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Nonlinear Filtering and Array Computation

IP.com Disclosure Number: IPCOM000131628D
Original Publication Date: 1983-Jun-01
Included in the Prior Art Database: 2005-Nov-11
Document File: 13 page(s) / 45K

Publishing Venue

Software Patent Institute

Related People

R. S. Bucy: AUTHOR [+6]

Abstract

MIT Lincoln Laboratory

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This record contains textual material that is copyright ©; 1983 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Contact the IEEE Computer Society http://www.computer.org/ (714-821-8380) for copies of the complete work that was the source of this textual material and for all use beyond that as a record from the SPI Database.

Nonlinear Filtering and Array Computation

R. S. Bucy, University of Southern California F. Ghovanlou, University of Southern California/Oak Adec J. M. F. Moura, Instituto Superior Tecnico, Portugal K. D. Senne, MIT Lincoln Laboratory

Equations that determine the best phase demodulator for signal processing must be iterated four million times in a single application -- an ideal task for array processors.

The architecture of the array processor is well suited to signal processing problems and the numerical solution of partial differential equations. Programming within the structures imposed by AP architecture often leads to deeper insight into the problem at hand, without draining the computing budget. Moreover, even if one could afford a faster alternative -- i.e., a supercomputer -- its sheer physical size could be a drawback in real-time applications. We believe that our experience with code development on an AP has applications to a wide group of problems and is particularly useful in breaking the tendency toward sequential and serial conceptions in relation to computer algorithms.

Our application concerns developing code to build the best phase demodulator for use in areas such as deepspace and submarine communications. The current linear design, known as the phase-lock loop, is suboptimal. ~ Our approach was to synthesize a nonlinear filter, addressing three specific problems. We used the Floating Point Systems AP-120B array processor in conjunction with the DEC POP 11-55 for all implementations and found the configuration much more economical than conventional means. Before going into detail on the efficiency of this system, however, we will discuss the nature of the signal processing, or filtering, problem in terms of the filtering equations involved.

We considered the problem of estimating a random process (t), which is the phase of signal sin (wt+~(t)) observed corrupted by additive noise. Our problem consists of determining the conditional density p of the signal (t), given past and present observations. We can show that p satisfies a Fokker-Planck partial differential equation forced by the observations. ~ The FokkerPlanck operator is determined by the random process (t), which is assumed to be a Markov diffusion.

To effectively compute p, we make both time and space discrete and convert the associated partial differential equations into a pair of nonlinear equations that determine the successive conditional densities En and Pn as time varies. These equations are the generalizations of the well-known d...