Drones and self-driving basicsMiddleLesson 2828 min read

Sensors: GPS, IMU, cameras and lidar

Every sensor is good at some things and bad at others. Learn what each one measures, where it fails, and why machines combine several of them.

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Sensors: GPS, IMU, cameras and lidar

Every sensor is good at some things and bad at others. Learn what each one measures, where it fails, and why machines combine several of them.

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In simple words

Close your eyes and stand on one foot. It is hard, but your inner ear still tells you if you are tipping. Now open your eyes: much easier, because your eyes and inner ear work together. Machines do the same. Each sensor is a bit wrong in its own way, and together they give a better answer. This is called sensor fusion.

A drone or a self-driving car cannot see the world directly. It only has numbers from its sensors, and every sensor has noise (small random errors), bias (a steady error in one direction) or blind spots. Knowing these weaknesses is half of robotics.

The main sensors

Sensor	What it measures	Good at	Weak at
GPS / satellite navigation	Position on Earth from satellite signals	Works anywhere with open sky; error does not grow over time	Often a few metres off; worse near tall buildings and trees; does not work indoors or in tunnels; updates only a few times a second
IMU: accelerometer	Acceleration, including the pull of gravity	Knows which way is down when the machine is still	Very noisy with vibration; cannot tell tilt from speeding up
IMU: gyroscope	How fast it is turning	Smooth and fast; great for short moments	A small bias adds up over time, so the angle slowly drifts
Magnetometer (compass)	Earth's magnetic field	Gives a heading	Confused by motors, steel, wires and buildings
Barometer	Air pressure, used for height	Cheap height estimate	Changes with weather and wind
Camera	Images: colour, texture, signs, lane lines	Rich detail; cheap; can read signs	Needs light; struggles with glare, darkness, fog and rain; depth is hard from one camera
Lidar	Distance, by timing pulses of laser light	Accurate 3D shape; works in the dark	Costly; heavy rain, fog and dust reduce range; glass and very dark surfaces can confuse it
Radar	Distance and speed, using radio waves	Works in rain, fog and dark; measures speed directly	Low detail; hard to tell what an object is
Ultrasonic	Distance, using sound echoes	Cheap; fine for very short range, like parking	Short range; soft or angled surfaces give weak echoes

Note

India has its own regional satellite navigation system, NavIC, built by ISRO. Some phones and receivers can use it along with GPS and other systems. Using several satellite systems together often gives a better fix.

Why one sensor is never enough

Look at the gyroscope and the accelerometer. The gyroscope is smooth, but it drifts: a tiny bias, added up every moment, slowly turns into a large error. The accelerometer does not drift, because gravity always points down, but it jumps around with every vibration from the motors. Their weaknesses are opposite. That makes them perfect partners.

Averaging: the simplest fusion

If readings have random noise and no bias, averaging several readings of the same thing reduces the noise. With four readings, the noise shrinks to about half. With sixteen, to about a quarter. Averaging does not remove bias: if every reading is 2 degrees too high, the average is also 2 degrees too high.

Python: averaging reduces random noise, not biaspython

import numpy as np

rng = np.random.default_rng(1)
true_value = 20.0          # say, a true tilt of 20 degrees
noise, bias = 3.0, 0.0     # try bias = 2.0 as well

for n in [1, 4, 16, 64]:
    # 2000 experiments, each averaging n readings
    readings = true_value + bias + rng.normal(0, noise, size=(2000, n))
    averages = readings.mean(axis=1)
    print(f"average of {n:2d} readings: typical error {averages.std():.2f}, "
          f"mean error {averages.mean() - true_value:+.2f}")

The complementary filter

A complementary filter blends the gyroscope and the accelerometer. At each step it takes the last angle, adds the gyroscope's turn, and then nudges the result a little towards the accelerometer's angle:

angle = alpha × (last angle + gyro rate × dt) + (1 − alpha) × accelerometer angle

With alpha close to 1, such as 0.98, the smooth gyroscope decides the short-term changes, and the accelerometer slowly pulls the angle back so it cannot drift away. Flight controllers use this idea or its big brother, the Kalman filter, which also keeps track of how uncertain each estimate is.

Weak design

Trust one sensor completely
Assume a sensor's number is the truth
Test only on a sunny day in an open field

Better design

Combine sensors whose weaknesses are different
Model noise and bias, and check them
Test in dark, rain, dust, near buildings and with vibration

Real example

A student team in Pune builds a line-following robot car with a camera. It works well in their lab. In the college corridor, afternoon sunlight makes bright patches on the floor, and the car keeps losing the line. They add a cheap distance sensor and slow down when the camera is unsure. The lesson: test where the machine will really run.

