The following abbreviations are used in this manuscript:
ARX	Autoregressive model with exogenous input
DC	Direct current
DIN	Designation of standards; German Institute for Standardization
EKF	Extended Kalman filter
FDD	Fault detection and diagnosis
IEC	Designation of standards; International Electrotechnical Commission
ISO	Designation of standards; International Organization for Standardization
KF	Kalman filter
PMSG	Permanent magnet synchronous generator
UKF	Unscented Kalman filter
The following nomenclature is used in this manuscript:
A	Amplitude
$A_F$	Matrix of the system dynamics
$\mathbf{F}$	State-input feedback matrix
$\mathbf{f}(\mathbf{x}\left(t\right),u_1\left(t\right))$	Nonlinear state function
$u_1$, $u_2$	Electrical voltages across the primary and secondary winding, respectively
$i_1$, $i_2$	Electrical currents of the primary and secondary winding, respectively
$L_1$, $L_2$, M	Primary, secondary, and mutual inductances of transformer, respectively
${\mathcal{L}}_{\mathbf{f}}^m$	Lie derivatives
$u_{\mathrm{s}}$	White noise variable
${\mathbf{U}}_{\mathrm{d}}$	Pre-compensation matrix
${\mathbf{h}}_{\mathbf{2}}$	Scalar output measurement function
${\mathbf{H}}_{\mathbf{1}},{\mathbf{H}}_{\mathbf{2}}$	Output Jacobian measurement matrix, respectively
J	Assessment criteria
${\mathbf{J}}_k$	Jacobian matrix
K	Inductive coupling coefficient
$\mathbf{k}$	Kalman gain
$\mathbf{O}\left(\mathbf{x}\right(t\left)\right)$	Nonlinear observability matrix
$\mathbb{N}$	Natural numbers
$N_{\mathrm{d}}$	Number of possible determinants
$p,n$	Numbers of columns and rows of observability matrix, respectively
${\mathbf{P}}_k^{+},{\mathbf{P}}_k^{-}$	Posterior and a priori estimation error covariance matrix
${\mathbf{Q}}_{\mathrm{EKF}1},{\mathbf{Q}}_{\mathrm{EKF}2}$	Covariance matrices ${\mathbf{Q}}_1,{\mathbf{Q}}_2$ of process noise, respectively
$r_1,r_2$	Variance matrices of soft sensors
$R_1,R_2,R_{\mathrm{L}}$	Primary and secondary winding and electrical load resistances, respectively
$t,t_{\mathrm{start}},t_{\mathrm{stop}}$	Continuous time, start time, and stop time, respectively
$T_{\mathrm{s}}$	Sampling period
$\mathbf{x}\left(t\right)$	System state
${\widehat{\mathbf{x}}}_k^{+}$	A posteriori estimation of system state
${\widehat{\mathbf{x}}}_k^{-}$	A priori estimation of system state
$\omega$	Angular frequency
$\varphi$	Angular phase
${\varphi }_1,{\varphi }_m$	Primary stray flux and core flux of transformer, respectively
${\mathrm{\Phi }}_{\mathrm{s}}$	Phase noises