Title: Erratum: Analytical Observability Analysis of INS with Vehicle Constraints (Vol. 61, No. 3, Fall 2014)
Author(s): Yaacov Rothman, Itzik Klein, Sagi Filin
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 62, Number 3
Pages: 249 - 249
Cite this article: Rothman, Yaacov, Klein, Itzik, Filin, Sagi, "Erratum: Analytical Observability Analysis of INS with Vehicle Constraints (Vol. 61, No. 3, Fall 2014)", NAVIGATION, Journal of The Institute of Navigation, Vol. 62, No. 3, Fall 2015, pp. 249-249.
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Abstract: This paper was first published online on 17 September 2014 (DOI: 10.1002/navi.63) and appears in the Fall 2014 issue of the journal (Volume 61, Issue 3, pp. 227 - 236). Subsequent to its publication online and in print, the authors would like to address two points in the paper which were erroneous: 1. In Fig. 5e, which depicts the degree of observability (DOO) for the heading error state, there are two points in which the graph converges. This was concluded to be due to observability at those points in time. In fact, the momentary convergence was due to an error in the implementation of the transfer between the dynamics (i.e., the change from acceleration to no acceleration and vice versa) at those time points. The reader’s sole attention should be on the behavior of the graph in general, i.e., divergent, thus showing that the heading error state is unobservable in the discussed scenario. 2. On page 5 (after Eq. (32) and before the Analysis section) the following was stated: "… if the vehicle is turning, the unobservable subspace cannot be found, since Eq. (29) is unsolvable due to rank defect. This means that the 12 error states are observable in this case. Thus, an accelerating and turning vehicle, with the aiding of the body velocity constraint, is observable in the velocity and orientation error states and the accelerometer and gyroscope bias residual states, meaning the drift and covariance of these states are reduced during the time of acceleration and maneuvers. The only error state that is unobservable, in this case, is the position error state." Clearly this paragraph is incorrect, as there are unobservable states for vehicles that are accelerating, including accelerations induced by turning with constant velocity (namely, heading, accelerometer biases in the x and y axes, and gyroscope bias in the z-axis).