Parallel Box Particle Filter Redistribution for Aircraft Navigation
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Solution Overview
Problem
Existing regularized box particle filtering methods require significant computing resources and are not efficiently implementable on field-programmable gate array (FPGA) circuits due to high computational demands, particularly in the redistribution step, which limits their application in real-time aircraft navigation.
Innovation Solution
A modified box particle filtering method that replaces the multinomial drawing method with a parallelizable redistribution step, utilizing random factor multiplication and comparison intervals to determine sub-intervals, ensuring deterministic execution time and reduced computational burden.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the multinomial drawing method is used for redistributing state intervals in particle filtering, then the method achieves accurate state estimation, but the computational resources required become excessively high and deterministic execution time cannot be guaranteed
Solution Approach 1:
The patent segments the redistribution process into deterministic sub-steps: calculating cumulative weights, generating random thresholds, and performing binary search. This segmentation transforms the originally non-parallelizable multinomial drawing into a structured process where the binary search can be efficiently implemented and parallelized across multiple state intervals, resolving the contradiction between accuracy and computation speed
Solution Approach 2:
The patent creates a sorted copy of the weight values to enable efficient binary search without modifying the original weight distribution. This copying approach allows the algorithm to maintain accurate state estimation while achieving deterministic execution time through the O(log n) binary search complexity, rather than requiring O(n) sequential processing of the original multinomial drawing method
2Measurement precision
If the regularized box particle filter is implemented with traditional methods, then accurate navigation state estimation is achieved, but the computational burden prevents efficient FPGA implementation
Solution Approach 1:
The patent introduces dynamic parallelization where the computational workload is adaptively distributed across multiple processing units based on the number of state intervals and their weights. The binary search mechanism dynamically adjusts the number of comparison operations required, enabling efficient utilization of FPGA parallel processing resources while maintaining estimation accuracy, thus reducing the overall device complexity requirement
Solution Approach 2:
The patent transforms the one-dimensional sequential multinomial drawing process into a two-dimensional parallel structure by implementing binary search across sorted weight arrays. This dimensional transformation enables simultaneous processing of multiple state intervals through parallel binary search operations, significantly reducing computational burden and enabling efficient FPGA implementation while preserving navigation state estimation accuracy
3Measurement precision
If the redistribution step is performed sequentially using traditional multinomial drawing, then accurate particle weights are obtained, but the execution time varies and real-time processing is compromised
Solution Approach 1:
The patent performs preliminary sorting of the weight values before the redistribution step, creating a sorted array that enables deterministic binary search. This preliminary action ensures that the subsequent weight assignment process follows a predictable O(log n) time complexity pattern, eliminating the execution time variability inherent in sequential multinomial drawing while maintaining particle weight accuracy through the structured search and assignment mechanism
Data Source
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AI summary
A method for box regularized particle filtering, used to predict a state of a system, is modified such that it can be implemented in a parallel manner. The modification relates to a step of redistributing state intervals and particularly determining a number of sub-intervals by which each state interval is intended to be replaced. The method is particularly suitable for being implemented in a navigation system using measurement correlation (10), for example an aircraft (20) navigation system using terrain correlation, and to be performed by a circuit with a field-programmable or fixed gate array.