We address the analysis of a nonlinear navigation filter used in Magneto-Inertial Dead- Reckoning (MIDR) whose input data are provided by a home-made device. This filter takes the measurements given by the magnetic sensors as inputs and returns the velocity of the body. Therefore, any unmodeled time-varying disturbance in the measurements impacts the estimation of the velocity and yields errors that distort the estimation. For dimensioning purpose, we aim to identify the bandwidth of the linearized part of this filter. To derive a model of this bandwidth, we first simplify our filter as a time-invariant Single-Input Single-Ouput (SISO) system in the situation where the steady-state regime is reached. The Best Linear Approximation (BLA) of this nonlinear system can hence be described by a conventional transfer function. We justify the validity of such a linear approximation for Extended Kalman Filters (EKF) and identify it with different methods, yielding a model for the bandwidth depending on the experimental conditions of navigation. We show that our filter is actually suitable for pedestrian navigation. Finally, simulations in realistic physical situations are used for validation.