A method of mitigating filter inconsistency in a heading estimate from a navigation filter designed to estimate a joint probability density function (PDF) of a position, a velocity, an attitude, and a heading of a strapdown inertial navigation system that uses at least one inertial measurement unit (IMU), the method comprising:
- estimating an initial-heading error using a first filter error state;
- and
- estimating an accumulated heading-change error using a second filter error state;
- wherein the first error state is an independent and distinct error state from the second filter error state.