Alignment of a flight vehicle based on recursive matrix inversion

A method for recursively determining alignment of a reentry body of a flight vehicle during flight, the method comprising:

• generating flight dynamics or trajectory data in a reference coordinate frame based on data from a reference inertial measurement unit (IMU) of the flight vehicle;
• generating flight dynamics or trajectory data in a second coordinate frame based on data from a second IMU located on the reentry body;
• wherein the flight dynamics or trajectory data in the reference coordinate frame and in the second coordinate frame is generated at a plurality of points in time during the flight;
• and
• at each point in time,
• constructing a first matrix based on the flight dynamics or trajectory data in the reference coordinate frame at that time;
• constructing a second matrix based on the flight dynamics or trajectory data in the second coordinate frame at that time;
• modifying a first accumulation matrix based on the first matrix and the second matrix using a weight based on the sine of the angular separation between the pseudo position and velocity;
• modifying a second accumulation matrix based on the second matrix using a weight based on the sine of the angular separation between the pseudo position and velocity;
• inverting the first accumulation matrix;
• and
• determining a direction cosine matrix defining the orientation of the reference coordinate frame with respect to the second coordinate frame based on the inverted first accumulation matrix and the second accumulation matrix.

A method for recursively determining alignment of a flight vehicle during flight, the method comprising:

• generating data in a reference coordinate frame and in a second coordinate frame at a plurality of points in time during the flight;
• recursively generating first and second matrices from the data in the reference coordinate frame and the second coordinate frame;
• and
• at each point in time, determining an alignment output based on the inverted first matrix and the second matrix.

A system for controlling alignment during a flight, comprising:

• a first flight vehicle having a reference inertial measurement unit with a reference coordinate frame;
• a second flight vehicle having a second inertial measurement unit with a second coordinate frame;
• an alignment processor, coupled to the reference IMU and the second IMU, the alignment processor adapted to receive data in the reference coordinate frame and in the second coordinate frame at a plurality of points in time from the reference IMU and the second IMU during the flight, recursively generate first and second matrices from the data in the reference coordinate frame and the second coordinate frame, and at each point in time, determine an alignment output based on the inverted first matrix and the second matrix;
• and
• a navigation computer, coupled to the processor, that is adapted to receive the alignment output to control the trajectory of the second flight vehicle.

A machine readable medium having instructions for performing a method for recursively determining alignment of a flight vehicle during flight, the method comprising:

• generating two flight dynamics or trajectory data in a reference coordinate frame and in a second coordinate frame at a plurality of points in time during the flight;
• and
• at each point in time,
• constructing a first matrix based on the two flight dynamics or trajectory data in the reference coordinate frame at that time;
• constructing a second matrix based on the two flight dynamics or trajectory data in the second coordinate frame at that time;
• modifying a first accumulation matrix based on the first matrix and the second matrix;
• modifying a second accumulation matrix based on the second matrix;
• inverting the first accumulation matrix;
• and
• determining an alignment output based on the inverted first accumulation matrix and the second accumulation matrix.

A machine readable medium having instructions for performing a method for recursively determining alignment of a reentry body of a flight vehicle during flight, the method comprising:

• generating flight dynamics or trajectory data in a reference coordinate frame based on data from a reference inertial measurement unit (IMU) of the flight vehicle;
• generating flight dynamics or trajectory data in a second coordinate frame based on data from a second IMU located on the reentry body;
• wherein the flight dynamics or trajectory data in the reference coordinate frame and in the second coordinate frame is generated at a plurality of points in time during the flight;
• and
• at each point in time,
• constructing a first matrix based on the flight dynamics or trajectory data in the reference coordinate frame at that time;
• constructing a second matrix based on the flight dynamics or trajectory data in the second coordinate frame at that time;
• modifying a first accumulation matrix based on the first matrix and the second matrix using a weight based on the sine of the angular separation between the pseudo position and velocity;
• modifying a second accumulation matrix based on the second matrix using a weight based on the sine of the angular separation between the pseudo position and velocity;
• inverting the first accumulation matrix;
• and
• determining a direction cosine matrix defining the orientation of the reference coordinate frame with respect to the second coordinate frame based on the inverted first accumulation matrix and the second accumulation matrix.

A machine readable medium having instructions for performing a method for recursively determining alignment of a flight vehicle during flight, the method comprising:

• generating data in a reference coordinate frame and in a second coordinate frame at a plurality of points in time during the flight;
• recursively generating first and second matrices from the data in the reference coordinate frame and the second coordinate frame;
• and
• at each point in time, determining an alignment output based on the inverted first matrix and the second matrix.