View source for Kalman Filter

==A simple overview for single dimension==
*'''x<sub>n</sub> = x<sub>n-1</sub> + K * (x<sub>in</sub> - x<sub>n-1</sub>)'''
:*K is the Kalman gain and is recalculated in every iteration <br />
:*Q and R are constants <br />
[[File:kalman-04.jpg|300px]]

==Simple explanations==
*[http://digi.physic.ut.ee/mw/images/d/d5/Poormankalman.pdf Poormankalman pdf]

*[http://credentiality2.blogspot.ie/2010/08/simple-kalman-filter-example.html Simple kalman filter example]

*[http://biorobotics.ri.cmu.edu/papers/sbp_papers/integrated3/kleeman_kalman_basics.pdf 1 Understanding and Applying Kalman Filtering, Lindsay Kleeman]

*[http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6279585 IEEE SIGNAL PROCESSING MAGAZINE Understanding the Basis of the Kalman FilterVia a Simple and Intuitive Derivation,Ramsey Faragher]



==Simple C examples==
===1-dimensional Kalman Filter, Arduino version===
*[http://orlygoingthirty.blogspot.ie/2013/06/1-dimensional-kalman-filter-arduino.html 1-dimensional Kalman Filter, Arduino version ]
[[File:Kalman-02.jpg|600px|thumb|right|1-dimensional Kalman Filter, Arduino version .ino ]]
[[File:Kalman-03.jpg|600px|thumb|right|1-dimensional Kalman Filter, Arduino version .h ]]
<pre>
//kalmanA.ino
// simple Kalman filter
// adapted from C code by Adrian Boeing, www.adrianboeing.com 

KalmanFilter::KalmanFilter(float estimate, float initQ, float initR)
{
  Q = initQ;
  R = initR;

  // initial values for the kalman filter
  x_est_last = 0;
  P_last = 0;

  // initialize with a measurement
  x_est_last = estimate;
}

// add a new measurement, return the Kalman-filtered value
float KalmanFilter::step(float z_measured)
{
  // do a prediction
  x_temp_est = x_est_last;
  P_temp = P_last + R*Q;

  // calculate the Kalman gain
  K = P_temp * (1.0/(P_temp + R));

  // correct
  x_est = x_temp_est + K * (z_measured - x_temp_est); 
  P = (1- K) * P_temp;

  // update our last's
  P_last = P;
  x_est_last = x_est;

  return (x_est);
}
</pre>

<pre>
//kalmanA.h
class KalmanFilter
{
public:
  KalmanFilter(float estimate, float initQ, float initR);
  float step(float measurement);
private:
  // initial values for the kalman filter
  float x_est_last;
  float P_last;

  // the noise in the system
  float Q;
  float R;

  float K;    // Kalman gain
  float P;
  float P_temp;
  float x_temp_est;
  float x_est;
};
</pre>

<pre>
and how to use:

// simplistic Kalman filter for encoder readings
KalmanFilter kf(0, 0.01, 1.0);
float avg_err = kf.step(track_err);

</pre>

----
From above code:
*'''x<sub>n</sub> = x<sub>n-1</sub> + K * (x<sub>in</sub> - x<sub>n-1</sub>)'''
:*K is the Kalman gain and is recalculated in every iteration
----
<br />
<br />

===single state kalman filtering===
*[http://pengu.student.utwente.nl/wordpress/?p=116 single state kalman filtering]
[[File:Kalman-01.jpg|600px|thumb|right|Single state Kalman filtering ]]
<pre>
/*kalman variables, Sz and Sw are also known as Q and R respectively
They should be initialized before use, in your own code.
usage example:
#include "kalman.c"
struct KALMAN kalman_data;
kalman_data.Sz = 0.005f;
kalman_data.Sw = 5.0f;
while(1){
stepKalman(&kalman_data, (float)some_kind_of_measurement);
printf("output: %f\n", kalman_data.x);
}
-----------------------------------------------------------------------------*/
#define KALMAN_TYPE float
struct KALMAN{
KALMAN_TYPE x;
KALMAN_TYPE x_last;
KALMAN_TYPE P;
KALMAN_TYPE P_last;
KALMAN_TYPE Sz;
KALMAN_TYPE Sw;
};
//
void stepKalman(struct KALMAN *kal, KALMAN_TYPE measurement){
KALMAN_TYPE P_temp, K, x_temp;
//predict
x_temp = kal->x_last;
P_temp = kal->P_last + kal->Sw; //Q
//update
K = (1/(P_temp + kal->Sz)) * P_temp; //R
kal->x = x_temp + K * (measurement - x_temp);
kal->P = (1 - K) * P_temp;
//save previous states
kal->x_last = kal->x;
kal->P_last = kal->P;
}
</pre>

==External Links==
*[http://greg.czerniak.info/node/5  Greg Czerniak]
*[https://secure.wikimedia.org/wikipedia/en/wiki/Kalman_filter wikipedia]
*[http://www.innovatia.com/software/papers/kalman.htm Kalman Filtering ]
*[http://mbed.org/users/madcowswe/libraries/Kalman/m76byd mbed library Oskar Weigl ]
*[http://mbed.org/users/narshu/libraries/Kalman/m93uhf mbed library Shuto Naruse  ]
*[http://kalman.sourceforge.net/ c++ library]
**[http://mbed.org/forum/mbed/topic/787/?page=1#comment-3862 in mbed forum]
*[http://stackoverflow.com/questions/5478881/kalman-filtering-for-programmers kalman-filtering-for-programmers at stackoverflow]
**[http://bilgin.esme.org/BitsBytes/KalmanFilterforDummies.aspx Kalman Filter For Dummies] 
*[http://www.dzone.com/snippets/simple-kalman-filter-c Simple Kalman Filter In C]
*[http://www.udacity-forums.com/cs373/questions/14592/kalman-filter-in-c-for-arduino-available Kalman filter in C++ for Arduino available]
**[http://urbanchallenge.svn.sourceforge.net/viewvc/urbanchallenge/Elcano/KalmanFilter.cpp?revision=72&view=markup  SourceForge.net > Find Software > urbanchallenge > SCM Repositories > urbanchallenge > Elcano > KalmanFilter.cpp ]
*[http://www.its.washington.edu/software/kalman_fil.html Kalman Filter Speed Estimation from Single Loop Data]
----
*Simplified kalman finally to low pass filter, but still usefull
**Read the comments
*[http://interactive-matter.eu/blog/2009/12/18/filtering-sensor-data-with-a-kalman-filter/ Filtering Sensor Data with a Kalman Filter...Implementing this filter in C code (e.g. for an Arduino) is quite simple. ]
**[http://interactive-matter.org/wp-content/uploads/2009/12/BMP085.pde_.zip script for the graphics ... for general use...]
**[https://github.com/interactive-matter/Processing/tree/master/lis302dl_kalman/ arduino .pde at github]

*[http://didikot.com/?p=345 Yet another Kalman filter implementation for Arduino]
**Checkout my implementation of Kalman filter. Original algorithm found here and wrapped into C++ class.
*[http://frcsparkteam.wordpress.com/2011/11/08/low-pass-filter-kalman/ Low Pass Filter – Kalman – PID]
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