Alpha Beta Filter - Relationship To Kalman Filters

Relationship To Kalman Filters

A Kalman filter estimates the values of state variables and corrects them in a manner similar to an alpha beta filter or a state observer. However, a Kalman filter does this in a much more formal and rigorous manner. The principal differences between Kalman filters and alpha beta filters are the following.

• Like state observers, Kalman filters use a detailed dynamic system model that is not restricted to two states.

• Like state observers, Kalman filters in general use multiple observed variables to correct state variable estimates, and these do not have to be direct measurements of individual system states.

• A Kalman filter uses covariance noise models for states and observations. Using these, a time-dependent estimate of state covariance is updated automatically, and from this the Kalman gain matrix terms are calculated. Alpha beta filter gains are manually selected and static.

• For certain classes of problems, a Kalman filter is Wiener optimal, while alpha beta filtering is in general suboptimal.

A Kalman filter designed to track a moving object using a constant-velocity target dynamics (process) model (i.e., constant velocity between measurement updates) with process noise covariance and measurement covariance held constant will converge to the same structure as an alpha-beta filter. However, a Kalman filter's gain is computed recursively at each time step using the assumed process and measurement error statistics, whereas the alpha-beta's gain is computed ad hoc.