| Abstract: |
The symmetric measurement equation approach to multiple target
tracking is revisited using unscented Kalman and particle filters.
The characteristics and performance of these filters are compared
to the original symmetric measurement equation implementation
relying upon an extended Kalman filter. The unscented Kalman
filter (UKF) promises more accurate approximation of
nonlinearities and simpler implementation of the SME approach than
the EKF. The particle filter implementation offers the ability to
explore the limits of the SME approach.
The performance of these filters paired with two sets of symmetric
measurement equations is analyzed using three criteria: track
maintenance, set estimation error, and average mean squared error.
Several counterintuitive aspects of the results are discussed,
including a previously unknown limitation of the unscented Kalman
filter. The point is made that the performance of the SME approach
is dependent on the interaction of the set of SME equations and
the filter used.
Taylor series expansions are used to evaluate and explain the
performance differences between Kalman filter-SME pairings. Using
the Taylor series representation, we show how the choice of SME
formulation affects the representation, and consequently
approximation, of uncertainty in the Kalman filters. This
analysis suggests that the Taylor series expansion might be used
as a design tool for constructing SME formulations tailored to the
tracking situation.
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