Factor Graph Optimization vs Recursive Bayesian Estimation

Factor Graph Optimization (FGO) excels at producing globally consistent maps and trajectories by solving the full nonlinear least-squares problem over a graph of robot poses and landmark observations. Implementations like iSAM2 exploit the sparsity of this graph to achieve real-time performance, making FGO the gold standard for large-scale SLAM where loop closures and batch accuracy are critical. For example, in a warehouse deployment, FGO can correct an entire fleet's trajectory history upon a single loop closure event, ensuring a drift-free map.

Recursive Bayesian Estimation, typified by the Extended Kalman Filter (EKF), takes a fundamentally different approach by marginalizing out past states to maintain a fixed computational and memory footprint. This incremental strategy results in a highly efficient, constant-time update cycle that is ideal for real-time, low-latency state estimation on embedded hardware. The trade-off is a vulnerability to linearization errors that can cause filter divergence, making it less robust to large-scale loop closures compared to iterative smoothing methods.

The key trade-off: If your priority is global map consistency and the ability to correct historical drift in post-processing or real-time for large environments, choose Factor Graph Optimization. If you prioritize a strict, deterministic compute budget per frame and minimal memory usage for high-rate sensor fusion on a resource-constrained humanoid, choose a Recursive Bayesian Estimator like an UKF.

Factor graph optimization (FGO) excels at producing globally consistent maps and trajectories because it revisits and re-linearizes the entire history of robot poses and landmark observations. For example, in a large-scale warehouse deployment, iSAM2 can exploit the sparsity of the underlying factor graph to achieve near real-time performance while maintaining centimeter-level accuracy over a 500,000-pose trajectory, a feat that would cause a recursive filter to accumulate prohibitive drift.

Recursive Bayesian estimation (RBE), such as an Extended or Unscented Kalman Filter, takes a fundamentally different approach by marginalizing out past states to maintain a fixed computational budget. This results in a constant-time update per new measurement, making it highly predictable for safety-critical real-time control loops on embedded hardware. However, this marginalization permanently linearizes the past, making the system vulnerable to catastrophic failure from a single bad data association that cannot be corrected later.

The key trade-off: If your priority is global map quality, long-term autonomy, and the ability to perform loop closures to correct historical drift, choose factor graph optimization. If you prioritize a strict, deterministic execution cycle measured in microseconds for low-level flight control or a simple filtering task with no memory requirement, choose a recursive filter. In modern robotics, FGO is the default architecture for localization and mapping, while RBE is the specialized exception for high-rate, memoryless estimation.