NAME
Math::KalmanFilter - Kalman Filter(also known as Linear Quadratic
Estimation) implementation for sensor fusion and such
VERSION
version 0.03
SYNOPSIS
use Math::KalmanFilter;
use Time::HiRes qw(time);
my $oldTime = time();
# Read State from state sensor, in a IMU this would be one of the accelerometer orientation angle
# e.g. Angle between orientation vector and X axis in degrees.
my $state = readStateSensor();
# Read rate of change of state, in a IMU gyroscope measures the delta i.e. the Rate of change of
# $state e.g. rate of change of angle between orientation vector and X axis in degree per second.
my $delta = readDeltaSensor();
#Created a Kalman filter object to hold state changes for your measurement target.
$kalman = Math::KalmanFilter->new(
angle => $state
);
while($keep_running){
my $newTime = time();
my $deltaTime = $newTime - $oldTime;
$oldTime = $newTime;
my $state = readStateSensor();
my $delta = readDeltaSensor();
my $angle = $kalman->getAngle($state,$delta,$deltaTime);
print "CURRENT ANGLE:$angle";
}
DESCRIPTION
The Kalman filter, also known as linear quadratic estimation (LQE), is
an algorithm that uses a series of measurements observed over time,
containing noise (random variations) and other inaccuracies, and
produces estimates of unknown variables that tend to be more precise
than those based on a single measurement alone.
Algorithm is recursive, which means it takes the output of its previous
calculations as a factor in calculating the next step which improves its
accuracy over time. The key to Kalman filters are two sensors with
different kind of accuracy issues in each. Sensor A or the state sensor
might give in-accurate value for a measurement on the whole but it
doesn't drift. Sensor B or delta sensor gives gives much more accurate
rate of change in value(or delta) but it drifts over time due to its
small inaccuracies as it only measures rate of change in value and not
the actual value. Kalman filter uses this knowledge to fuse results from
both sensors to give a state value which is more accurate than state
value received from any of these filters alone.
An example of application for this is calculating orientation of objects
using Gyroscopes and Accelerometers.
While Accelerometer is usually used to measure gravity it can be used to
measure the inclination of a body with respect to the surface of earth
along the x and y axis(not z axis as Z axis is usually facing the
opposite direction as the force of gravity) by measuring the direction
in which the force of gravity is applied.
Gyroscope measures the rate of rotation about one or all the axis of a
body. while it gives fairly accurate estimation of the angular velocity,
if we use it to calculate the current inclination based on the starting
inclination and the angular velocity, there is a lot of drift, which
means the gyroscope error will accumulate over time as we calculate
newer angles based on previous angle and angular velocity and the error
in angular velocity piles on.
A real life example of how Kalman filter works is while driving on a
highway in a car. If you take the time passed since when your started
driving and your estimated average speed every hour and use it to
calculate the distance you have traveled your calculation will become
more inaccurate as you drive on.
This is drift in value. However if you watch each milestone and
calculate your current position using milestone data and your speed
since the last milestone your result will be much more accurate. That is
approximately close
to how Kalman filter works.
ATTRIBUTES
qAngle
* default: 0.001
qBias
* default: 0.003
rMeasure
* default: 0.03
bias
* starting value(default): 0
* recalculated(optimised) at each new sensor reading.
covariance
This is the covariance matrix, it is stored as a 2d array ref * starting
value(default): [[0,0],[0,0]] * recalculated(optimised) at each new
sensor reading.
angle
Calculated angle
METHODS
getAngle
Calculate new state based on observed reading from state sensor, delta
sensor and time elapsed since last reading.
SUPPORT
Bugs / Feature Requests
Please report any bugs or feature requests through github at
. You will
be notified automatically of any progress on your issue.
Source Code
This is open source software. The code repository is available for
public review and contribution under the terms of the license.
git clone git://github.com/shantanubhadoria/math-kalmanfilter.git
AUTHOR
Shantanu Bhadoria
CONTRIBUTORS
* Shantanu Bhadoria
* Shantanu Bhadoria
COPYRIGHT AND LICENSE
This software is copyright (c) 2013 by Shantanu Bhadoria.
This is free software; you can redistribute it and/or modify it under
the same terms as the Perl 5 programming language system itself.