Ultra-wideband (UWB) based localization systems became popular to navigate unmanned aerial vehicles (UAV) indoors, e.g. for light shows. The developed UWB localization system outperforms other systems due to the flexibility of the auto-calibration method for the anchor positions and the increased multipath resistance achieved with an aperture-coupled microstrip patch antenna. A dedicated Time Diference of Arrival (TDoA) based message exchange procedure allows a position update rate of up to 200 Hz with a constant measurement delay of 8.4 ms. Furthermore, the reliability is increased by including redundancy in the message exchange procedure. A standard deviation of the position within 3.5 cm is achieved with an operating range exceeding 100 m.
antenna. This section lines out the limitations of the multipath detection with omnidirectional antennas and proposes a solution with an aperture-coupled microstrip patch antenna. In Section 5, a new TDoA message exchange procedure is presented, which allows a position update rate of 200 Hz and an independent measurement delay and contains redundancy to increase reliability. Finally, results are shown and conclusions are drawn in Section 6 and 7, respectively.
is the master device in the system. It controls all procedures and carries out all calculations. Furthermore, the CLE generates the reference clock using a temperature-compensated crystal oscillator (TCXO). The anchors in the proposed system are time-synchronized over cable to increase accuracy and position update rate, making air-time for clock synchronization unnecessary. The maximum cable length is limited to 100 m due to the attenuation of the clock signal.
The transceivers in the clock distribution network are chosen to minimize clock jitter; thus, no clock reprocessing is required. Each anchor consists of the DW1000 UWB chip, a microprocessor and a UWB antenna. The tag is mounted on a UAV and consists the same elements. Fig. 2 shows the designed tag and anchor with the aperture-coupled microstrip patch antenna. Fig. 3 shows the UAV with the mounted tag.
To locate a tag, all anchor coordinates have to be known. Therefore, auto-calibration algorithms are used, because determining all coordinates manually on a stage is tedious work.
However, many auto-calibration algorithms either assume no prior knowledge about the anchor positions [3] or locate remaining anchors based and a few known anchors [4, 5]. Beyond that, to use the system in TDoA mode, all cable delays i have to be known as well. Typically, the cable delays have to be determined separately [6].
The auto-calibration algorithm proposed here solves several problems simultaneously. In many practical anchor constellations, certain anchor coordinates can often be easily measured, whereas others, possibly from the same anchor, cannot. The height above ground (-coordinate) of an anchor hanging from the ceiling, for example, can be easily determined using a laser meter, unlike the - and -coordinates, which are more dificult to determine accurately. The best trade-of between the time required to set up the system and the accuracy of the auto-calibration algorithm is achieved when as many (easy to measure) coordinates as possible can be provided to the auto-calibration algorithm. Additionally, together with all unknown coordinates, all cable delays are determined at the same time.
Let A1 to A denote all anchors, each with corresponding coordinates , , and . The Euclidean distance , between anchor and is calculated as
√︁
, =
( − )2 + ( − )2 + ( − )2.
(
It should be noted that if the anchors can be arranged in a constellation as shown in Fig. 4 and described in the aforementioned example, the system of equations will be well-conditioned without the need to measure a single distance. However, since, for example, the heights of anchors A5 to A8 can probably easily be measured using a laser meter, these coordinates could also be provided to the algorithm as known coordinates and would further increase the calibration accuracy.
The reference clock is generated on the CLE and distributed to all anchors via cables. However, since only the relative delays matter, 1 can be defined to be zero and hence all other delays, 2 to , refer to the time at anchor A1. The estimated delays ^2 to ^ can be initialized with zero.
In the following, it is described how the remaining coordinates and cable delays can be determined automatically. Let tx, denote the time of transmission of a message from anchor A and let rx,, be the time of arrival of this message at anchor A . By measuring the timestamps for all combinations of receivers and transmitters, the following system of equations can be formulated:
^1,2/ + 1 − ^2 Here, refers to the speed of light and ^, to the Euclidean distance between anchor A and A based on the estimated coordinates. Thus, for the example illustrated in Fig. 4, ^1,2 can be calculated as
^1,2 = √︀(^2 − 1)2 + (2 − 1)2 + (2 − 1)2.
