You know how fast you were going, so you can guess how far you traveled.
: Estimating a constant voltage or a single object’s position. Navigation & Tracking
% Update y = z(k) - H * x_pred; S = H * P_pred * H' + R; K = P_pred * H' / S; x_est = x_pred + K * y; P = (eye(2) - K * H) * P_pred; You know how fast you were going, so
He introduces the filter using simple scalar examples (like estimating the voltage of a battery or the temperature of a room) before scaling up to multi-dimensional positioning matrices. Focus on Tuning ( ): The book demystifies the system noise covariance ( ) and measurement noise covariance (
Choose Q and R:
: Linearizes nonlinear systems locally using partial derivatives (Jacobian matrices). It is widely used in aerospace and vehicle navigation.
. This matrix determines how much weight to give the measurement compared to the prediction: If the sensor is very accurate, Kkcap K sub k is high (trust the measurement). If the model is very accurate, Kkcap K sub k is low (trust the prediction). MATLAB Examples: Putting Theory into Practice Focus on Tuning ( ): The book demystifies
Essential for real-world robotics because most systems are non-linear (e.g., a robot turning in a circle).
If measurement noise $R$ is high, $K$ becomes small. The filter trusts the model prediction more than the measurement. If process noise $Q$ is high (making $P$ large), $K$ becomes large, and the filter trusts the measurement more. This matrix determines how much weight to give
x_hist = zeros(1,N); for k=1:N % Predict x_pred = x_est; P_pred = P + Q;