Abstract: To address the difficulty of extracting extended target trajectories in the presence of clutter, missed detections, and measurement noise, a trajectory random finite set (RFS)-based cardinality-balanced multi-Bernoulli extended filtering algorithm is proposed. Based on the random-matrix representation of extended targets, the complete state sequence from target birth to the current time is modeled as a trajectory variable, where each state consists of both kinematic parameters and an associated extent matrix. Using finite-set statistics, multiple extended-target trajectories are jointly modeled as a multi-Bernoulli RFS, leading to the development of the trajectory-cardinality-balanced multi-Bernoulli (TCB MeMBer) filter. Assuming linear Gaussian target dynamics and measurement models, the posterior density of the TCB MeMBer filter is approximated by a Gamma Gaussian inverse Wishart (GGIW) mixture. Recursive closed-form prediction and update equations are then derived. Finally, pruning and merging operations are performed on the Bernoulli and GGIW components to mitigate the effects of missed detections and false alarms, thereby improving filtering accuracy. Simulation results demonstrate that the proposed algorithm can accurately reconstruct complete extended-target trajectories and achieves robust performance in complex environments.