in this video we'll discuss why you will
use Kalman filters if you're not
familiar with the topic you may be
asking yourself what is a common filter
is it a new brand of coffee filter that
proves the symbolist tasting coffee no
it's not a common filter is an optional
estimation algorithm today we'll discuss
two examples that demonstrate common
uses of Kalman filters in the first
example we'll see how a common filter
can be used to estimate a system state
when it cannot be measured directly to
illustrate this let's go to Mars before
anyone asked us if your spacecraft's
engine can burn fill at a high enough
temperature it can create trust that
will let you fly to Mars by the way
according to NASA liquid hydrogen is a
light and powerful rocket propellant
that burns with extreme intensity at
5,500 degrees Fahrenheit but be careful
because a to high temperature can put
the mechanical components of the engine
at risk and this can lead to the failure
of some of the mechanical parts if that
happens you might be stuck in your small
spacecraft where you've got to eat from
tubes to provide such a situation you
should closely monitor the internal
temperature of the combustion chamber
this is not an easy task since a sensor
place inside the chamber would melt
instead it needs to be placed on a
cooler surface close to the chamber the
problem you're facing here is that you
want to measure internal temperature of
the chamber but you can't instead you
have to measure external temperature
illustration you can use a common filter
to find the best estimate of the
internal temperature from an indirect
measurement this way you're extracting
information about what you can't measure
from what you can
now that you know the solution to your
problem you can continue your journey to
Mars but are you scared of traveling in
space let me tell you this on Mars
you're gonna weigh 62 percent less than
what you weigh on earth still nuts go
west okay then let's go back and take a
look at another scenario that takes
place on earth in this example we're
going to see how the carbon filter can
be used to estimate a state of the
system by combining measurements from
different sources that may be subject to
noise you have guests visiting from
overseas and you need to pick them up
from the airport you're using your car's
navigation system let's look at the
sensors you have onboard which help you
find your position and navigate you to
the airport
the inertial measurement unit uses
accelerometers and gyroscopes to measure
the cars acceleration and angular
velocity the odometer measures the
relative distance traveled by the car
the GPS receiver receives signals from
satellites to locate the car on Earth's
surface if you live in Boston as I do
you gotta travel through the big thick a
very very long tunnel and in the tunnel
it gets harder to estimate your position
through GPS since the receivers
line-of-sight to satellites is blocked
and GPS signal is weak in this case you
may want to trust the IMU readings which
give you the acceleration however
acceleration itself doesn't tell you
much about the car's position for that
you need to take the double integral of
the acceleration unfortunately this
operation is prone to drift due to small
errors accumulating over time to get
better position estimates you can use
IMU measurements along with odometer
readings but note that odometer measure
may be affected by the tire pressure and
road conditions to summarize your
sensors measuring the relative position
of your car give you fast updates but
they are prone to drift the GPS receiver
provides your absolute location but it
gets updated less frequently and it may
be noisy in this scenario a Kalman
filter can be used to fuse these three
measurements to find the optimal
estimate of the exact position of the
car let's look at some facts about
Kalman filters the Kalman filter is
named after Rudolph Kalman who is the
primary developer of s theory it is an
optimal estimation algorithm that
predicts the parameter of interest such
as location speed and direction in the
presence of noisy measurements common
applications of Kalman filters include
guidance navigation and control systems
computer vision systems and signal
processing one of the first applications
of Kalman filters was in the 1960s do
you have any guesses as to what it
helped with engineers use it in the
Apollo projects where the Kalman filter
was used to estimate trajectories of the
manned spacecraft to the moon and back
let's summarize what we've seen in this
video
Kalman filters are used to optimally
estimate the variables of interests when
they can't be measured directly but an
indirect measurement is available they
are also used to find the best estimate
of states by combining measurements from
various sensors in the presence of noise
in the next videos we'll cover what
Kalman filters are and how they work
Kalman filtering is a method to design
optimal state observers therefore in the
next video we'll learn state observers
and then we'll continue our discussion
with optimal state as
the mater's