All language subtitles for 01_particle-filter.en

In this lecture, we will talk about
a probabilistic state estimation technique

using a sampling-based distribution
representation known as

the Particle Filter.

Instead of a fully defined function,
the Particle Filter represents

a distribution with a set of samples,
referred to as particles.

These particles represent
the distribution.

The statistics of the samples match
the statistics of the distribution,

such as the mean or standard deviation.

However, they can be more
complicated metrics as well.

In this way, there are no parameters
as were seen in the mean and

covariances of the Gaussian models.

Instead, a full population is tracked.

In essence, the particle filter
population represents a mixture

of Gaussian distributions that
we have seen in the first week.

Here, the variance will go to 0.

With 0 variance,

the Gaussian distributions
become Dirac Delta functions.

Initially, a set of particles
represent the underlying belief state.

Each particle is a pair of the pose and
the weight of that pose.

This is similar to representing
a probability function

where the weight is the probability of
that pose in the underlying distribution.

Here, darker colors represent
higher weights, and

lighter colors represent lower weights.

Just like the Kalman filter,

a motion model will move
the underlying distribution.

Here, the particles move based on odometry
measurements taken from the robot.

A companion uncertainty model captures
the noise underlying the motion model.

For instance, this could be wheel slip or
friction changes.

In the particle filter,
where we do not track the motion model

in explicit parameters, we add sampled
noise from the motion noise model.

In this case,

we use a Gaussian distribution to model
noise with 0 mean and non-0 covariance.

Noise is uniquely added to each particle.

So separate samples are made for
each particle.

After the noise is added,

the dispersion of the particles captures
the uncertainty due to movement.

Like the Kalman filter,
we can use a separate set of observations

to constrain our noise and
update our belief distribution.

Here we will leverage
the LIDAR correlation

from previous lectures
on map registration.

We will update the weights of the
particles to reflect the correlation score

from the map registration by utilizing
the current weights as a prior belief.

The new set of particles captures
the distribution after odometry and

sensor measurements.

However, this may not be the optimal
set to represent the distribution.

Here, you can see that only a few
particles have significant weights.

Most of the particles
are lightly colored and

do not give much information
about the distribution.

To make the set of particles
more accurately represent

the belief state distribution, we check
the number of effective particles.

The number of effective particles
acts as a criterion for

when to resample particles.

This resampling process provides
a probabilistically motivated way

to prune out lower weighted particles.

With the set of large and

small weights, using the cumulative
probability function can aid in sampling.

With normalized weights,
the sum of the weights is 1, and

can be represented as a monotonically
increasing cumulative function.

We sample a number ,uniformly,
between 0 and

1 of the cumulative range and
find which weight includes that number.

The particles with the indices
found in the resampling approach

become the new set of particles to be
fed into the next odometry update.

Particles may be duplicated, but

the odometry noise will
differentiate these particles.

This approach provides a good way to
approach a multi-nodal belief state

distribution and
non-linear effects of your motion model.