A self-calibrating gyroscope system provides improved estimates of, and compensation or calibration for, scale factor errors and bias errors. The gyroscope system employs a plurality of gyroscope units having sense or input axes in a mutually non-parallel arrangement. The number of gyroscope units is preferably at least one more than the number of axes for which rate estimates is required. A Mode Reversal technique is used to obtain an estimate of bias error for a selected gyroscope. A Random Closed-Loop Scale Factor technique is used to obtain an estimate of scale factor error for a selected gyroscope. Because the Mode Reversal technique temporarily disrupts operation of the affected gyroscope, each of the gyroscopes may be taken offline temporarily, in turn, for calibration, and thereafter returned to normal operation. Because at least one redundant gyroscope is provided, when a selected gyroscope is offline, rate information from the remaining operating gyroscopes can be used to derive a reference rate about the axis of the offline gyroscope.