Perception and localization outdoors

ROB-310 and ROB-340 developed the probabilistic tools for estimating a robot's position and building maps: Bayes filters, Kalman and particle filters, and SLAM in its many forms. Those methods assume sensors that behave roughly as modelled. Outdoors, sensors meet sunlight, rain, snow, dust, fog, vegetation, featureless fields and satellite signals that are blocked, reflected or deliberately jammed. This lesson is about the sensors and the failure modes that matter in the field, how to quantify drift when the best sensors drop out, and how robust field systems detect degradation and fall back gracefully. It refers to ROB-340 for the estimation algorithms themselves, and to CON-250 lesson 4 for the surveying side of GNSS and real-time kinematic positioning.

Satellite positioning in the field

Global navigation satellite systems (GPS, GLONASS, Galileo and BeiDou) are the backbone of outdoor localization. A single-frequency standalone receiver gives positions good to a few metres. Dual-frequency receivers remove most ionospheric delay. Real-time kinematic (RTK) positioning uses carrier-phase measurements and corrections from a nearby base station or a network to reach centimetre accuracy, which is why it is standard on autonomous tractors, haul trucks and survey robots. Precise point positioning (PPP) uses precise satellite orbit and clock products instead of a local base, converging to decimetre or better accuracy over minutes; several services now deliver PPP corrections by satellite or internet, including combined PPP-RTK products.

In Canada, Natural Resources Canada provides the free CSRS-PPP online service for post-processing and maintains the Canadian Spatial Reference System; provincial and commercial RTK networks cover most farming regions. Coverage is thinner in the North, where low satellite elevations and ionospheric disturbances near the auroral zone make high-accuracy GNSS harder.

In the field, accuracy depends as much on the environment as on the receiver. Tree canopy, steep valley walls, open-pit mine walls and buildings block satellites and reflect signals, causing multipath errors that can reach metres and loss of RTK fix. The geometry of the visible satellites is summarized by the dilution of precision (DOP); when satellites are clustered in one part of the sky, the horizontal DOP rises and so do position errors. A rule of thumb is that horizontal error is roughly HDOP times the range error per satellite.

GNSS signals are extremely weak at the Earth's surface, so they are easy to jam and, with more effort, to spoof. Interference from illegal jammers, military activity and unintentional sources has been reported widely in recent years, including in regions near conflict zones where aviation and shipping have experienced large-scale disruption. Field robots that depend on GNSS should monitor signal-to-noise ratio, sudden position jumps and disagreement with inertial and odometry estimates, and treat GNSS as one input to a filter rather than as ground truth.

Dead reckoning and drift

When GNSS is unavailable, a robot falls back on dead reckoning: integrating wheel odometry, inertial measurements or visual odometry from a known start. Every dead-reckoning method drifts, and the shape of the drift matters. Random noise in a velocity measurement produces position error that grows roughly with the square root of time, like a random walk. A constant bias in a gyroscope produces a heading error that grows linearly with time, and because position is the integral of velocity in the wrong direction, the cross-track position error grows with the square of time or distance. A heading error of \( \delta\psi \) radians over a straight distance \( d \) produces a cross-track error of about \( d\,\delta\psi \).

# Monte Carlo drift of wheel-odometry + gyro dead reckoning on a 2 km straight drive
import numpy as np
rng = np.random.default_rng(460)
v, dt, T = 1.0, 0.1, 2000.0                 # 1 m/s for 2000 s
steps = int(T / dt)
def run(gyro_bias_deg_h, gyro_noise_deg_rt_h, odo_scale_err, trials=300):
    b = np.radians(gyro_bias_deg_h) / 3600 * rng.choice([-1, 1], trials)
    arw = np.radians(gyro_noise_deg_rt_h) / 60      # angle random walk per sqrt(s)
    psi = np.zeros(trials); x = np.zeros(trials); y = np.zeros(trials)
    scale = 1 + odo_scale_err * rng.standard_normal(trials)
    for _ in range(steps):
        psi += b * dt + arw * np.sqrt(dt) * rng.standard_normal(trials)
        x += v * scale * np.cos(psi) * dt
        y += v * scale * np.sin(psi) * dt
    err = np.hypot(x - v * T, y)
    return np.percentile(err, 50), np.percentile(err, 95)
for name, args in {"consumer MEMS IMU": (10.0, 0.3, 0.01),
                   "industrial MEMS IMU": (1.0, 0.1, 0.005),
                   "tactical-grade IMU": (0.1, 0.02, 0.002)}.items():
    p50, p95 = run(*args)
    print(f"{name:20s} median error {p50:6.1f} m   95th percentile {p95:6.1f} m  ({p95/20:.2f} % of distance)")

consumer MEMS IMU    median error   98.5 m   95th percentile  107.8 m  (5.39 % of distance)
industrial MEMS IMU  median error   12.1 m   95th percentile   21.2 m  (1.06 % of distance)
tactical-grade IMU   median error    2.6 m   95th percentile    7.5 m  (0.38 % of distance)

