Navigation using angle measurements

Abstract

While GPS navigation has become the standard for most operations, complete reliance on the GPS for a navigation solution can be dangerous in many applications. Spoofing of a GPS signal or suffering the loss of GPS signals due to blockage, such as from skyscrapers in major cities, can cause the system or operator to drift from the desired path. One example is with the U.S. Navy's submarine fleet entering and departing a harbor. Reliance on GPS could endanger not only the submarine in the channel but also surrounding vessels. Image navigation is one approach to use as an aide or for replacing GPS navigation. For a submarine, the imagery taken from the periscope could be used to locate landmarks and track the vehicle position. In such an approach, the video-navigation problem would then become an angle-only tracking problem. Angle-only tracking is known to be fraught with difficulties, since the unobservable space is not the null space. When using a Kalman filter estimator to perform the tracking, significant errors arise which could endanger the submarine. This work analyzes the performance of the Kalman filter when angle-only measurements are used to provide the target tracks. Estimation unobservability is considered, as is the minimal set of requirements that are needed to address it for this complex but real-world problem. Three major issues are addressed: the knowledge of navigation beacons/landmarks' locations, the minimal number of these beacons needed to maintain the course, and the update rates of the angles of the landmarks as the periscope rotates and landmarks become obscured due to blockage and weather. The goal is to address the problem of navigation to and from the docks relying solely on the image-based data, with a solution that can traverse the harbor channel while maintaining maritime rules. The minimal number of beacons will be considered. For this effort, the image correlation from frame to frame is assumed to be achieved perfectly. Variation in the update rates and the dropping of data due to rotation and obscuration is not considered. The analysis will be based on a simple straight-line channel harbor entry to the dock, similar to a submarine entering the submarine port in San Diego.