Resolvable Group Target Tracking: A Bernoulli Filter With Extended Group-Center State

This letter develops an extended group-center state (EGCS)-based Bernoulli filter (BerF) for tracking a single resolvable group target (RGT) with a fixed number of members in a nearly rigid formation. The EGCS combines the group-center kinematics with a minimal set of member-relative offsets. On this augmented state space, a linear-Gaussian transition density and a clutter-normalized set-valued likelihood are derived to account for member detections, missed detections, clutter, and member-measurement association while retaining one group-level Bernoulli existence variable. The resulting association-hypothesis update admits an exact Gaussian mixture (GM) realization and a gated top-hypothesis approximation that bounds the number of retained posterior updates. Simulations show that under the tested scenarios, the proposed EGCS-BerF attains lower tracking errors than representative random-finite-set-based RGT filters with moderate computational cost.