Satellite Positioning Accuracy with Age-of-Data Error Modeling
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Solution Overview
Problem
Satellite positioning systems face challenges in maintaining accurate positioning and timing information over extended periods without frequent updates due to the quadratic growth of errors in Extended Kalman Filters, especially in adverse environments where ground assets are compromised.
Innovation Solution
Employing a dimension-limited Koopman processing technique combined with dynamic mode decomposition to separate deterministic components from chaotic residues, using a constrained Koopman operator to manage dimensionality and integrate with an adaptive filter for precise satellite positioning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Extended Kalman Filter is used to process measurement data, then positioning accuracy is improved locally, but error grows quadratically over time globally
Solution Approach 1:
The patent transforms the state representation by adding a new dimension for the derivative of position with respect to age of data. This creates an augmented state vector that includes both position and its rate of change, allowing the filter to model quadratic error growth explicitly rather than assuming constant velocity. The dimensionality change enables the system to capture global error behavior while maintaining local accuracy.
Solution Approach 2:
The patent modifies the state vector parameters to include not only position but also the derivative of position with respect to age of data. This parameter transformation allows the Extended Kalman Filter to account for time-varying error characteristics, changing the model from one assuming constant motion to one that explicitly models accelerating error growth over time.
2Reliability
If measurement data is not updated frequently, then ground asset vulnerability is reduced, but positioning error increases quadratically
Solution Approach 1:
The patent prepares for potential communication disruptions by pre-augmenting the state vector to include derivative information. This preliminary action ensures that when updates are infrequent or unavailable, the system already has the mathematical structures needed to model and compensate for quadratic error growth, rather than needing to react to the problem as it occurs.
Solution Approach 2:
The patent makes the error model dynamic by incorporating the derivative of position with respect to age of data into the state vector. This allows the system to adapt to varying update frequencies and model the evolving error characteristics as age of data increases, transitioning from a static constant-velocity model to a dynamic accelerating-error model.
Data Source
AI summary
Embodiments regard improved satellite position determination with age of measurement data. A method includes receiving measurement data from a satellite, in a first iteration, increasing a dimensionality of the measurement data to a specified number of dimensions resulting in N-dimensional input data, performing dynamic mode decomposition on the N-dimensional measurement data resulting in a Koopman operator and modes of the N-dimensional measurement data, adaptive filtering a time domain residue resulting in a filtered residue, and updating, based on the filtered residue and a time domain deterministic component of the N-dimensional measurement data, a state vector of an object associated with the satellite measurement data.