave 8 APPENDIX B RANGE BIAS FIGURES FOR 900 MHZ CHANNELS The DW1000 supports two 900 MHz bandwidth channels Ch 4 amp 6 These channels have a different range bias characteristic due to their wider bandwidth 900 MHz Bandwidth 40 30 20 m A Range Bias A o PRF 16 MHz PRF 64 MHz Received Signal Level dBm Figure 17 Range bias error vs received signal level for 900MHz channels Table 5 Range bias correction factors vs received signal level for 900MHz channels Rar PRF 16 MHz PRF 64 MHz 900 MHz 900 MHz cm cm 61 27 5 29 5 63 24 4 26 6 65 21 0 23 5 67 17 6 19 9 69 13 8 15 0 71 9 5 10 0 73 5 1 5 8 75 0 0 0 0 77 4 2 4 9 79 9 7 9 1 81 15 8 12 7 DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express w
19. r channel 2 Range Bias Correction Factor Applied Measured TWR distance For channel 2 cm up PRF 16 MHz PRF 64 MHz 1 00 21 13 1 25 20 11 1 50 19 11 1 75 19 10 2 00 18 10 3 8 Design Specific Details The description of the EVK1000 s DecaRanging software above presents a simplified example of compensating for this range bias effect This explanation describes getting the measured distance of the system and applying a correction factor to correct for the range bias effect which is dependent on the measured distance However the effect of range bias is actually dependant on received signal level RSL at the pins of the chip This is affected by antenna gain transmitted power and any other sources of loss or gain in the system The EVK1000 has a transmit power of 41 3 dBm MHz and a 0dB antenna gain Should your system transmit at a different power level use a low noise amplifier LNA or have other Sources of power gain or loss in the system then the correction factor you need to apply will be different A more in depth understanding will be required in this scenario The RSL can be calculated using the formula described in the next section and this can be used in a table relating RSL to range bias figure also presented in the next section to determine what range bias correction factor you need to apply 3 4 Friis path loss formula and range bias correction value In the case of a line of s
20. ritten permission of the author Page 20 of 21 5011 Sources of error in TWR schemes deca Wave 83 21 0 15 3 85 25 4 17 5 87 29 4 19 7 89 32 1 23 3 91 33 9 24 5 93 35 6 26 4 95 39 4 28 4 DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the author Page 21 of 21
21. signal level and in particular on high signal levels This leads to an error in the reported time stamp and a corresponding error in the distance calculated using that time stamps unless an appropriate correction factor is applied The appropriate correction factor depends on the incident signal power at the chip and is affected by system design elements such as antenna gain PCB losses and so on Each system needs to be characterized to establish these gains losses so that the actual incident signal power can be determined and the appropriate correction factor applied to the reported distance to give the true distance Depending on the required accuracy of the distance measurements for the particular application this correction may not be necessary DecaWave 2014 This document is confidential and contains information which is proprietary to DecaWave Limited No reproduction is permitted without prior express written permission of the Page 15 of 21 author 5011 Sources of error in TWR schemes a decaWave 5 REFERENCES 5 1 Listing Reference is made to the following documents in the course of this Application Note Table 4 Table of References Ref Author Date Version Title 1 DecaWave Current DW1000 Data Sheet 2 DecaWave Current DW1000 User Manual 3 Hewlett orent Fundamentals of Quartz Oscillators Application Packard Note AN200 2 DecaWave 2014 This document is confide
22. the final response message device A can measure the round trip time of the transaction as follows trounda 2TOF trepiyg And extract the time of flight TOF 2TOF trounaa trepiyB Because of the clock drift device A actually measures an estimated TOF which is given by 2TOF trounaa 1 4 trepiyg 1 The difference between the true TOF and the estimated TOF gives the error in the ranging transaction 2TOF 2TOF trounda 1 trepiyg 1 T trounaA treplyB Substituting for t ounaa yields the final error 2 1 TOF TOF TOF 5 trepiyg a iz 7 2 SDS TWR with clock drift Now each device measures a round trip time as follows trounda 2TOF trepiyg troundp 2TOF trepiya We can extract the TOF by combining these two round trip times as follows 4TOF trounda treptya trounap treptyB As before due to clock drift device A and device B measure estimated round trip times so the estimated TOF is given by 4TOF trounda treptya 1 trounaB treptyp 1 The difference between the estimated TOF and the true TOF gives the error in the ranging transaction as 4TOF 4TOF trounada m treptya 1 trounap z treptyp 1 E trounada m treplya F treplys 4TOF 4TOF trounaA treplya ea trounaB treplys Jes DecaWave 2014 This document is confidential and contains
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