Basic Kalman Filter_SCILAB

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Basic Kalman filter

Language: Scilab

Processor: Not Relevant

Submitted by Sylvain B on Jan 20 2011

Licensed under a Creative Commons Attribution 3.0 Unported

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DSP Code Sharing > Basic Kalman filter

Basic Kalman filter

This is the most basic implementation of a Kalman filter.

For measured position, velocity and acceleration, the Kalman filter estimates the true datas.

This example works with Scilab.

// Clear initialisation

clf()

// Time vector

t =[0:0.5:100];

len_t = length(t);

dt = 100 / len_t;

// Real values x: position v: velocity a: acceleration

x_vrai = 0 * t;

v_vrai = 0 * t;

a_vrai = 0 * t;

// Meseared values.

x_mes = 0 * t;

v_mes = 0 * t;

a_mes = 0 * t;

// Initialisation

for i = 0.02 * len_t: 0.3 * len_t,

a_vrai(i) = 1;

end

for i = 0.5 * len_t: 0.7 * len_t,

a_vrai(i) = 2;

end

// State of kalman filter

etat_vrai = [ x_vrai(1); v_vrai(1); a_vrai(1) ];

A = [ 1 dt dt*dt/2; 0 1 dt; 0 0 1];//transition matrice

for i = 2:length(t),

etat_vrai = [ x_vrai(i-1); v_vrai(i-1); a_vrai(i) ];

etat_vrai = A * etat_vrai;

x_vrai(i) = etat_vrai(1);

v_vrai(i) = etat_vrai(2);

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8/6/2013



end

max_brt_x = 200;

max_brt_v = 10;

max_brt_a = 0.3;

// Random noise

x_brt = grand(1, len_t, 'unf', -max_brt_x, max_brt_x);

v_brt = grand(1, len_t, 'unf', -max_brt_v, max_brt_v);

a_brt = grand(1, len_t, 'unf', -max_brt_a, max_brt_a);

// Compute meas

x_mes = x_vrai + x_brt;

v_mes = v_vrai + v_brt;

a_mes = a_vrai + a_brt;

// START

x_est = 0 * t;

v_est = 0 * t;

a_est = 0 * t;

etat_mes = [ 0; 0; 0 ];

etat_est = [ 0; 0; 0 ];

inn = [ 0; 0; 0 ];

// Matrix of covariance of the bruit.

// independant noise -> null except for diagonal,

// and on the diagonal == sigma^2.

// VAR(aX+b) = a^2 * VAR(X);

// VAR(X) = E[X*X] - E[X]*E[X]

R = [ max_brt_x*max_brt_x 0 0; 0 max_brt_v*max_brt_v 0; 0 0

max_brt_a*max_brt_a ];

Q = [1 0 0; 0 1 0; 0 0 1];

P = Q;

for i = 2:length(t),

// Init : measured state

etat_mes = [ x_mes(i); v_mes(i); a_mes(i) ];

// Innovation: measured state - estimated state

inn = etat_mes - etat_est;

// Covariance of the innovation

S = P + R;

// Gain

K = A * inv(S);

// Estimated state

etat_est = A * etat_est + K * inn;

// Covariance of prediction error

// C = identity

P = A * P * A' + Q - A * P * inv(S) * P * A';

// End: estimated state

x_est(i) = etat_est(1);

v_est(i) = etat_est(2);

a_est(i) = etat_est(3);

end

// Blue : real

// Gree : noised

// Red: estimated

subplot(311)


8/6/2013



Tweet 1 0 1

deepasaini wrote: 1/9/2012

Sylvain B wrote: 1/9/2012





plot(t, a_vrai, t, a_mes, t, a_est);

subplot(312)

plot(t, v_vrai, t, v_mes, t, v_est);

subplot(313)

plot(t, x_vrai, t, x_mes, t, x_est);

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Rating: 2 | Votes: 3

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posted by Sylvain B

Comments

Hi,

i have to use kalman filter for my problem and i am using above code for that but in this code real and measured value both are same

please guide me about the process which have

used in above code. i have little knowledge of scilab and basic about kalman filter. please suggest about the input constraints in above

code.

Hello,

The mesured values are computed by adding random noise to the theorical ones :

// Compute meas




(sorry for the non translated value : vrai == real )

Hello,

thanx for your support ...

But i have some query, in this code real values(x_vrai,v_vrai, a_vrai) initialized with help of for loop. but in my prob i have make it general

and to pass real values through form.

what type of problem we can solve by t his ?

Can we estimate the true values of position , velocity and acceleration of any vehicle...?

What type of modification are neccessary to make it general....??

You should fill "x_mes" with the value you got from acquisition !

Then the algo computes the x_est (estimated values !)

Then you can delete the x_vrai which are the theoritical to make this snapshot !

// Compute meas




in above line measure values obtained by adding random noise in real values.....

are you saying that pass measured noisy values(measured values which have sum noise also) through form... as input?

Like 0


8/6/2013







UNGY_STARS wrote: 1/12/2012


UNGY_STARS wrote: 1/13/2012

Yes,

replace the lines, by :

x_mes = your_values_from_acquisition

thanks a lot .....for this kind response!!

is there any particular range of time duration.........?

as used t =[0:0.5:100]; in this code .....

is there any specific limit..??

It depends on the simulation measures, and the errors at the end. If you put an infinite time, it could be that at the end the filter is totally

lost.

You can increase the time to have a longer simulation.

what type of problem can be solve by t his code..??

please give me any example..!!

This is a filte, to do estimation.

You provide "meseaured" values, and it gives you the "theoritical" ones, with less error.

thanks.....

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Basic Kalman Filter_SCILAB

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