Systems and methods for a hybrid transition matrix

A method for navigating a vehicle, the method comprising:

• executing a filter algorithm having a state transition matrix that calculates an update to a state vector based on a state vector for a previous instance in time;
• receiving inertial measurement data from at least one inertial sensor;
• receiving data from at least one navigation aid;
• monitoring for the existence of one or more conditions based on a known error characteristic of the at least one inertial sensor or the at least one navigation aid;
• when the one or more conditions exist, calculating at least one element of the one or more elements of the state transition matrix based on the data from the at least one navigation aid;
• and
• when the one or more conditions do not exist, calculating the one or more elements of the state transition matrix based on the inertial measurement data.

A computer readable medium having computer-executable instructions for performing a navigation method using a filter algorithm having a state transition matrix, method comprising:

• calculating an update to a state vector based on a product of a state vector for a previous instance in time multiplied by the state transition matrix;
• receiving inertial measurement data from at least one inertial sensor;
• receiving data from at least one navigation aid;
• and
• selectively calculating one or more elements of the state transition matrix using one of the inertial measurement data or the data from the at least one navigation aid based on a known error characteristic of the at least one inertial sensor or the at least one navigation aid.