Allan variance and random error identification

background

Allan variance It is a powerful tool to identify random noise . adopt Allan curve The main random noise items that can be identified include quantization noise 、 Random walk 、 Zero bias 、 Rate random walk 、 Speed ramp .Allan variance It is a tool to quantify and identify the random noise of inertial sensors . This tool draws Allan The double logarithm curve of standard deviation and data cluster time reflects the performance of each noise . Allan The variance has the following relationship with the power spectral density of random noise ：

Quantization noise

Quantization noise is the error introduced in the process of converting analog signal into digital signal by analog-to-digital converter , Its essence is the difference between the actual amplitude of the analog signal and the resolution of the analog-to-digital converter , Its power spectral density is ：

From the above formula (4.18) See , When T= Radical sign 3 when , The quantized noise figure can be obtained ; And the slope of the part is -1.

angle - Speed random walk

Angle random walk is represented by white noise of rate output . The angular random walk power spectral density is ：


From the above results (4.20) It can be seen that , When T=1 when , Angle random walk coefficient can be obtained , And the curve affected by the angle random walk shows the slope -1/2.

Zero bias instability

The zero bias error comes from the flicker error of electronic components , It is expressed as the output deviation of the data . The power spectral density of the zero bias instability is ：


From the above results (4.22) It can be seen that , The zero bias instability coefficient can be obtained from the flat part of the curve B

angular velocity - Acceleration random walk

Rate random walk is a noise with an ambiguous source , Some literatures consider it as the limit case of exponential noise with long correlation time ; There are also literatures that think it is the result of acceleration integral , It is shown as acceleration white noise ( White noise integral is followed by random walk ), The power spectral density of rate random walk is ：
From the above results (4.24) It can be seen that , When T=3 when , The rate random walk coefficient can be obtained K, And the curve affected by rate random walk shows the slope 1/2.

Drift rate ramp

The drift rate ramp appears as （ horn ） The rate output changes slowly with time , Although the error is random , But it is usually treated as systematic error , It is generally regarded as （ horn ） Constant acceleration error , Its power spectral density is ：


From the above results (4.26) It can be seen that , When T= Radical sign 2 when , The drift rate ramp coefficient can be obtained , The slope of the curve affected by the rate slope is 1.

reference

《INS/GNSS Research on error compensation of integrated navigation function model 》- Longxingyu