Over the past few weeks I have been working to try to find the optimal method for eliminating the null bias without using sensor fusion methods (e.g. other sensors and a Kalman filter). The elimination of null bias is of particular importance in our application since the rate is integrated over time to find the total angular deflection; a bias leads to an erroneous deflection that is linear in time. The method that was most reported in the literature, including one found on the Analog Devices webpage, was to take stationary measurements for a period of time, average the data, and subtract from future measurements; this method did not provide adequate results. As seen in the attached plot, the stationary gyro reports a wide range of apparent deflections most showing some degree of linear dependence, indicating that the bias was not entirely eliminated to a reasonable degree.

The null bias determination process took 200 samples over a 30 second time interval and then subtracted the calculated value from all subsequent readings. A moving filter (averaging window of 32) was also applied to eliminate noise.

An Allan Variance curve was determined and future steps will include null bias determination over a period that captures bias instability (approximately 200 seconds) to see if it improves bias resolution.

My questions are as follows:

- - Are their any other recommended methods for null bias elimination you could suggest?
- - Since the sensor is already temperature compensated is there any need to further calibrate?
- - Do you believe the a null bias that captures the bias instability would greatly improve performance?

Hey gnekut,

Unfortunately, a time zero calibration will not be enough to effectively eliminate bias errors in gyroscopes. This is true for any gyroscope on the market, as all gyroscopes have some level of inherent bias instability. Even if you reduce the "time zero" offset errror to less than 0.001°/s, after several minutes of operation it is likely that the null output of the gyroscope has drifted to a slightly different value. Your initial calibration is, in effect, no longer accurate and a DC error term will have been introduced into your calculation. The characteristic of this drift is, as you mention, described by the Allan Variance characteristic. As angle random walk truly is random, it is quite difficult to compensate without additional, uncorrelated measurement sources.

That aside, i do have some pointers for you when performing calibrations. You describe your existing calibration routine as comprising 200samples taken over a 30 second time interval. This is roughly a 6Hz data rate. This is not an optimum condition for performing bias compensation. The ADXRS450 output data rate is 500Hz, and the output bandwidth of the rate signal is 80Hz. i would recommend that you sample the output at 200Hz or higher. The ADXRS450 output is largely Gaussian. By sub-sampling the output at 6Hz, the resulting dataset that you generate is not guaranteed to reflect the Gaussian nature of the actual device output. Essentially, the average value of your data set might not reflect the actual average value that the gyro output during that same time. Additionally, it is not necessary to sample data for 30 seconds to achieve an accurate measurement of the null bias. using a sufficiently high sample rate, it should only be necessary to sample ~5 seconds of data. a 5 second average will improve the bias resolution to about 0.005°/s. longer averages than this will have diminishing returns with regards to improving the bias accuracy.

The ADXRS40 is compensated for ambient offset only. if you require highest possible bias stability, i would recommend the ADXRS453. this device has a full temperature compensation routine that uses a second order equation to reduce offset error over the full operation temperature range.

as for your last question, i would not recommend to increase the "time zero" calibration to encompass 200 seconds of operation. Implementing such a long average would result in a calibration value that is half way between the bias at time zero, and the bias at t=200sec. however, without the ability to predict the subsequent random walk of the output, its not possible to determine that any improvement would be gained through this method.