Lockheed Missiles and Space Company

Abstract: By replacing the sigmoid activation function often used in neural networks with an exponential function, a probabilistic neural network (PNN) that can compute nonlinear decision boundaries which approach the Bayes optimal is formed. Alternate activation functions having similar properties are also discussed. A fourlayer neural network of the type proposed can map any input pattern to any number of classifications. The decision boundaries can be modified in real-time using new data as they become available, and can be implemented using artificial hardware “neurons” that operate entirely in parallel. Provision is also made for estimating the probability and reliability of a classification as well as making the decision. The technique offers a tremendous speed advantage for problems in which the incremental adaptation time of back propagation is a significant fraction of the total computation time. For one application, the PNN paradigm was 200,000 times faster than back-propagation.

Abstract: This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the problems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is included to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.

Abstract: The primary problem dealt with in this paper is the following. Given some description of a visual object, find that object in an actual photograph. Part of the solution to this problem is the specification of a descriptive scheme, and a metric on which to base the decision of "goodness" of matching or detection.

Abstract: The behavior of a cantilever beam built into a rigid body that is performing a specified motion of rotation and translation is studied with two objectives in mind. First, because the subject is of interest in connection with spacecraft antennae, helicopter rotor blades, robot arms, and other systems that perform complex motions, we create an algorithm that can be used to predict the behavior of the beam when the base undergoes general three-dimensional motions. Effects such as centrifugal stiffening and vibrations induced by Coriolis forces are accommodated automatically, rather than with the aid of ad hoc provisions. The second objective is to draw attention to fundamental flaws in certain multibody computer programs currently under development or already in use. To this end, we construct a second simulation algorithm, one that embodies the procedure apparently employed in the programs in question, and then compare simulation results produced by computer programs based on the two algorithms. Conflicts between the two approaches that thus come to light are discussed in detail.