Performance of Predictors with Non-Gaussian Inputs

The trajectory of a maneuvering aircraft can be described by piecewise-constant-coefficient second-order polynomials which constitute a non-Gaussian process at the input of a linear fire control predictor. Consequently, the ?on- target? probability which is determined by the predictor output cannot be analytically evaluated. Using this a priori assumption for this type of target trajectory, the structure of a finite-time polynomial filter is determined. By using the ?go-no-go? characteristic of the loss function, the smoothing time of the predictor can be optimized to yield the highest possible ?on-target? probability. The results obtained constitute lower bounds whose validity is verified by digital simulation of the system. This shows that, on the average, they are 15 percent below the exact values. The simulation program is also used in a comparative study, with a conventional predictor and a Wiener-type predictor. The results demonstrate that the finite time polynomial predictor is markedly superior to both systems for a wide range of parameters and their combinations.     

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

On-Line Vehicle Motion Estimation from Visual Terrain Information Part I: Recursive Image Registration

This paper addresses estimation of motion from the optical flow observed by an airborne down looking electro-optical sensor. The paper is in two parts. Part I addresses the development and analysis of a velocity-to-height ratio estimation algorithm and its principal error characteristics. In part II, it is shown how the information provided by the motion estimator can be integrated with additional on-board sensors to provide a complete autonomous navigation system. Part I as presented here is a summary version of the full length paper.? The algorithm implements recursive registration of successive images by using the gradient of a similarity function between them to control the tracking of their relative shift. The shift estimate provides velocity/height information. Substantial saving in memory and computation as compared to conventional full frame registration is achieved by using only a single line in the TV frame. Stochastic mathematical models for the image, terrain and vehicle velocity perturbations are used in the analysis. The choice of the most appropriate similarity function in the registration algorithm is addressed. Performance analysis indicates very small error variances, as illustrated by numerical examples.