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Stochastic properties of the H ∞ filter
In this paper, we propose adaptive algorithms of gain tuning for Kalman filters and switching Kalman and H
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub>
filters for discrete systems. Both of the gain tuning and switching rely on square means of innovations. This paper also provides stability analyses on time-varying Kalman filters and derives a sufficient condition for their asymptotic stability, on which our gain-tuning algorithm is based. It should be noted that the stability condition is available for even nonstabilizable systems having their uncontrollable poles on the unit circle. To illustrate those algorithms, we perform simulations using a harmonic oscillator model that is nonstabilizable and has its poles on the unit circle. Furthermore, we apply the algorithms to estimation of a ship's oscillation, particularly, with time-varying frequencies by simulations and model experiments. Consequently, all the results of stability analyses, simulations, and experiments have convinced that the algorithms are solid and effective.
This paper is concerned with the application of the H∞ and the Kalman filtering techniques to GPS positioning, specially to a recursive estimation algorithm for the static carrier phase differential method. In order to speed up the algorithm and to keep the positioning accuracy, we propose an algorithm utilizing the H∞ filter in the early stage of the estimation, and then switching to the Kalman filter. Finally, the experimental results by using real receiver data obtained at static points are shown.
In this paper, a GPS positioning algorithm using the H<sub>∞
</sub> filter is presented. The algorithm is derived by combining the H
<sub>∞</sub> filter with the LAMBDA (least squares ambiguity
decorrelation adjustment) method which can efficiently solve an integer
least squares problem. In the H<sub>∞</sub> filtering, the filter
performance strongly depends on the design parameter
“γ”, so that the choice of the value of
“γ” is very important. After briefly reviewing the H
<sub>∞</sub> filter, we also propose a simple algorithm that gives
adequate value of “γ”. Finally, the proposed algorithm
is examined by using the real receiver data which were obtained at two
static points
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