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. 2019 Feb 25;19(4):979. doi: 10.3390/s19040979
A, A11, A12, A21, A22, BT, BD state-space model matrices of active defense
Ai, bi, Ci, di state-space model matrices of aircraft’s internal dynamics
aM, aT, aD acceleration of attacking missile, target, and defender
aMN, aTN, aDN acceleration component of attacking missile, target, and defender along the Y-axis
k1, k2, kM, kT, kuT guidance parameters of the attacking missile
NPN, NAPN, NOGL navigation gains of PN, APN, and OGL
nM, nT, nD dimension of the internal state vector of the attacking missile, target, and defender
qM, qT, qD internal state vector of the attacking missile, target, and defender
Rk measurement noise covariance matrix at time instant k
tfMD, tfMT, tgoMT D–M and M–T interception time, time-to-go of M–T engagement
uM, uT, uD guidance command of the attacking missile, target, and defender
uMN, uTN, uDN guidance command of the attacking missile, target, and defender along the Y-axis
uTNA, uDNA adaptive guidance laws of the target and defender
X, XM state vector of active defense kinematic model and state vector of the attacking missile
X^j jth model-conditioned state estimate of active defense
X^M(k|k), P(k|k) state estimate and error covariance of attacking missile
X^Mj(k|k), Pj(k|k) jth model-conditioned state estimate and error covariance of the attacking missile
yMD, yMT, y˙MD, y˙MT D–M and M–T relative displacements and relative velocity along the Y-axis
ZMD, ZMT D–M and M–T zero-effort miss distances
z(k), zMD(k), zMT(k) measurement vector, D–M and M–T angle measurement at time instant k
z˜j(k|k), Pzzj(k|k1) jth model-conditioned innovation and innovation covariance at time instant k
α, β penalty weights in the cost function
γM, γT, γD flight-path angle of the attacking missile, target, and defender
Λj(k), μj(k) jth model-conditioned likelihood function and jth model probability
λMD, λMT D–M and M–T line-of-sight angle
ν, νMD, νMT white Gaussian noise vector, D–M and M–T angle measurement noise
ρ, Φ expected evasion miss distance, transition matrix
τM, τT, τD time constant of the attacking missile, target and defender