A method of mitigating filter inconsistency of a heading estimate in an inertial navigation system, the method comprising: inputting inertial measurements from at least one inertial measurement unit, IMU, in the inertial navigation system; inputting an initial-heading from at least one heading-information source that is not the at least one IMU; inputting an initial-heading uncertainty level associated with an error in the inputted initial-heading; initializing an initial-heading estimate, Ψ̂ 0, with the inputted initial-heading; initializing an initial-heading uncertainty estimate with the inputted initial-heading uncertainty level; initializing an accumulated heading-change estimate to zero at a startup of the at least one IMU; initializing an accumulated heading-change uncertainty estimate with an initial accumulated heading-change uncertainty level that is a value less than the inputted initial-heading uncertainty level;estimating an initial-heading error using a first filter error state; periodically updating the accumulated heading-change estimate with the inertial measurements input from the at least one IMU; inputting at least one measurement from at least one relative aiding sensor which is unable to directly sense the initial-heading; updating the navigation filter with the at least one relative aiding measurement inputted from the at least one relative aiding sensor; 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; and ensuring the first error state and the second error state directly correspond to navigation quantities explicitly computed in the inertial navigation system. inputting inertial measurements from at least one inertial measurement unit, IMU, in the inertial navigation system; inputting an initial-heading from at least one heading-information source that is not the at least one IMU; inputting an initial-heading uncertainty level associated with an error in the inputted initial-heading; initializing an initial-heading estimate, Ψ̂ 0, with the inputted initial-heading; initializing an initial-heading uncertainty estimate with the inputted initial-heading uncertainty level; initializing an accumulated heading-change estimate to zero at a startup of the at least one IMU; initializing an accumulated heading-change uncertainty estimate with an initial accumulated heading-change uncertainty level that is a value less than the inputted initial-heading uncertainty level;estimating an initial-heading error using a first filter error state; periodically updating the accumulated heading-change estimate with the inertial measurements input from the at least one IMU; inputting at least one measurement from at least one relative aiding sensor which is unable to directly sense the initial-heading; updating the navigation filter with the at least one relative aiding measurement inputted from the at least one relative aiding sensor; 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; and ensuring the first error state and the second error state directly correspond to navigation quantities explicitly computed in the inertial navigation system.