Consistent Estimation

NEES of smoothers


State estimation problems without absolute position measurements routinely arise in navigation of unmanned aerial vehicles, autonomous ground vehicles, etc., whose proper operation relies on accurate state estimates and reliable covariances. Unaware of absolute positions, these problems have immanent unobservable directions. Traditional causal estimators, however, usually gain spurious information on the unobservable directions, leading to over-confident covariance inconsistent with actual estimator errors. The consistency problem of fixed-lag smoothers (FLSs) has only been attacked by the first estimate Jacobian (FEJ) technique because of the complexity to analyze their observability property. But the FEJ has several drawbacks hampering its wide adoption.


To ensure the consistency of a FLS, we introduce the right invariant error formulation into the FLS framework and analyze the observability of a FLS with the right invariant error.

Key results

  • Right invariant fixed-lag smoothers (RI-FLS) keep the observability property and estimate covariances consistent to actual estimation errors.

  • Landmark parameters in a camera frame, IMU biases, etc., do not impact consistency, and therefore do not need to use so-called first estimates.

Related papers:

Jianzhu Huai
Postdoc researcher

My research interest is economic mapping and navigation.