Kalman filter and UKF

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Kalman filter and UKF [Copy link]

UKF can be expressed as an uncolored or unbiased Kalman filter.

The standard Kalman filter is the best linear filter under the minimum mean square error criterion,
that is , it minimizes the mean square error between the state vector of the system and the predicted value of the state vector.
It uses the state equation and recursive method for estimation, and its solution is given in the form of estimated values. Since it
can establish a certain model for the motion of the object, it is often used in tracking. When the observation equation is not
linear, the above standard Kalman filter equation is no longer applicable, but if the state estimate is not
far from the true value, the observation equation can be locally linearized to obtain the extended Kalman filter (EKF).
Since the EKF uses the first-order approximation of the Taylor expansion, it often causes a large cumulative error in
parameter . For this reason, the Unscented Kalman Filter (UKF) no longer approximates the observation
equation. It still uses Gaussian random variables to represent the state distribution, but
describes it . Compared with the EKF, the error of the UKF only appears in the moments above the third order, and the calculation is also
simple, while the EKF is only accurate to the first order moment. In general, Kalman filtering is a linear estimator that
can effectively track the movement and shape changes of objects, but it is based on two assumptions: one is that the background is relatively
clean ; the other is that the motion parameters follow a Gaussian distribution. Therefore, its scope of application is limited, and for complex multi-peak situations,
other methods must be used.