LiDAR and mission sensors

Example 1 Pulse density of three LiDAR setups

Assume a single pass with no overlap, pulses spread evenly, and one pulse counted per shot.

import math

def pulse_density(prr, h, v, fov_deg):
    swath = 2 * h * math.tan(math.radians(fov_deg / 2))
    return swath, prr / (v * swath)

cases = [
    ("solid-state 240k", 240_000, 60, 8, 70),
    ("same, higher and faster", 240_000, 120, 15, 70),
    ("small mechanical 20k", 20_000, 100, 12, 70),
]
for name, prr, h, v, fov in cases:
    w, d = pulse_density(prr, h, v, fov)
    level = "meets QL1" if d >= 8 else "meets QL2" if d >= 2 else "below QL2"
    print(f"{name:<24} swath {w:5.1f} m, {d:6.1f} pulses/m^2, spacing {1 / math.sqrt(d):.2f} m, {level}")

solid-state 240k         swath  84.0 m,  357.0 pulses/m^2, spacing 0.05 m, meets QL1
same, higher and faster  swath 168.0 m,   95.2 pulses/m^2, spacing 0.10 m, meets QL1
small mechanical 20k     swath 140.0 m,   11.9 pulses/m^2, spacing 0.29 m, meets QL1

Flying higher and faster covers more area per flight, but density falls by the product of both. A low-rate sensor can still meet QL1 if it flies slowly enough. In practice, overlapping passes raise density, while the edges of the scan and non-reflective surfaces lower it.

Example 2 Range resolution and beat frequency

C = 299_792_458

for bw in (4e9, 1e9, 250e6):
    print(f"bandwidth {bw / 1e9:.2f} GHz -> range resolution {C / (2 * bw) * 100:.2f} cm")
S = 30e12                                   # Hz/s chirp slope (30 MHz/µs)
for d in (5, 10, 20):
    print(f"target at {d:>2} m -> beat frequency {S * 2 * d / C / 1e6:.2f} MHz")

bandwidth 4.00 GHz -> range resolution 3.75 cm
bandwidth 1.00 GHz -> range resolution 14.99 cm
bandwidth 0.25 GHz -> range resolution 59.96 cm
target at  5 m -> beat frequency 1.00 MHz
target at 10 m -> beat frequency 2.00 MHz
target at 20 m -> beat frequency 4.00 MHz

A 4 GHz bandwidth gives 3.75 cm resolution, matching the example in TI’s document, and range is proportional to beat frequency, so the radar separates ranges by separating frequencies.

Example 3 Scoring matrix and sensitivity to weights

Scores from 1 to 5 agreed by the team (hypothetical values).

criteria = ["height accuracy", "sees ground under crop", "mass on VTOL", "cost", "processing effort"]
scores = {
    "LiDAR": [5, 5, 2, 1, 3],
    "RGB photogrammetry": [3, 1, 5, 5, 3],
    "mmWave radar altimeter": [2, 2, 4, 4, 4],
}
weight_sets = {
    "accuracy first": [0.35, 0.25, 0.15, 0.15, 0.10],
    "budget first": [0.15, 0.25, 0.15, 0.35, 0.10],
}
for label, w in weight_sets.items():
    assert abs(sum(w) - 1) < 1e-9
    ranked = sorted(((sum(a * b for a, b in zip(w, s)), name) for name, s in scores.items()), reverse=True)
    print(f"{label}: " + ", ".join(f"{name} {total:.2f}" for total, name in ranked))

accuracy first: LiDAR 3.75, RGB photogrammetry 3.10, mmWave radar altimeter 2.80
budget first: RGB photogrammetry 3.50, mmWave radar altimeter 3.20, LiDAR 2.95

When accuracy matters most, LiDAR wins; when budget carries the most weight, RGB photography comes first. The team must agree the weights from the data users’ needs before looking at scores, and record the reasons.