Increasing Time Resolution of State Estimation Using Kalman Filtering
Abstract
The problems of state estimation using the Kalman filtering in the presence of a sensor with a less time resolution of measurements compared to required one are considered. Two ways of solving the problem are highlighted: the output sampling rate lifting using a single sensor and introducing into the system a second one that satisfies the requirement for time resolution of the output data, but is not accurate enough, followed by a fusion of these readings. The analysis of known methods for the state estimates lifting using a single sensor is completed, some modifications are proposed. Using these results, some versions of fusion algorithms based on the known ones developed for combining measurements with the same sampling rates and adapted to considered problem, including measurement fusion before Kalman filter, state vector fusion and its succeeding modifications, are proposed. Well-known published fusion algorithms originally designed for multi-rate sensor fusion are also presented. A comparison of the results of all the algorithms is performed by state estimation using the measurements with various noise and various ratios of the intervals between samples, response to changing the band-pass properties of filter loop is studied. Some advances to choose the optimal method for a special set of values are proposed. A comparison with single sensor technique is completed by evaluation the estimation error, conclusion remarks on advisability of using each of two described techniques are given.
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