Kalman Filter Double Differenced Update Processing
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Solution Overview
Problem
Current range finding systems, such as Global Navigation Satellite Systems (GNSS), face challenges in accurately processing double differenced updates in a Kalman filter, particularly in maintaining high accuracy with sequential updates and uncorrelated measurements.
Innovation Solution
The method involves calculating single differenced observables between antennas, subtracting a common bias stored as a state in the Kalman filter to generate double differenced residual values, which are then used to update position states, effectively maintaining the common error at a small value and allowing for high-accuracy tracking equivalent to a double-differenced model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If batch updates with off-diagonal covariance matrix removal are used to achieve double differenced model accuracy, then measurement precision is improved, but device complexity and processing time increase
Solution Approach 1:
The patent segments the complex batch update process into sequential single-differenced measurements that are processed individually through the Kalman filter. By dividing the problem into manageable sequential steps rather than requiring complex batch processing, the system achieves double-differenced model accuracy without the computational burden of covariance matrix manipulation.
Solution Approach 2:
The patent introduces an intermediary approach by using single-differenced measurements as intermediate steps that are sequentially processed. This intermediary method allows the system to reach the same accuracy as double-differenced models without directly implementing the complex batch update procedures, effectively using sequential processing as a mediator between simple processing and high accuracy requirements.
2Productivity
If sequential updates with uncorrelated measurements are used, then processing speed is improved, but measurement precision deteriorates
Solution Approach 1:
The patent applies dynamics by making the measurement processing adaptive and sequential rather than static and batch-based. The Kalman filter dynamically processes each single-differenced measurement as it becomes available, allowing the system to maintain high processing speed while achieving accuracy equivalent to double-differenced models through the sequential update mechanism.
Solution Approach 2:
The patent changes the parameter representation by using single-differenced observables instead of traditional double-differenced measurements. This parameter transformation allows sequential processing to achieve the same accuracy as batch processing, effectively changing the mathematical parameters to enable faster processing without precision loss.
3Measurement precision
If double differenced model is implemented to achieve high accuracy, then measurement precision is improved, but loss of time increases due to batch processing requirements
Solution Approach 1:
The patent performs preliminary action by pre-computing single-differenced measurements that can be sequentially processed. This preliminary transformation of the data into single-differenced form enables subsequent rapid sequential updates, avoiding the time-consuming batch processing that would otherwise be required to achieve double-differenced model accuracy.
Solution Approach 2:
The patent ensures continuity of useful action by implementing continuous sequential updates rather than intermittent batch processing. The Kalman filter continuously processes incoming single-differenced measurements, maintaining uninterrupted position tracking with double-differenced model accuracy, thereby eliminating the time losses associated with periodic batch processing cycles.
Data Source
AI summary
Systems and methods are provided for sequentially updating a Kalman filter in a navigation system. Respective signals from a plurality of transmitters containing range-finding data are received at a plurality of antennas. For each of the plurality of transmitters, a single differenced observable is calculated between a given pair of the plurality of antennas. A common bias, stored as a state in a Kalman filter, is subtracted from the calculated single differenced observable for each of the plurality of transmitters to provide respective double differenced residual values. A plurality of states stored in the Kalman filter are updated using the double differenced residual values.