A review of relative-observation-based online error estimation and cooperative calibration for multiple rotating inertial navigation systems without external references

Abstract

Rotation modulation can suppress part of the constant sensor errors in a rotating inertial navigation system (RINS), but residual sensor and structural errors can still propagate into navigation errors. In addition, some error parameters can be calibrated offline before operation, but their values may vary with temperature, operating conditions, and long-term use. A single RINS has limited ability to identify and compensate for some time-varying errors and weakly separable parameters online, which motivates cooperation among multiple RINSs using inter-system relative information. This review examines online error estimation and cooperative calibration for multiple RINSs without external references during online estimation. It summarizes the construction and basic models of relative observations and classifies existing methods into result-level information fusion, state-level online error estimation, and parameter-level cooperative calibration. Typical system configurations, methodological development, main methods, and application scenarios are reviewed. Representative studies are also compared with respect to observation construction, estimation capability, and applicability. Existing studies show that inter-system navigation differences, fixed geometric relationships, and relative rotation information can improve navigation performance and support online estimation of selected error states and physical parameters when effective relative observations are available. However, the estimable states and parameters depend on the system configuration, rotation scheme, motion condition, and observation type. Common-mode error components may be weakened or canceled in relative observations. Increased inter-system correlation during cooperation may also reduce the differential information available for subsequent estimation. Time-varying differential errors, parameter coupling, and poor numerical conditioning can further limit reliable error separation and parameter estimation. Future work should focus on observability and identifiability analysis for specific configurations and rotation conditions, preservation of information diversity during cooperation, modeling and separation of time-varying differential errors, robust estimation of reliably identifiable parameters, and more consistent reporting and evaluation methods.