The Allan Variance technique is a very powerful mathematical method which allows a user to assess the real performance of any gyro in relation to the dynamics of his application, taking into account the effects of bias, noise, drift and long term sensor instability. It's beyond the scope of this glossary to fully describe the technique (contact us or browse the web for more information) but here is a summary of the key points: Bias is always measured by averaging successive data samples - the challenge is always to select a suitable time over which to average sampled data. Averages taken over short time intervals will be dominated by noise, those over a longer period by longer term drift. The technique involves selecting a range of time intervals (eg from 0.01s to 500s) over which to average data. The variation (standard deviation) from one averaged time period to the next is calculated and plotted against the averaging interval in log-log form. The resulting graph has a characteristic 'bathtub' shape. By examination of this graph, it is possible to compute the key defining characteristics of the gyro, namely
- Angular random walk
- Bias instability
- Rate random walk
This is a measure of gyro noise and has units of °/rt hour or °/rt sec. It can be thought of as the variation (or standard deviation), due to noise, of the result of integrating the output of a stationary gyro over time.
So, for example, consider a gyro with an ARW of 1°/rt sec being integrated many times to derive an angular position measurement: For a stationary gyro, the ideal result - and also the average result - will be zero. But the longer the integration time, the greater will be the spread of the results away from the ideal zero. Being proportional to the square root of the integration time, this spread would be 1° after 1 second and 10° after 100 seconds.
The bias, or bias error, of a rate gyro is the signal output from the gyro when it is NOT experiencing any rotation. Even the most perfect gyros in the world have error sources (the old axiom applies here too - "you gets what you pays for") and bias is one of these errors. Bias can be expressed as a voltage or a percentage of full scale output, but essentially it represents a rotational velocity (in degrees per second). Again, in a perfect world, one could make allowance for a fixed bias error. Unfortunately bias error tends to vary, both with temperature and over time. The bias error of a gyro is due to a number of components:
- calibration errors
- switch-on to switch-on
- bias drift
- bias variation over temperature
- effects of shock (g level)
Individual measurements of bias are also affected by noise, which is why a meaningful bias measurement is always an averaged series of measurements. A very effective means of describing gyro bias performance in a wide-ranging form is provided by the Allan Variance technique.
Don't confuse this with the more colloquial term drift rate. This refers specifically to the variation of the bias over time, assuming all other factors remain constant. Basically this is a warm-up effect, caused by the self heating of the gyro and its associated mechanical and electrical components. This effect would be expected to be more prevalent over the first few seconds after switch-on and to be almost non-existent after (say) five minutes.
Bias Instability is a fundamental measure of the 'goodness' of a gyro. It is defined as the minimum point on the Allan Variance curve, usually measured in °/hr. It represents the best bias stability that could be achieved for a given gyro, assuming that bias averaging takes place at the interval defined at the Allan Variance minimum.
See also 'Bias Drift' which is a temperature-based effect.
The ambient temperature has an effect on the bias, and performance parameters are only relevant with the specified operating temperature range. Temperature effects tend to be predictable on a per-gyro basis and it is possible to improve the gyro bias performance dramatically by calibration. Some gyros (eg the SiRRS01 range) offer an internal temperature sensor to aid this process.
The nominal scale factor of a gyro describes the basic transfer function of the device - how many volts (or bits) are expected for any given rotation rate sensed. It is the measure of the gradient of the best straight line through the points on a graph describing the expected gyro output against input rate, measured over the specified dynamic range of the gyro and at room temperature (using 20degC or 23degC). For an analogue gyro this is measured in volts per deg/s. For example the CRS03-02 gyro has a scale factor of 20mV per deg/s. Therefore its output will increase from its stationary output of 2.5V by 20mV for every positive deg/s of rotation up to 100 deg/s, and similarly for rotation in the negative direction.