The simulation shows why IMU grade matters so much for long GNSS outages. With a consumer-grade gyro, errors after 2 km approach 100 m, about 5 per cent of the distance; an industrial unit keeps them near 10 to 20 m and a tactical-grade unit to a few metres, at a much higher price. Odometry scale error adds along-track error that grows linearly with distance. Field robots therefore combine dead reckoning with absolute corrections whenever they are available: GNSS when it returns, recognized landmarks, matching against a prior map, or terrain-relative navigation that compares sensed terrain shape with a stored elevation model.

Lidar, cameras and radar in bad weather

Lidar is the workhorse of mapping and obstacle detection, but its laser pulses are scattered and absorbed by rain, snow, fog and dust. Two effects matter. Attenuation reduces the returned power, shortening the useful range; in a uniform medium with extinction coefficient \( \alpha \) the received power falls as \( e^{-2\alpha R} \) in addition to the usual range loss. Backscatter from droplets, snowflakes and dust creates false returns close to the sensor, which can look like obstacles. Many lidars report multiple returns per pulse, and filtering by intensity, return number and the spatial pattern of points removes much of the clutter; learned filters trained on adverse-weather data sets do better still. Sensor windows also get dirty, wet or iced, so field robots often have wipers, washers, air knives or heaters, and monitor the fraction of expected returns to detect blockage.

Cameras suffer from glare, low light, shadows, rain on the lens and the changing appearance of vegetation through the seasons; a place-recognition model trained in summer may fail in winter. High-dynamic-range sensors, polarizing filters and active illumination help, and thermal infrared cameras see people and animals in darkness and through light smoke. Radar, especially millimetre-wave radar around 77 GHz, penetrates dust, fog, rain and snow far better than lidar or cameras, at the cost of lower angular resolution and noisy returns. Imaging radars and radar odometry have become practical for mining and off-road vehicles, where dust can make lidar nearly useless.

Degradation-aware localization

Robust field systems do not simply fuse every sensor all the time. They estimate the health of each sensor and adapt. A mine vehicle may switch from lidar-based localization to radar and inertial navigation when dust levels rise; an orchard robot may rely on row-following with cameras when GNSS fix is lost between trees and return to RTK at the headland. Techniques include monitoring the innovation, the difference between predicted and actual measurements in a Kalman filter, and rejecting measurements whose normalized innovation squared exceeds a chi-square threshold; checking for degeneracy in lidar scan matching, which happens in long featureless tunnels and open fields where geometry does not constrain motion in every direction; and maintaining multiple hypotheses when the robot may be in one of several similar places.

Teams in the DARPA Subterranean Challenge showed the value of such resilience. Leading systems fused lidar, cameras, thermal cameras and IMUs, detected when one modality was degraded and switched estimators, and shared maps among robots when communication allowed. Many published field systems now report results across seasons, weather and lighting conditions, because a method that works on a sunny day is not yet a field method.

# Innovation gating: reject GNSS fixes that disagree with the filter prediction
import numpy as np
rng = np.random.default_rng(7)
pred = np.array([100.0, 50.0])              # predicted position (m)
P = np.diag([0.30**2, 0.30**2])             # prediction covariance
R = np.diag([0.05**2, 0.05**2])             # RTK fix covariance
S = P + R                                   # innovation covariance
gate = 9.21                                 # chi-square 99 % for 2 degrees of freedom
fixes = [pred + rng.normal(0, 0.3, 2) for _ in range(4)] + [pred + np.array([4.0, -3.0])]
for i, z in enumerate(fixes):
    nu = z - pred
    nis = float(nu @ np.linalg.solve(S, nu))
    print(f"fix {i}: innovation {np.round(nu, 2)}  NIS {nis:7.2f}  {'accept' if nis < gate else 'reject (multipath or spoofing?)'}")

fix 0: innovation [0.   0.09]  NIS    0.09  accept
fix 1: innovation [-0.08 -0.27]  NIS    0.84  accept
fix 2: innovation [-0.14 -0.3 ]  NIS    1.16  accept
fix 3: innovation [0.02 0.4 ]  NIS    1.75  accept
fix 4: innovation [ 4. -3.]  NIS  270.27  reject (multipath or spoofing?)

The last fix, five metres away from the prediction, is rejected. A real system would not reject GNSS forever: if several consecutive fixes disagree consistently, the filter may be the one that is wrong, for example because the wheels were slipping, so the system needs logic to re-initialize. Designing these rules, and testing them with recorded data from real outages, is a large part of making outdoor localization dependable.