Try this. In the averaging code, set bias = 2.0 and run it again. Which number gets smaller as you average more, and which one does not?

Watch and read more

Lab

An average function and a working complementary filter that beats both the gyroscope and the accelerometer alone.

~25 min

The problem

This runs in your browser with made-up sensor data: a drone rocking gently, a gyroscope with a small bias, and a very noisy accelerometer.

Finish average(readings).
Finish complementary_filter: at each step, blend gyro_guess with the accelerometer angle using alpha.
Run it and compare the three errors printed at the end. The filter should beat both sensors alone.
Try alpha = 0.5 and 0.999. Write one sentence on what goes wrong at each end.

Practice lab

Edit the code and run it. Python runs in your browser — nothing is sent to our server.

Ctrl + Enter to run

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(7)
dt = 0.01                                   # 100 readings per second
t = np.arange(0, 10, dt)
true_angle = 10 * np.sin(0.5 * t)           # degrees: the drone rocks gently
true_rate = 5 * np.cos(0.5 * t)             # degrees per second
gyro = true_rate + 1.0 + rng.normal(0, 0.3, t.size)   # bias of 1 deg/s, a little noise
accel = true_angle + rng.normal(0, 3.0, t.size)       # no drift, but very noisy

def average(readings):
    # TODO: return the mean of the readings
    return readings[0]

def complementary_filter(gyro_rates, accel_angles, dt, alpha=0.98):
    angles = [accel_angles[0]]
    for i in range(1, len(gyro_rates)):
        gyro_guess = angles[-1] + gyro_rates[i] * dt
        # TODO: blend gyro_guess with accel_angles[i] using alpha
        angles.append(gyro_guess)
    return np.array(angles)

def rms(err):
    return float(np.sqrt(np.mean(np.square(err))))

fused = complementary_filter(gyro, accel, dt)
gyro_alone = complementary_filter(gyro, accel, dt, alpha=1.0)
print("average of first 50 accel readings:", round(average(list(accel[:50])), 2))
print("error, accelerometer alone:", round(rms(accel - true_angle), 2))
print("error, gyroscope alone:    ", round(rms(gyro_alone - true_angle), 2))
print("error, your filter:        ", round(rms(fused - true_angle), 2))

plt.plot(t, accel, ".", markersize=2, alpha=0.3, label="accelerometer")
plt.plot(t, gyro_alone, label="gyroscope alone")
plt.plot(t, fused, label="filter")
plt.plot(t, true_angle, "k--", label="true angle")
plt.xlabel("seconds"); plt.ylabel("degrees"); plt.legend(); plt.show()

Output

No output. Add print(...) to see values.

You are done when

average() works for any list of numbers
The filter's error is clearly lower than both the gyroscope alone and the accelerometer alone
The plot shows the gyroscope-only line drifting away and the filter line following the true angle
The alpha experiment explains both ends: too low is noisy, too close to 1 drifts

Hard questions

Try to answer before you reveal. If you can answer these, you understood the lesson.

Q1Why can the accelerometer not be trusted for tilt when the drone speeds up or brakes?Reveal

An accelerometer feels gravity and the drone's own acceleration mixed together. When the drone speeds up, the extra push looks just like a tilt. When it is still or moving steadily, only gravity is left, so the tilt reading is right. That is why the filter uses it only as a slow correction, not for quick changes.

Q2How would you choose alpha for a real drone, not made-up data?Reveal

Record real flights, ideally with a reference such as a more accurate sensor or a motion-capture setup, and try several values. Look at the trade-off: lower alpha follows the accelerometer's vibration noise; higher alpha lets gyroscope drift grow. The best value depends on the sample rate, vibration and how big the gyroscope bias is. A Kalman filter can adjust this balance automatically from noise estimates.

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Questions people ask

What does IMU stand for?

Inertial measurement unit. It usually combines an accelerometer and a gyroscope, and often a magnetometer. A small IMU chip is inside most phones, which is how your phone knows when you turn it sideways.

Why not use only lidar, if it is so accurate?

Lidar gives good shape and distance, but it cannot read a traffic light's colour or a sign's text, it is costly, and bad weather reduces its range. Cameras add colour and meaning; radar adds speed and bad-weather range. Different teams choose different mixes, and each choice has trade-offs.

Can a phone be used as a robot's sensor?

Yes, for learning. A phone has an IMU, a camera and satellite navigation. Several free apps can stream or log these readings, which is a cheap way to see real noise and drift for yourself.

What is the difference between noise and bias?

Noise is random: sometimes too high, sometimes too low. Averaging helps. Bias is steady: always off in the same direction. Averaging does not help; you need calibration or another sensor to correct it.

Lesson test

5 questions. Get 3 right (60%) to pass and complete this lesson.