Fano-Based Information Theoretic Method for Nonlinear System Optimization
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Solution Overview
Problem
Existing information systems theories struggle to effectively characterize information flow and loss in nonlinear systems under uncertainty, particularly in RF sensing systems, where uncertainty sources complicate the design and optimization of waveforms and radar systems.
Innovation Solution
The method combines Fano's equality with the Data Processing Inequality in a Markovian channel construct to characterize information flow and loss in nonlinear systems. It determines discrete decision states, models system uncertainty parameters, calculates entropy and mutual information, and correlates these to component-level information loss and probability of error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If Fano's equality and Data Processing Inequality are combined in a Markovian channel construct to characterize information flow in nonlinear systems, then the ability to characterize component-level uncertainty and information loss is improved, but the complexity of the analysis framework increases
Solution Approach 1:
The patent segments the information flow analysis into discrete components by applying Fano's equality to individual channels within the Markovian construct. This allows component-level uncertainty and information loss to be characterized separately, then aggregated to understand overall system behavior, making the complex nonlinear system analysis manageable through systematic decomposition
Solution Approach 2:
The Markovian channel construct serves as an intermediary framework that bridges the gap between theoretical information theory and practical nonlinear system analysis. By introducing this structured intermediate model, the patent enables the application of Fano's equality and Data Processing Inequality to complex systems while maintaining analytical tractability
2Adaptability or versatility
If the system operates in high dimensional nonlinear spaces inherent in signature sensor systems, then the capability to process complex target signatures is improved, but the difficulty of characterizing information flow increases
Solution Approach 1:
The patent replaces traditional geometric or algebraic approaches to analyzing high-dimensional nonlinear spaces with information-theoretic methods. By substituting mechanical/mathematical system analysis with information flow characterization using entropy and mutual information, the patent simplifies the detection and measurement of information properties in complex signature sensor systems
3Reliability
If component design trades are performed to minimize overall information loss, then the system performance is improved, but the computational cost and time for optimization increases
Solution Approach 1:
The patent performs preliminary characterization of information flow and uncertainty at the component level using Fano's equality before conducting full system optimization. By pre-calculating channel-specific information loss metrics and uncertainty parameters, the patent reduces the computational burden of subsequent optimization iterations, enabling faster convergence to optimal component design trades
Data Source
AI summary
Methods are provided for identifying and quantifying information loss in a system due to uncertainty and analyzing the impact on the reliability of system performance. Models and methods join Fano's equality with the Data Processing Inequality in a Markovian channel construct in order to characterize information flow within a multi-component nonlinear system and allow the determination of risk and characterization of system performance upper bounds based on the information loss attributed to each component. The present disclosure additionally includes methods for estimating the sampling requirements and for relating sampling uncertainty to sensing uncertainty. The present disclosure further includes methods for determining the optimal design of components of a nonlinear system in order to minimize information loss, while maximizing information flow and mutual information.