For navigation problems based on Flat Earth equations with inertial sensor biases, the system’s equivariance principle on the semi-direct tangent group ( \(\textbf{SE}_2(3)\ltimes \mathfrak {se}_2(3)\) ) enables the design of filters that improves estimation error and covariance compared to the widely known extended Kalman filter (EKF) and imperfect-invariant-extended Kalman filter (IEKF). We derived the equivariance principle for comprehensive navigation on a rotating, round Earth by choosing appropriate reference frames and filter architecture to preserve natural symmetries in the system equations. For the filter design, we chose a right-equivariance structure with a left error (in the local reference frame) of the estimation state and compared it to the usual academic choice of right error (in the global reference frame). This approach aims to take advantage of inertial sensor outputs during filter propagation and avoid making the observation matrix dependent on attitude error. In the end, we compare the performances of bias estimation, covariance dynamics, and estimated error accuracy of our left-equivariant filter (L-EqF) filter against both EKF and IEKF in a simulation representative of a scenario without global navigation satellite system (GNSS) receiver and a case of fast alignment.