US 5,649,065 A · Optimal filtering by neural networks with range extenders and/or reducers

A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of:

(1) selecting a recurrent neural network paradigm;
(2) selecting an estimation error criterion;
(3) generating training data comprising realizations of said signal process and corresponding realizations of said measurement process;
(4) constructing a training criterion;
(5) selecting at least one range transformer;
(6) synthesizing said training data into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer;
(7) implementing said primary filter;
and
(8) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.

6 more elements

A primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.

A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of:

(1) selecting a recurrent neural network paradigm;
(2) selecting an estimation error criterion;
(3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function;
(4) constructing a training criterion;
(5) selecting at least one range transformer;
(6) synthesizing said augmented training data into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer;
(7) implementing said primary filter with augmented input terminals;
and
(8) receiving one measurement vector of said measurement process and one vector of said p-dimensional vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.

6 more elements

A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of:

(1) selecting an ancillary signal process on the basis of said estimation error statistic process;
(2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process;
(3) selecting an ancillary recurrent neural network paradigm;
(4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process;
(5) constructing an ancillary training criterion;
(6) selecting at least one ancillary range transformer;
(7) synthesizing said augmented ancillary training data into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer;
(8) implementing said ancillary filter with augmented input terminals;
and
(9) receiving one vector of said p-dimensional vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.

7 more elements

A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.

An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.

A method for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of:

(1) selecting a recurrent neural network paradigm;
(2) selecting an estimation error criterion;
(3) generating training data comprising realizations of said signal process and said measurement process;
(4) constructing a training criterion;
(5) selecting at least one range transformer;
(6) synthesizing said training data, while taking into account said interactive environment, into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer;
(7) implementing said primary filter;
and
(8) receiving one measurement vector of said measurement process and at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.

6 more elements

A primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process with respect to a selected estimation error criterion in an interactive environment composed of an environment transition system and an environment observation system, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.

A method for processing a vector-valued measurement process to estimate a vector-valued signal process, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of:

(1) selecting a recurrent neural network paradigm;
(2) selecting an estimation error criterion;
(3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function;
(4) constructing a training criterion;
(5) selecting at least one range transformer;
(6) synthesizing said augmented training data, while taking into account said interactive environment, into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer;
(7) implementing said primary filter with augmented input terminals;
and
(8) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.

6 more elements

A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of:

(1) selecting an ancillary signal process on the basis of said estimation error statistic process;
(2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process;
(3) selecting an ancillary recurrent neural network paradigm;
(4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process and corresponding realizations of said ancillary signal process;
(5) constructing an ancillary training criterion;
(6) selecting at least one ancillary range transformer;
(7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer;
(8) implementing said ancillary filter with augmented input terminals;
and
(9) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.

7 more elements

A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of:

(1) selecting an ancillary signal process on the basis of said estimation error statistic process;
(2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process;
(3) selecting an ancillary recurrent neural network paradigm;
(4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process;
(5) constructing an ancillary training criterion;
(6) selecting at least one ancillary range transformer;
(7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer;
(8) implementing said ancillary filter with augmented input terminals;
and
(9) receiving one vector of said vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.

7 more elements

A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.

An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.

Optimal filtering by neural networks with range extenders and/or reducers

Life of this patent

Optimal filtering by neural networks with range extenders and/or reducers

Life of this patent

Abstract

Claims94