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

(6.13)

where the bearing θ_{n} 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 u_{n} is not needed so the dynamic transition equation is given by

(6.14)

with

(6.15)

and v_{n−1} a zero-mean Gaussian random dynamic acceleration noise process defined by , where

(6.16)

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 ...

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