ISSN : 1796-203X
Volume : 2    Issue : 6    Date : August 2007

Adaptive-Gain Kinematic Filters of Orders 2-4
Naum Chernoguz
Page(s): 17-25
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The kinematic filter is a common tool in control and signal processing applications dealing with
position, velocity and other kinematical variables. Usually the filter gain is given a fixed value
determined due to dynamic and measurement conditions. Most studies provide analytical solutions
for optimal gains in particular scenarios. In practice, due to a lack of information (or under
timevarying conditions) these recipes are mostly inapplicable and the kinematic filter requires
appropriate adaptation tools instead. In its simplest form, the problem may be formulated as the
gain adaptation under the tracking index uncertainty. We suggest a simple adaptive-gain kinematic
filter based on minimization of the innovation variance which is known to give the optimal Kalman
gain. The study deals with commonly used kinematic models of order 2-4. As shown, for any order
of the kinematic filter its transfer function matches the moving-averaging (MA) model parameterized
by the filter gain. In this view, the adaptive kinematic filter may be implemented in a variety of forms
either based on the MA identification or by a direct gain adaptation. Optimal closed-form solutions
may be incorporated into the adaptive filter as constraints. With the optimally constrained gain-vector
components, the multipleparameter adaptive filter is translated into a beneficial single-parameter
version. The simulation study demonstrates behavior of suggested filters in a wide range of

Index Terms
kinematic/tracking filter, adaptive gain, timeseries identification