Feed-Forward Network EKF for Efficient Nonlinear State Estimation
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Solution Overview
Problem
Existing approaches fail to perform recursive computations efficiently and exactly for nonlinear dynamical systems, particularly in scenarios where physics-based models are inadequate, using Extended Kalman Filters (EKF) with feedforward networks.
Innovation Solution
Implementing a processor-based method that uses a feed-forward network (FFN) to recursively compute partial derivatives through forward and backward passes, identifying recursive relationships and applying partial derivative functions to achieve efficient and exact computations for state and observation equations in EKF.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If physics-based models are used for nonlinear maps in EKF, then computational efficiency is improved, but model accuracy deteriorates when physics models are inadequate
Solution Approach 1:
The patent changes the functional form of the nonlinear maps from physics-based equations to neural network parameterizations. This allows the system to adapt to complex nonlinear dynamics that cannot be accurately captured by traditional physics models, thereby improving model accuracy while maintaining computational efficiency through the structured computation of partial derivatives in the neural network framework.
Solution Approach 2:
The patent substitutes traditional mechanical physics-based modeling with a data-driven neural network approach. By replacing physics equations with learned neural network representations, the system can capture complex nonlinear behaviors without being constrained by the accuracy limitations of physics models, while still enabling efficient recursive computation through the proposed partial derivative methods.
2Measurement precision
If neural networks are used to approximate nonlinear maps, then model accuracy is improved, but computational complexity increases due to derivative calculations
Solution Approach 1:
The patent segments the computation of partial derivatives into two distinct directional passes: forward pass for computing derivatives with respect to inputs, and backward pass for computing derivatives with respect to weights. This segmentation transforms the complex multi-dimensional derivative calculation into a series of simpler, structured computations that can be efficiently implemented in the neural network framework.
Solution Approach 2:
The patent employs backward recursion to compute partial derivatives, which is the reverse of the forward propagation direction. By computing derivatives in the backward direction from output to input layers, the method simplifies the computational complexity compared to direct forward differentiation, enabling efficient implementation of EKF with neural networks.
3Measurement precision
If exact recursive computations are performed in EKF, then inference accuracy is improved, but computational time increases
Solution Approach 1:
The patent performs preliminary computation of partial derivatives through structured forward and backward passes before the main EKF recursion. By pre-computing these derivatives in an organized manner, the subsequent recursive filtering steps can proceed efficiently without repeated complex calculations, thereby achieving exact inference accuracy with reduced computational time.
Solution Approach 2:
The patent maintains continuous and efficient computation of partial derivatives through the forward-backward pass framework. Rather than computing derivatives separately at each EKF step, the method establishes a continuous computational flow where derivatives are systematically propagated through the network, reducing redundant calculations and improving overall computational efficiency while maintaining exactness.
Data Source
AI summary
An Extended Kalman filter (EKF) is a general nonlinear version of the Kalman filter and an approximate inference solution which uses a linearized approximation performed dynamically at each step and followed by linear KF application. Extended Kalman Filter involves dynamic computation of the partial derivatives of the non-linear functions system maps with respect to the input or current state. Existing approaches have failed to perform recursive computations efficiently and exactly for such scenarios. Embodiments of the present disclosure efficient forward and backward recursion-based approaches wherein a forward pass is executed through a feed-forward network (FFN) to compute a value that serves as an input to jth node at a layer l from a plurality of network layers of the FFN and partial derivatives are estimated for each node associated with various network layers in the FFN. The feed-forward network is used as state and/or observation equation in the EKF.