This article presents a time of arrival and time di erence of arrival fusion for Decawave ultra-wideband transceivers. The presented techniques combine the time-of-arrival and time-di erence-of-arrival measurements without losing the advantages of each approach. The precision and accuracy of the distances measured by the Decawave devices depends on three e ects: signal power, clock drift, and uncertainty in the hardware delay. This article shows how all three e ects may be compensated with both measurement techniques.
Localization systems have become indispensable for everyday life. Satellite
navigation[
Figure 1 illustrates the concept of TWR and the timestamp shift caused by signal power, as well as the error due to hardware delay. In our implementation, the reference station is the initiator. The rst message is sent by the reference station with timestamp T R
1 . The timestamp of the received message at the tag is a ected by the signal power, resulting in a timestamp shift of E1. The same applies to the response message, this time at the reference station. It is important to note that the timestamps T1R and T2T are not a ected by the receiving signal power. However, the hardware delay (A,B) must always be considered. The sending delay is assumed to be equal to the receiving delay. Without correction, the TWR signal travel time is 0:5 T2R T1R T2T T1T .
TR1
E2
TR2
TR1
A
Reference station
A
TR2 TOA
TOA
TOA
TOA
Tag E1 TT1
TT2
Tag B
TT1
B TT2
The values E1 and E2 are deduced from the signal power correction curve. Note that the signal power may a ect the tag and the reference station di erently. At lower signal power, the time di erence T1R;2 increases. In the previous section, we showed that the clock drift can be corrected by three messages. Figure 2 demonstrates how this principle can be adapted for two-way ranging. The last message is used to calculate the clock drift error C1R;3T = T1R;3 T1T;3. Observe that the signal power E1 does not a ect the timestamp di erence T1T;3.
TR1
E2
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TR3
The previous section showed how the clock drift and the hardware o set in uence
the time-of-arrival position estimate. In this section, we show how to combine
TOA with TDOA. Unlike TDOA, two-way ranging (TWR) based on TOA does
not require clock synchronization. One approach to synchronizing the TDOA
clock is to use an additional signal [
In the TDOA application, the in uence of the hardware delay is assumed to be the same for both timestamps T1S and T2S . Therefore, the TDOA equation
TOA
TDOA
E3 Station N
TS1
E4
TS2
TOA
TDOA Station N
C TS1
C TS2 is independent of the hardware delay. However, a new o set K appears, representing the delay between the signal of the tag with respect to the signal of the reference station. If both stations send the signal at exactly the same time, this o set K is zero. 4
Two-dimensional position estimation with four stations In this section, the theoretical concepts are veri ed with real measurements. The rst test scenario uses TOA measurements to estimate the unknown position of the tag. In the second test scenario is the position of the tag estimated by the fused measurements of TDOA and TOA. The tests were carried out with a Decawave EVB DW1000. The Decawave supports di erent message types, which are speci ed for the discovery phase, ranging phase and nal data transmission. Depending on the update rate and the preamble length, each message can vary from 190 s to 3.4 ms. In our experiments, we only used 190 s messages, also called blink messages. The general settings of the Decawave transceivers are listed in table 1. TR1 1. tag with identi cation number (ID) 2 is assumed to be unknown. The other stations are used to estimate the position of this tag. The station identi ed as the reference station changes during TWR positioning. This is because the distances between the tag and the other stations must be calculated successively for TWR trilateration. Unlike TWR, the reference station remains the same for TDOA; in this example, the reference station is the station with ID 1. This also explains why TDOA is much faster than TWR.
The following table 4 shows the standard deviation of the precision of the TOA and TDOA position estimates. The y-axis scattering is almost exactly equal for both measurement techniques. On the other hand, the x-axis scattering of TDOA is higher than that of TOA, depicted in Table 3.
This e ect is due to the asymmetry of the TDOA, which is actually a fusion of TWR and TDOA. An alternative reference station would change the distribution. The compensation of this e ect is described in a previous publication [?]. When combined with a lter, highly accurate results can be obtained. The position of the anchors a ects the tag localization; better results are obtained with tags that are more centered with respect to the anchors [?]. TDOA
TOA -0.1 -0.05 0 0.05 X-Axis [m] 0.1 This paper introduces a method for TOA and TDOA fusion for Decawave ultrawideband transceivers, which is able to use clock drift correction and the power correction curve. We showed how wireless clock calibration can be performed for the time di erence of arrival using an additional station. The corrected time of arrival and time di erence of arrival measurements were combined to increase the number of equations for the time di erence of arrival position estimate.