0:04

This week we will learn about the Kalman filter for

Â Bayesian estimation in robotics.

Â The Kalman Filter is an optimal tracking algorithm for

Â linear systems that is widely used in many applications.

Â Examples of tracking includes pedestrian and vehicle tracking for

Â self-driving cars or items traveling along a conveyor belt on an assembly line.

Â We will start by discussing the system model and

Â the measurement model of the Kalman filter.

Â And then we will talk about the maximum-a-posterior estimates

Â in the filter.

Â 2:02

When a robot is deployed in the real world,

Â it will receive a steady stream of visual data from its camera.

Â Applying the principles from module one,

Â the robot can identify the position of the ball from the sensor data.

Â However, due to noise, the position may not be very accurate.

Â 2:31

The concepts of measurements should be disambiguated from the concepts of state.

Â There's a true state of the world, but

Â the robots can only observe a shadow of that world.

Â For instance, the true position of the soccer ball may be 11 meters away from

Â the robot, but the robot thinks that it is 11.32567 meters away.

Â The robot observes this position of the ball through its camera, and

Â this measurement through the camera gives a noisy estimate of the state.

Â One source of the noise is the collection of pixels that can be misclassified

Â between the ball and the surrounding area.

Â We saw this kind of noise in module one.

Â 3:05

The robot is interested in the high-level concept of the hidden state

Â in order to make decisions about how to act.

Â The state of an object includes specific information to the task at hand.

Â A soccer playing robot may care only about the position and velocity of a ball.

Â For other tasks, such as aircraft control,

Â orientation can represent a critical aspect of state,

Â where the inertial measurement units and the GPS provide measurement data.

Â A firefighting robot may care to track a fire and

Â require temperature information to augment color and size estimates.

Â Each task is different, so

Â it is very important to delineate what constitutes the state.

Â For this module we simply will track our position and velocity.

Â Thus we declare our state to be a collection of x, y, z, dx,

Â dy, and dz.

Â When measuring the state,

Â we do not always receive information in the same units as the state.

Â For instance, to track the orientation of an aircraft,

Â we may only receive angular velocity measurements and

Â an the indication of where the gravity vector is pointing.

Â In the case of tracking ball velocity, we only observe position measurements.

Â No direct velocity observations are made.

Â This discrepancy between measurements and state makes tracking hard.

Â To motivate this module,

Â here's an example of data captured from our trusty soccer playing robot.

Â The robot uses its head camera and

Â vision algorithms to observe the position of the ball in time.

Â The critical decision that the robot goalie needs to make is when to dive.

Â 4:32

If you look at the plot on the right, the position measurements are quite noisy.

Â In the next lecture, we will provide Bayesian filtering methods to estimate

Â the true state of the ball from these noisy measurements.

Â