“…The rank deficiency of G z leads to ambiguity in sensor measurements, i.e., adding more measurements does not affect the observability conditions, and the system will only remain partially observable with a non-observable mode, as can be seen in the null space basis (9) and (11). For example, if the robot gathers sensor measurements while moving from x 1 = [0, 0, 0] T with a fixed heading, the non-observable modes can be derived as [0, 0, −1, 0] T and [0, 0, 0, −1] T from (11).…”