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\begin{array}{c|c|l}
\text{LaTex Syntax} & \text{MATLAB Variable Syntax} & \text{Description} \
\hline
\bar{q} & q_bar & \text{Regular 4-Dimensional quaternion} \
\hat{x}{k+1,k} & x_hat_1 & \text{Estimate of the state x at time k+1} \
\hat{x}{k, k} & x_hat_k & \text{Estimate of the state x at time k} \
\hat{b}{k+1, k} & b_hat_1 & \text{Estimate of the gyroscope bias at time k+1} \
\hat{b}{k, k} & b_hat_k & \text{Estimate of the gyroscope bias at time k} \
\hat{\bar{q}}{k+1, k} & q_bar_hat_1 & \text{Estimate of the quaternion at time k+1} \
\hat{\omega}{k+1, k} & omega_hat_1 & \text{Estimate of the new turn rate at time k+1} \
\bar{\omega} & omega_avg & \text{Average turn rate} \
\Phi & Phi & \text{State transition matrix} \
Q_d & Q_d & \text{Discrete time noise covariance matrix} \
P_{k+1, k} & P_1 & \text{State covariance matrix at time k+1} \
H(k) & H & \text{Measurement matrix} \
r & r & \text{Residual} \
z(k+1) & z_1 & \text{Current measurement} \
S & S & \text{Covariance of the residual} \
R & R & \text{Measurement noise covariance matrix} \
K & K & \text{Kalman gain} \
\Delta \hat{x}(+) & Delta_x_hat & \text{Correction term} \
\delta \hat{q} & delta_q_hat & \text{Error quaternion. } \
\delta \bar{q} & delta_q_bar & \text{Small rotation associated with the error quaternion} \
\delta \theta{q} & delta_theta & \text{Error angle vector. 3-Dimensional} \
\tilde{x} & x_tilde & \text{Error vector