Tracking Accuracy Evaluation Using Covariance Matrices
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Solution Overview
Problem
Conventional positioning and tracking devices face challenges when the number of receiving stations is insufficient to estimate the target position, leading to inability to calculate three-dimensional positions and evaluation indices for positioning accuracy, especially due to issues like blocking by obstacles or poor station placement.
Innovation Solution
A positioning and tracking device that includes an observed value acquiring unit, a Jacobian matrix calculator, a positioning accuracy evaluation index calculator, a tracking error covariance matrix calculator, and a tracking accuracy evaluation index calculator, which use nominal observation error parameters to calculate and present evaluation indices for tracking accuracy even in situations where positioning accuracy indices cannot be calculated.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the number of receiving stations is reduced below the minimum required for position estimation, then the device complexity is reduced, but the positioning accuracy and ability to calculate evaluation indices deteriorates
Solution Approach 1:
The patent changes the parameter from instantaneous positioning evaluation to temporal tracking evaluation. By calculating tracking error covariance matrices over multiple observation points in time sequence, the system can provide accuracy evaluation even when individual positioning measurements are unavailable due to insufficient receiving stations.
Solution Approach 2:
The system pre-calculates and stores tracking error covariance matrices at multiple observation points before final evaluation. This preliminary computation allows the system to quickly determine tracking accuracy without requiring complete positioning data at each moment, resolving the contradiction between fewer stations and accuracy evaluation.
2Object-affected harmful factors
If obstacles block the signal between receiving stations and target, then the reliability of position measurement deteriorates, but the device structure remains simple
Solution Approach 1:
The patent maintains continuous tracking evaluation by utilizing data from multiple observation points in time sequence. Even when signals are blocked at certain moments, the continuous accumulation of tracking error covariance matrices from other observation points ensures uninterrupted accuracy evaluation.
Solution Approach 2:
The system prepares tracking error covariance matrices from multiple prior observation points as a buffer. When signal blocking occurs at any observation point, these pre-computed matrices serve as cushioning data that maintains the reliability of tracking accuracy evaluation despite temporary measurement failures.
3Device complexity
If the minimum number of receiving stations is not met, then the device configuration is simplified, but the ability to calculate three-dimensional position and positioning accuracy indices is lost
Solution Approach 1:
The patent transitions from three-dimensional spatial positioning evaluation to four-dimensional tracking evaluation by adding the time dimension. By observing and evaluating tracking accuracy across multiple observation points in time, the system compensates for insufficient spatial station configuration.
Solution Approach 2:
The system changes the evaluation parameter from instantaneous positioning accuracy (requiring minimum station numbers) to temporal tracking accuracy (robust to station number variations). This parameter transformation enables accuracy evaluation with fewer stations by leveraging temporal correlations in target motion.
Data Source
AI summary
A tracking error covariance matrix updating unit 6 that updates a tracking error covariance matrix Pk (−) before update at a sampling time k by using a nominal distance difference error parameter σΔrnom and that outputs the tracking error covariance matrix Pk (+) after update is disposed, and a TrackDOP calculating unit 7 calculates an evaluation index TrackDOP for tracking accuracy for a target by using both the tracking error covariance matrix Pk (+) after update, and the nominal observation error parameter σΔrnom.