This nonlinear system of equations is solved using Newton’s method. Therefore, partial
derivatives have to be evaluated only for the estimated coordinates. The first equation of (
0 . . . 0 ⎤ ⎡⎢ ΔΔ23 ⎤⎥ ⎡ rx,2,1 − tx,1 − − ...1 .. .. .. 0... ⎥⎥⎥⎥⎥ ⎢⎢⎢⎢⎢ Δ...5 ⎥⎥⎥⎥⎥⎥ = ⎢⎢⎢⎢⎢⎢ rx,3,1 − tx,1 − − 0...1 ... ... ... 00... ⎥⎥⎥⎦⎥⎥ · ⎢⎢⎢⎢⎣⎢⎢ ΔΔΔ... 238 ⎥⎥⎥⎥⎦⎥ ⎢⎢⎣⎢⎢ rrxx,,31,,22 −− ttxx,,22 −− ⏟ ⏞ ⏟ which is solved with the standard least squares method The estimated values are then updated according to = ( )− 1 . ^2 ^8 = ^2 + Δ2 . . .
= ^8 + Δ 8.
Equations (
UWB-based indoor localization systems typically use omnidirectional antennas [3, 2, 7], such as monopole chip antennas or cone antennas. Although the UWB technology is known to be insensitive to multipaths, not all multipaths can be detected with single omnidirectinal antennas. The system developed in [8] addresses this problem by utilizing an antenna array. This section highlights the limitations of the multipath detection with omnidirectional antennas and proposes a solution using a aperture-coupled microstrip patch antennas.
Multipaths can easily be detected in UWB systems if the length of the reflected path is at least one pulse length p longer than the direct path , where equals the speed of light and p refers to the pulse length in time. For shorter multipaths, the direct and the reflected pulse overlap so that the multipath is no longer discernible. The radii M and M of the zone of undetectable multipaths can be calculated as and M =
√︃ M =
. . . . . . ⏞ ^1,2 ⎤
− 1 + ^2 ^1,3 − 1 + ^3 ⎥⎥ ⎥ ⎥ ^1,2 ⎥⎥,
− ^2 + 1 ⎥⎥
^2,3 ⎥
− ^2 + ^3 ⎥⎦
(
Detectable multipath
Fresnel Zone bF bM aF aM
rx d Undetectable multipath
Zone of undetectable multipaths for the frequency of operation .
It is remarkable that the zone of undetectable multipaths is significantly larger than the first Fresnel zone. Multipaths generated by reflections of objects outside the zone of undetectable multipaths (marked as detectable multipath in Fig. 5) show up as a separate pulse at the receiver and can thus be detected.
However, assume the transmitter of a UWB message is a UAV. Then, the direct path and the immediate vicinity of the UAV, apart from the UAV itself, is typically free of obstacles. Note that this is not necessarily true for the anchors, since they have to be attached to something, for example a tripod, a wall, or in the case of on-stage use, an aluminum truss. These objects, are likely to be in the zone of undetectable multipaths, behind the receiver. A multipath generated by such objects is illustrated with the red path (marked as undetectable multipath) in Fig. 5. Such a multipath can have a signal power comparable to the direct path, because the reflected path is only marginally longer. Furthermore, if the receiver antenna has an omnidirectional radiation pattern, signals from the direct path and a multipath can be received with similar antenna gain. Consequently, the reflected signal can significantly afect the signal from the direct path.
An elegant way to reduce the impact of reflections from the environment behind the anchor is to use an antenna whose radiation pattern has a zero at the back or at least only a small backlobe. In addition, the antenna should not have zeros in the front hemisphere. These requirements are fulfilled with the designed aperture coupled microstrip patch antennas, which have been successfully adopted for many wireless applications since their inception [9]. In this case, they are natural contenders for a multitude of reasons. First, it is well known that (a) (b)
(c) model including cables. they can provide a large enough bandwidth. Second, while their design methodology is rather straightforward, they also allow for easy tuning to comply with manufacturing tolerances and other uncertainties. Although still being electrically small overall, the ground planes should make the antenna characteristics less susceptible to influences of the cables. Two patch antennas have been designed, one for the 4 GHz IEEE 802.15.4 channels 2 and 4, and one for the 6.5 GHz channels 5 and 7. Fig. 6 shows the designed 4 GHz patch antenna and Tab. 1 lists the dimensions for both antennas. Parameters of the developed patch antennas (in mm).
