Table 1. List of motion variables and mathematical notations.

	Motion variables
$\Omega$	Head rotation velocity (in space)
G	Head Tilt
$A$	Linear Acceleration
$C$	Canals dynamics
${\Omega }_{TS}$	Trunk in space rotation velocity (variant of the model)
${\displaystyle {\mathrm{\Omega }}_{HT}}$	Head on trunk rotation velocity (variant of the model)
$N$	Neck position (variant of the model)
$X$	Matrix containing all motion variables in a model
	Sensory variables
$V$	Semicircular canal signal
$F$	Otolith signal
$P$	Neck proprioceptive signal
$Vis$	Visual rotation signal
$S$	Matrix containing all sensory variables in a model
	Accent and superscripts (motion variables)
$X$	Real value of a variable
${\displaystyle \hat{X}}$	Final estimate
${\displaystyle {\hat{X}}^p}$	Predicted (or preliminary) estimate
$X^u$	Motor command affecting the variable
$X^{\epsilon }$	Perturbation or motor error affecting the variable (standard deviation ${\sigma }_X$)
${\sigma }_X$	Standard deviation of $X^{\epsilon }$
$X^k$	Kalman feedback on the variable
	Accent and superscripts (sensory variables)
$S$	Real value of a variable
${\displaystyle {\hat{S}}^p}$	Predicted value
$S^{\eta }$	Sensory noise
${\sigma }_S$	Standard deviation of $S^{\eta }$
$\delta S$	Sensory error
$k_{\delta S}^X$	Kalman gain of the feedback from S to a motion variable X
	Other
$\delta t$	Time step used in the simulations
$M^{\text{'}}$	Transposed of a matrix M
${\displaystyle {\tau }_c}$	Time constant of the semicircular canals