FixedLagSmoother

Overview¶

The FixedLagSmoother class is the base class for BatchFixedLagSmoother and IncrementalFixedLagSmoother.

It provides an API for fixed-lag smoothing in nonlinear factor graphs. It maintains a sliding window of the most recent variables and marginalizes out older variables. This is particularly useful in real-time applications where memory and computational efficiency are critical.

Mathematical Formulation¶

In fixed-lag smoothing the objective is to estimate the state $\mathbf{x}_t$ given all measurements up to time $t$, but only retaining a fixed window of recent states. The optimization problem can be expressed as:

where $L$ is the fixed lag, $\mathbf{h}_i$ are the measurement functions, and $\mathbf{z}_i$ are the measurements. In practice, the functions $\mathbf{h}_i$ depend only on a subset of the state variables $\mathbf{X}_i$, and the optimization is performed over a set of $N$ factors $\phi_i$ instead:

The API below allows the user to add new factors at every iteration, which will be automatically pruned after they no longer depend on any variables in the lag.