Indoor positioning

Why this matters

Inside a warehouse there is no GNSS signal, so the drone must know its position from other sensors. UAT 363 introduced indoor positioning methods and UWB position fixes. This course asks the next question: is the position good enough to fly between racks only a few metres apart? Error comes from several sources at once. Unless the team adds them all up, it may fly closer to the racks than it realises.

The whole course uses one hypothetical case: a parts factory with a 60 × 30 m high-bay rack warehouse that uses three drones to count stock at night. All numbers are made up for practice. The Python code for every module can be downloaded from /downloads/uat-366/.

The position data chain

The PX4 guide to vision and motion-capture positioning says external position should be sent at 30–50 Hz; if the rate is too low, EKF2 will not fuse the data. The parameter EKF2_EV_CTRL selects whether horizontal position, vertical position, velocity or yaw is used, and EKF2_EV_DELAY sets the delay of the vision data relative to the IMU, which the guide says must be tuned experimentally. Uncompensated latency means the position being used is a past position, off by the speed multiplied by the delay.

The error budget

Independent errors from several sources combine as a root sum square (RSS). The largest source dominates, so shrinking small sources helps little.

import math

SPEED, LATENCY = 1.5, 0.040
sources = {
    "UWB position": 0.10,
    "anchor survey": 0.05,
    "uncompensated latency": SPEED * LATENCY,
    "map-to-tag offset": 0.03,
}
total = math.sqrt(sum(v ** 2 for v in sources.values()))
for name, v in sources.items():
    print(f"{name:<22} {v:.3f} m  ({v ** 2 / total ** 2:.0%} of variance)")
print(f"total (RSS) {total:.3f} m")
fixed = math.sqrt(total ** 2 - sources["uncompensated latency"] ** 2)
print(f"after compensating latency with EKF2_EV_DELAY: {fixed:.3f} m")

UWB position           0.100 m  (59% of variance)
anchor survey          0.050 m  (15% of variance)
uncompensated latency  0.060 m  (21% of variance)
map-to-tag offset      0.030 m  (5% of variance)
total (RSS) 0.130 m
after compensating latency with EKF2_EV_DELAY: 0.116 m

VIO drift

VIO (visual-inertial odometry) estimates motion from a camera and an IMU without installing anything in the building, but its error grows with distance travelled. AprilTag markers (Olson, 2011) placed at known positions reset the error whenever the camera sees one, so the error follows a sawtooth.

DRIFT, TAG_ERR, ROUTE_M = 0.01, 0.03, 120

for spacing in (60, 30, 15):
    worst = TAG_ERR + DRIFT * spacing
    print(f"tags every {spacing:>2} m: worst error {worst:.2f} m")
print(f"no tags over {ROUTE_M} m: {TAG_ERR + DRIFT * ROUTE_M:.2f} m")
for limit in (0.20, 0.10):
    print(f"to stay below {limit:.2f} m, place tags at most every {(limit - TAG_ERR) / DRIFT:.0f} m")

tags every 60 m: worst error 0.63 m
tags every 30 m: worst error 0.33 m
tags every 15 m: worst error 0.18 m
no tags over 120 m: 1.23 m
to stay below 0.20 m, place tags at most every 17 m
to stay below 0.10 m, place tags at most every 7 m

The building coordinate frame

Every source must refer to the same frame. Define the room’s origin and axis directions (for example, the south-west corner with x along the aisles), survey the UWB anchors and tags with instruments several times more accurate than the requirement, and convert to the frame PX4 uses (NED), as covered in the ENU and NED conversion in UAT 322.

Module lab

Common mistakes

Summary

• Errors from several sources combine by RSS, and the largest source dominates the total.
• Uncompensated latency produces an error of v·Δt; set EKF2_EV_DELAY and send data at 30–50 Hz.
• VIO drifts; reference tags reset it, and tag spacing follows from the acceptable error.
• Every source must share one precisely surveyed coordinate frame.

Check your understanding

1. What is the RSS of error sources of 0.06 m and 0.08 m?
2. Flying at 2 m/s with 50 ms of uncompensated latency, how large is the error?
3. VIO drifts 2% of distance, a tag resets the error to 0.02 m, and the limit is 0.2 m. What is the maximum tag spacing?
4. At what rate does PX4 recommend sending external position?
5. Why does reducing the smallest error source help so little?