Parameter Patch length × Distance patch-aperture
width Stub length × width Aperture (slot) length × width 4 GHz Antenna
6.5 GHz Antenna gain in the front direction compared to a monopole antenna has the additional advantage of increasing the operating range. Thus, a 90% two-way communication success ratio between anchors and tags has been achieved at a distance of 170 m.
The goal of the message exchange procedure is to avoid collisions while maximizing the position update rate. Furthermore, redundancy shall be included to increase the reliability. The proposed UWB message exchange procedure is illustrated in Fig. 9 and can be described as follows: Let denote the number of anchors and T denote the number of tags in the system, respectively. First, the CLE transmits previously calculated positions to the tags T(− 1) mod , T(− 2) mod (if T ≥ 3), and T(− 3) mod (if T ≥ 4) via the anchor which has received the UWB message φ-cut simulated φ-cut measured θθ--ccuutt smimeausluarteedd 30◦
45◦ 60◦ 75◦ 90◦ 105◦ 120◦ 135◦ 150◦ from tag T(− 1) mod with the highest signal strength. Then, tag T(+1) mod transmits a UWB message (blink message), which is received and timestamped at all anchors. In the meantime, the CLE calculates the position of the tag T based on the timestamps recorded in the previous round. Next, the newly measured timestamps from tag T(+1) mod are collected from all anchors. Finally, the counter variable is updated according to = ( + 1) mod (12) and the procedure starts over. With a total time requirement of 5 ms per position, a position update rate of 200 Hz can be achieved.
This message exchange procedure contains redundancy to increase reliability. If a tag position is not received the first time (green arrow in Fig. 9), it will be retransmitted two additional times (orange and red arrows). The tag calculates the time until it retransmits its blink message depending on the attempt at which it has received its position and the total number of tags in the system.
The delay between the transmission of the timestamped pulse of a tag and the reception of the calculated position on the same tag is approximately 8.4 ms and it is independent of the total number of tags and anchors in the system. Such a low and constant latency is highly advantageous for the flight controller. In addition, the system is able to track fast-moving objects because the position can be calculated with only one UWB message.
An absolute accuracy of 10 cm with respect to the ground truth can be achieved with a cubeshaped anchor constellation as shown in Fig. 10. Fig. 11 shows the histogram and the cumulative distribution function for localization measurements performed with an anchor constellation presented in Fig. 10. As can be observed, 68% and 95% of all positions lie within a sphere of radius = 3.5 cm and = 6.3 cm, respectively. Up to 200 positions per second with a constant measurement delay of 8.4 ms can be determined with the proposed message exchange procedure. Due to the redundancy, the position can be determined in 99.5% of all cases. In the remaining cases, either not enough anchors have received the tag’s blink message or the tag has not received the finally calculated position. The designed aperture-coupled microstrip 700 600 500 400 300 200 100 68% 95%
Empirical CDF PDF Histogram 0.9 1 0.8 0.7 0.6 )
r 0.5 F(
F
D 0.4 C 0.3 0.2 0.1 x y patch antenna increases immunity to multipaths generated by objects in close proximity to the transceivers and lets the operating range exceed 100 m.
Three typical issues for UWB-based indoor localization systems have been addressed in this paper. The auto-calibration algorithm proposed in Sec. 3 can determine unknown coordinates and cable delays at the same time. For each anchor position, it can be individually selected which coordinates are known or can be measured accurately. This makes the system suitable to be used on a stage, where the anchor constellation can be complicated.
In Sec. 4, the limitations of the multipath detection in a UWB system with omnidirectional antennas are outlined. Immunity to reflections from objects in close proximity behind the anchors can be achieved by using aperture-coupled microstrip patch antennas because of their low backlobes. The higher gain in the region of interest additionally increases the operating range.
Finally, the message exchange procedure described in Sec. 5 contains redundancy and allows a position update rate of 200 Hz. In addition, every tag, independent of the total number of tags and anchors in the system, receives its position after a constant amount of time. All these properties make the proposed indoor localization system ideal for navigating fast-moving UAVs with a precision down to the size of an apple.