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ZMGWZero-Mean Gaussian White Noise
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[[??].sub.CSJ] (t) denotes the covariance of the zero-mean colored Jerk noise, and w(t) denotes zero-mean Gaussian white noise. Other parameters are defined as SJ model.
where the target state [x.sub.k] = [[[x.sub.k] [[??].sub.k] [y.sub.k] [[??].sub.k]].sup.T]; [x.sub.k] and [y.sub.k] denote the positions and [[??].sub.k] and [[??].sub.k] denote the velocities in x and y directions, respectively; [x.sub.s] and [y.sub.s] denote the positions of radar installing and three radars are used as tracking sensors; [OMEGA] is a known and constant turn rate; [DELTA]t is the time interval between two consecutive measurements; the process noise [w.sub.k] and measurement noise [v.sub.m,k] are cross-correlated zero-mean Gaussian white noise with covariance [Q.sub.k] and [R.sub.m,k], and [Q.sub.k] satisfies
where [F.sub.G] and [G.sub.G] are system transition matrix and system noise distribution matrix, respectively; system noise vector [W.sub.G] = [[[[eta].sub.x] [[eta].sub.y] [[eta].sub.z]].sup.T] is a zero-mean Gaussian white noise vector with covariance [Q.sub.G] = [Q.sub.[eta]].
where measurement vector [Z.sub.G] = [DELTA][OMEGA]; measurement matrix [H.sub.G] = [[??] [??] [I.sub.3x3] [I.sub.3x3] - [I.sub.3x3]]; measurement noise [mathematical expression not reproducible] is a zero-mean Gaussian white noise sequence with covariance [R.sub.G].
where [a.sub.0] = 0.05, [a.sub.1] = 0.1, and [a.sub.2] = 0.15 and [b.sub.0] = 0.04, [b.sub.1] = 0.08, and [b.sub.2] = 0.12; [[epsilon].sub.k] is uncorrelated zero-mean Gaussian white noises with unity covariances.