EKF-SLAM was the original solution to simultaneous localization and mapping — one big Kalman filter tracking the robot's pose and every landmark at once. Elegant, historic, and the reason engineers later switched to graph-based methods.
EKF-SLAM keeps a single running estimate of where the robot is AND where every landmark is, updating them together every time the robot senses. It was the first real answer to mapping and localizing at the same time.
When robots first solved SLAM — mapping a place while figuring out where they are in it — the answer was a single, elegant idea: put everything into one Kalman filter. That's EKF-SLAM.
The idea
The filter's state is the robot's pose plus the position of every landmark it has seen. As the robot moves and senses, an extended Kalman filter updates all of it together, along with a giant covariance matrix that captures how uncertain each thing is — and, crucially, how they're correlated.
One filter estimates robot + map together
Every observation corrects not just the seen landmark but the robot pose and, through correlations, the whole map at once.
The beautiful part
The correlations are the secret. When the robot re-sees an old landmark, the correction ripples through the covariance and sharpens the entire map — the mathematical version of "now that I recognize this corner, everything else snaps into place." This insight (that the map's correlations matter and converge) is what made SLAM provably solvable.
Why it fell out of favor
That same covariance is EKF-SLAM's downfall. It couples every landmark to every other, so each update costs O(N²) in the number of landmarks — a map with thousands of features grinds to a halt. It also inherits the EKF's weakness: linearization error. The EKF approximates nonlinear motion and sensing with a first-order Taylor expansion, and over a long trajectory those small errors compound and can make the filter overconfident and inconsistent.
What replaced it
Modern systems moved to pose-graph optimization and factor graphs, which exploit sparsity and re-linearize, scaling to huge maps. FastSLAM kept the filter idea but used a particle filter to break the O(N²) bottleneck. EKF-SLAM is now mostly taught as the foundational idea rather than deployed at scale.
Why it matters
EKF-SLAM is where SLAM began — the first rigorous answer to the chicken-and-egg problem of mapping and localizing together. Understanding its structure (and its O(N²) wall) is the key to appreciating why today's graph-based SLAM works the way it does.
