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Bayesian Estimation and Tracking: A Practical Guide by Anton J. Haug

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6.4 Application of the LKF to DIFAR Buoy Bearing Estimation

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) equation

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. img 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

(6.14) equation

with

(6.15) equation

and vn−1 a zero-mean Gaussian random dynamic acceleration noise process defined by img, where

(6.16) equation

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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