Filter-based vs optimization-based SLAM

WHY THIS TESTS: It probes whether you understand the estimation-theoretic reasons modern SLAM stacks abandoned filters in favor of graph optimization, not just the names of the two approaches.

A GOOD ANSWER COVERS: EKF-SLAM maintains one belief, a mean and covariance over the current robot pose plus every landmark, updated recursively as measurements arrive. Marginalizing out past poses keeps the state small in pose count but makes the landmark covariance dense, so cost grows roughly with the square of the number of landmarks, and any linearization done early is frozen forever. Optimization-based SLAM instead retains a window or full history of poses connected by measurement constraints, forming a sparse graph; bundle adjustment jointly refines camera poses and 3D points, while pose graph optimization refines poses linked by relative-motion and loop-closure edges. Because the information matrix is sparse and the solver re-linearizes each iteration, it reaches higher accuracy and corrects past errors.

COMMON WRONG ANSWERS: Saying filters are more accurate because they run online. Believing optimization cannot run in real time, ignoring sliding-window and incremental solvers like iSAM that exploit sparsity. Forgetting that the EKF covariance becomes fully dense after landmarks are correlated through marginalization.

LIKELY FOLLOW-UPS: Why is the optimization information matrix sparse. How does a loop closure get incorporated as an edge. What makes incremental smoothing fast enough for real time. How does linearization error differ in practice between the two approaches over a long run.

ONE CONCRETE EXAMPLE: A robot drives a long loop. An EKF, having linearized early poses just once, cannot retroactively fix accumulated drift, so the map seams misalign visibly at the loop closure point. A pose-graph optimizer instead adds a loop-closure edge and re-linearizes, distributing the correction across all intermediate poses and snapping the entire map into a globally consistent layout that the filter could never recover.