Adaptive PDF Grid Layout for Accurate Bayesian State Estimation
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Solution Overview
Problem
Bayesian estimators face limitations in accuracy due to the finite number of grid points used in discrete probability density function approximations, leading to approximation errors, despite advancements in computation.
Innovation Solution
A system that adapts grid parameters, such as distance, shape, and location, of predictive and filtered estimates using a grid adaptation system, allowing for a constant number of grid points while reducing approximation errors by shifting, inflating, or deflating the grid based on the significance of the probability density function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of grid points is increased to improve estimation accuracy, then the approximation error decreases, but the computational complexity and resource requirements increase
Solution Approach 1:
The patent implements dynamic grid adaptation where grid parameters (location, shape, distance between points) are adjusted based on the significance of the probability density function at different time steps. This allows the system to maintain high estimation accuracy by concentrating grid points in regions of high probability density while using fewer points in regions of low significance, thereby reducing computational complexity without sacrificing precision.
Solution Approach 2:
The system changes grid parameters dynamically based on the PDF significance. Specifically, the grid location, shape, and spacing are adapted according to the estimated PDF, allowing the same number of grid points to provide variable resolution where needed. This parameter adaptation resolves the contradiction by maintaining accuracy through intelligent parameter selection rather than simply increasing the number of points.
2Productivity
If the number of grid points is limited due to computational constraints, then the computational load is manageable, but approximation errors increase
Solution Approach 1:
The patent applies local quality by making different regions of the grid have different densities of points based on their significance. Grid points are concentrated in regions where the PDF has high values (high significance) and spaced more sparsely in regions of low significance. This allows the system to maintain high estimation accuracy in critical regions while using fewer overall points, thus preserving computational efficiency.
Solution Approach 2:
The grid configuration is updated dynamically at each time step based on the current PDF estimation. The grid adapts its parameters to follow the significant portions of the PDF, ensuring that computational resources are always allocated to the most important regions. This dynamic adaptation maintains accuracy despite limited grid points.
3Ease of operation
If a fixed grid is used for predictions, then the computational process is simplified, but the grid may not capture significant information in subsequent filtered estimates
Solution Approach 1:
The patent implements a dynamic grid adaptation process where the grid parameters are updated based on the significance of the PDF at each time step. This allows the grid to transition from a fixed configuration during prediction to an adapted configuration during filtering, ensuring that significant information is captured while maintaining computational simplicity through systematic adaptation rules.
Solution Approach 2:
The system uses feedback from the PDF estimation to adjust grid parameters. The significance of the PDF is computed, and this information feeds back into the grid adaptation process, which adjusts the grid location, shape, and spacing to better capture significant information in subsequent estimates. This feedback mechanism resolves the contradiction by using simple adaptation rules based on PDF significance.
Data Source
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AI summary
A system is provided. The system comprises: a processing system comprising a memory coupled to a processor; wherein the processing system is configured to be coupled to at least one sensor; wherein the memory comprises a grid adaptation system, a system model, measurement data, and an estimation system; wherein the measurement data comprises data measured by the at least one sensor; wherein the estimation system is configured to provide probability density functions (PDFs) for a predictive estimate and a filtered estimate of a state in a form of a point-mass density; and wherein the grid adaption system is configured to adapt grid parameters of a predictive estimate and a filtered estimate.