What is scale factor?

The scale factor refers to the ratio of the gyroscope output to the input angle rate, expressed by the slope of a specific straight line. This straight line is obtained by fitting the least squares method based on the input and output data measured within the input angular rate range.

The linear model of the relationship between the input and output of the gyroscope sensors is as followings;

F_{j： The output value of the gyroscope when the j}th _{input angular rate is entered.}

_{K:   Scale factor}

_{F0：    Fitting zero position}

_{Vj：     Fitting error}

_{Ωij:      The j}th _{input angular rate}

_{The scaling factor has nonlinearity and asymmetry. Therefore, important parameters are introduced in the gyroscope and accelerometer parameter performance indicators, namely "scale factor nonlinearity", "scale factor asymmetry", "scale factor repeatability" and "scale factor temperature Sensitivity".}

_{It is used to characterize the deviation between the actual input and output of the sensor and determine the credibility of the fitted data. Its numerical value directly reflects the accuracy of the gyroscope/accelerometer.}

_{Scale factor non-linearity:}

_{Scale factor nonlinearity (Kn) refers to the ratio of the maximum deviation value of the gyroscope output relative to the least squares fitted straight line to the maximum output within the input angular rate range. Unit: %, ppm. It represents the degree of deviation between the actual input and output data of the gyroscope and determines the credibility of the fitted data.}

_{Our high-precision MEMS gyroscope scale factor nonlinearity index can reach 100ppm.}

_{Scale factor asymmetry}

       _{Scale factor asymmetry (Ka) refers to the ratio of the scale factor difference between the gyroscope's input angular rate in the forward and reverse directions and its average value within the input angular rate range. Unit: %, ppm.}

_{Scale factor repeatability}

_{Scale factor repeatability (Kr) refers to the degree of consistency between repeated measurements of gyroscope scale factors under the same conditions and within a specified interval. Expressed as the ratio of the standard deviation of the scaling factor obtained from each test to its average value, unit: %, ppm.}

_{The scale factor repeatability of our high-precision MEMS gyroscopes can reach 100ppm, and the scale factor repeatability of quartz flexible accelerometers can reach 10ppm.}

_{Scale factor temperature sensitivity}

_{Scale factor temperature sensitivity (Kt) refers to the ratio of the relative change in the gyroscope or accelerometer scale factor caused by temperature changes to the temperature change relative to the room temperature standard scale factor. It is generally expressed as the maximum value, unit: % /℃, ppm/℃.}

_{The scale factor temperature sensitivity of quartz flexible accelerometers from Hitech Sensors can reach ±10ppm.}