Kalman Navigation Updates With Quantization Error State Modeling
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Solution Overview
Problem
Navigation systems, such as GPS, face reliability and accuracy issues due to weak signal strength and interference from environmental and man-made obstructions, leading to inaccurate position updates with traditional Kalman filtering methods that accumulate error over time.
Innovation Solution
A navigation system that models quantization errors as part of the estimated state using a Kalman filter, rather than in a noise measurement matrix, to accurately estimate and update the position of a mobile object, thereby bounding the total error associated with quantized measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional Kalman filtering methods are used to update position information, then the position updates can be performed continuously, but the accumulated error grows with the number of measurements or updates
Solution Approach 1:
The patent segments the error source by distinguishing between quantization errors (bounded, systematic) and other measurement errors (unbounded, random). By separating the modeling of these error types - placing quantization errors in the state vector and other errors in the measurement noise matrix - the system can handle each type appropriately, preventing the unbounded growth of accumulated error while maintaining continuous position updates
Solution Approach 2:
The patent changes the parameter representation by modeling quantization errors as states with bounded variables rather than unbounded noise parameters. This parameter transformation allows the Kalman filter to maintain stability by recognizing that quantization errors are systematic and bounded, leading to bounded accumulated error in position estimates
2Device complexity
If quantization errors are modeled in the measurement noise matrix, then the filtering process is simpler, but the accumulated error grows unbounded with time
Solution Approach 1:
The patent segments the error modeling into two distinct parts: quantization errors are placed in the state vector (requiring augmented state modeling) while other measurement errors remain in the measurement noise matrix. This segmentation increases algorithmic complexity but ensures that quantization errors are properly bounded, making the system reliable for long-term operation
Solution Approach 2:
The patent adds a dimension to the state vector by including quantization error terms as additional state variables. This dimensional expansion transforms the filtering problem from a simple noise-modeling approach to a more comprehensive state-augmentation approach, where the extra dimensions capture the bounded nature of quantization errors
Data Source
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AI summary
A navigation apparatus determines an estimated position of an object. Navigation information that includes a sequence of quantized measurements is received. Each quantized measurement has a corresponding quantization error that is negatively correlated with the quantization error of a prior quantized measurement. The apparatus iteratively performs a navigation update operation that includes determining a state and a covariance matrix of the object for a current iteration based on a state and covariance matrix in a prior iteration. The state includes an end quantization error and a start quantization error. The covariance matrix includes end and start covariance values corresponding to the end and start quantization errors, respectively. Determining the state and the covariance matrix for the current iteration includes replacing the start quantization error with the end quantization error determined in a prior iteration, and updating the state and the covariance matrix via a Kalman filter update operation.