Kalman Filter Position Estimation with Time-Weighted GPS Error Handling
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Solution Overview
Problem
Current position estimation systems using Kalman filters fail to accurately estimate vehicle location due to colored errors in GPS signal observations, which are not accounted for in existing technologies.
Innovation Solution
A position estimation system that includes a GPS reception unit, an observation unit, and an estimation unit using a Kalman filter, where the estimation unit calculates prediction and estimation values for state quantities and assigns weights based on the period from the first timing to the second timing when the GPS signal is not reflected in the observation, effectively handling colored errors in GPS positioning errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If GPS signals are used for position estimation with a Kalman filter, then position estimation can be performed, but colored errors in GPS observations cause inaccurate estimation results
Solution Approach 1:
The invention changes the parameter representation by transforming colored errors into an equivalent white error model through time-weighted processing. The Kalman filter processes GPS observations with time-dependent weighting, where older observations receive reduced weights, effectively converting correlated colored errors into uncorrelated white errors that satisfy the filter's assumptions
Solution Approach 2:
The invention introduces time-weighted processing as an intermediary mechanism between the colored GPS errors and the Kalman filter. This intermediary transforms the error characteristics by applying time-dependent weights to observations, creating a modified observation sequence with white error properties that the Kalman filter can process accurately
2Device complexity
If standard Kalman filter is applied to GPS position estimation, then computational processing is simplified, but the filter assumes white errors which do not match actual GPS error characteristics
Solution Approach 1:
The invention modifies the error parameter representation by transforming colored errors into white errors through time-weighted processing. This parameter transformation maintains compatibility with the standard Kalman filter framework while accurately representing the temporal correlation structure of GPS errors, thereby improving estimation accuracy without increasing system complexity
Data Source
AI summary
A navigation system includes a GPS reception unit receiving a GPS signal, an observation unit observing observables including a GPS vehicle position based on the received GPS signal, and an estimation unit estimating state quantities concerning the present location based on the observables and on the Kalman filter, the estimation unit calculates prediction values of the state quantities and errors of the prediction values, calculates estimation values of the state quantities and errors of the estimation values, based on the prediction values, the errors of the prediction values and errors of the observables observed, and, when calculating the estimation values and the errors of the estimation values, assigns a weight based on a period from a first timing to a second timing in which the GPS signal received in the first timing is not reflected in observation of the GPS vehicle position, to an error of the GPS vehicle position.