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I am implementing a particle filter using MATLAB. I am implementing it first time. I have written the system model and measurement model. Given below:

%% SYSTEM MODEL
noise1 = sd*randn(1, 1); v_init(i)= (normrnd(mean,sigma));
x_init(i)=(x_init(i-1)*noise1+v_init(i-1)); %p(x_k | x_(k-1))
%% MEASUREMENT MODEL
noise2 = var(wgn(10,1,1)); n_init(i) = (normrnd(mean,sigma));
y_init(i) = noise2*x_init(i)+ n_init(i);    %p(y_k | x_k)

As far as I know, the prediction step involves the following equation:

$$ p\left ( x_{k} \right|D_{k-1} ) = \int p\left ( x_{k} \right | x_{k-1} )p\left (x_{k-1} \right|D_{k-1} ) dx_{k-1} $$

I cannot understand, how do I implement it. Kindly guide me what should be my next step?

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The prediction step is to pass every particle's state [for e.g (x,y, theta)] through the system model that you have written as p(xk|xk-1). You have to update the state for each particle using this model. This comprises of the prediction step in the particle filter.

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  • $\begingroup$ I have taken particle's state as feature extracted from the moving image as dot. And write the prediction step in this form: x_predict(i) = x_init(i-1)+dot(i-1)+sin(x_init(i-1)-2); So, is it the correct way to write? $\endgroup$
    – TariqS
    Apr 8, 2020 at 8:02
  • $\begingroup$ I did not understand the use of sin ? $\endgroup$
    – vanshil shah
    Apr 9, 2020 at 9:18
  • $\begingroup$ purpose of sin is just to add some noise only $\endgroup$
    – TariqS
    Apr 10, 2020 at 6:50

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