I am confused by what precisely the term "Indirect Kalman Filter" or "Error-State Kalman Filter" means.
The most plausible definition I found is in Maybeck's book [1]:
As the name indicates, in the total state space (direct) formulation, total states such as vehicle position and velocity are among the state variables in the filter, and the measurements are INS accelerometer outputs and external source signals. In the error state space (indirect) formulation, the errors in the INS- indicated position and velocity are among the estimated variables, and each measurement presented to the filter is the difference between INS and external source data.
20 years later Roumeliotis et al. in [2] write:
The cumbersome modeling of the specific vehicle and its interaction with a dynamic environment is avoided by selecting gyro modeling instead. The gyro signal appears in the system (instead of the measurement) equations and thus the formulation of the problem requires an Indirect (error-state) Kalman filter approach.
I cannot understand the bold part, since Lefferts et al. in [3] write much earlier:
For autonomous spacecraft the use of inertial reference units as a model replacement permits the circumvention of these problems.
And then proceed to show different variants of EKFs using gyro modeling that are clearly direct Kalman Filters according to Maybeck's definition: The state only consists of the attitude quaternion and gyro bias, not error states. In fact, there is no seperate INS whose error to estimate with an error-state Kalman filter.
So my questions are:
Is there a different, maybe newer definition of indirect (error-state) Kalman Filters I am not aware of?
How are gyro modeling as opposed to using a proper dynamic model on the one hand and the decision whether to use a direct or indirect Kalman filter on the other hand related? I was under the impression that both are independent decisions.
[1] Maybeck, Peter S. Stochastic models, estimation, and control. Vol. 1. Academic press, 1979.
[2] Roumeliotis, Stergios I., Gaurav S. Sukhatme, and George A. Bekey. "Circumventing dynamic modeling: Evaluation of the error-state kalman filter applied to mobile robot localization." Robotics and Automation, 1999. Proceedings. 1999 IEEE International Conference on. Vol. 2. IEEE, 1999.
[3] Lefferts, Ern J., F. Landis Markley, and Malcolm D. Shuster. "Kalman filtering for spacecraft attitude estimation." Journal of Guidance, Control, and Dynamics 5.5 (1982): 417-429.