Covariance matrix calculation for data accuracy

Reduces errors in navigation systems via more precise modeling of roll, pitch, and yaw angles

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Navy scientists have developed an angle correction technique applicable to radar tracking systems. The patented technology is available via license agreement to companies that would make, use, or sell it commercially.

The Navy’s covariance matrix technique reduces errors in navigational components such as roll/pitch/yaw angle measurement systems on sea, air, and space vessels. (David Mark/Pixabay)

Modern combat systems comprise an ever-increasing number and diversity of sensors. For example, inertial navigation components, such as the roll/pitch/yaw angle measurement system, play a critical role in operating a radar transceiver onboard a combat ship.

The sea represents an unstable environment which causes the vessel to rotate about at least one of the ship’s axes: longitudinal (stern-to-bow), lateral (starboard-to-port) and vertical (keel-to-deck) respectively, roll, pitch, and yaw. This motion can be quite severe under sufficiently high sea states. Radar systems on board are subject to the same rolling, pitching and yawing action.

Unfortunately, all these sensor systems report measurement data that contains errors due to the finite resolution of the measurement electronics as well as the impact of ambient temperature and humidity. These errors, referred to as noise, vary randomly from one measurement to another. and the incorrect value reported may be slightly higher (positive error), and in the next slightly lower (negative error) than the correct value.

Navy researchers have developed a technique for removing angle errors and correcting for roll, pitch, and yaw angular motion. The measurement technique includes establishing an unstabilized body reference frame and a stabilized East-North-Up reference frame. Then, an unstabilized pre-transform covariance matrix is calculated from the position variance of the body reference frame.

In addition to conventional spatial correction, the method also includes measurements of roll, pitch and yaw in the body reference frame as respective angle values, the calculation of a measured angle error sensitivity matrix from the angle values, as well as a tri-diagonal angle error component matrix with square values of angle variance in the body reference frame. The angle covariance is then incorporated into a total error covariance matrix, and a Kalman gain matrix is calculated based on the total error covariance matrix. Applying the Kalman gain matrix to a predicted state estimate for correcting the measurement vector is the final step.

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