The LKF can be applied to a single DIFAR buoy using its bearing observations to estimate a state vector that includes bearing and bearing rate. That is, let the state vector be defined as
where the bearing θn is the angle between the y-axis, which points to true North, and the line drawn from an origin at the buoy to the target ship, with the convention that −180 deg <θ ≤ 180 deg. is the bearing rate of change. For this simple problem, the control variable un is not needed so the dynamic transition equation is given by
and vn−1 a zero-mean Gaussian random dynamic acceleration noise process defined by , where
The Q used here is the dynamic noise covariance of a continuous noise process with q, the variance of the bearing acceleration noise, set at 0.1 for this example. A complete derivation of ...