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kalman Filter Demo

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Published on Feb 4, 2012

Kalman Filter Demo:

x(k) = Ax(k -- 1) + Bu(k) + w(k -- 1),
z(k) = Hx(k) + v(k),

A(k) is the state transition model which is applied to the previous state x(k−1);
B(k) is the control-input model which is applied to the control vector u(k);

w(k) and v(k) represent the process and measurement noise respectively.
p (w) ∼ N (0, Q ) where Q = process noise covariance
p (v) ∼ N (0, R ) where R = measurement noise covariance


In this example: // A matrix data // A is transition matrix. It relates how the states interact // For single input fixed velocity the new value // depends on the previous value and velocity- hence 1 0 1 0 // on top line. New velocity is independent of previous // value, and only depends on previous velocity- hence 0 1 0 1 on second row const float A[] = { 1, 0, 1, 0, //x + dx 0, 1, 0, 1, //y + dy 0, 0, 1, 0, //dx = dx 0, 0, 0, 1, //dy = dy };

The blue indicator represents state data and green indicator represents measurement data for prediction. Gaussian noise is the noise model.

Note: This video is for educational and demonstration purpose only. No copyright intended. Meta-algorithms applied or developed through code are a part of my research and are my original.

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