Error detection and reduction within DriftLessTM

This thesis presents an algorithm that can reduce the estimation errors made with the DriftLessTM bias estimation technique. The algorithm utilizes the autocorrelation function to detect the presence of errors, and a minimization function to reduce these errors. The algorithm has been validated with simulations. A sensor signal contains noise, bias and the measurand signals. Bias is a non-constant, non-random, additive error on the measurement signal of a sensor. DriftLessTMuses two sensors that measure a vectorial quantity e.g. accelerometers or gyroscopes. To estimate the bias these sensors are rotated mechanically, physically with respect to each other. DriftLessTM rotates the sensor signals back numerically to make both sensors measure the same measurand virtually. Then these signals are subtracted from each other which results in a signal that is ideally independent of the measurand because the two measurands measured by the sensors will cancel each other out. The newly created signal still contains the biases. From this DriftLessTMsignal vector the bias is estimated. In reality the rotations are known with finite accuracy and precision. This causes an estimation error because a part of the measurand signal remains in the DriftLessTM signal vector. An estimate of the magnitude of the estimation error can be made by calculating the sample autocorrelation of each entry of the DriftLessTMsignal vector after correcting for the bias. The algorithm works by minimizing the autocorrelation of the bias corrected DriftLessTMsignal vector with respect to a numerical rotation matrix. Then the bias is re-estimated with the numerical rotation matrix that solved the previous minimization. Solving for a numerical rotation matrix and re-estimating the biases is repeated until convergence of the bias estimation. The algorithm increases the accuracy and precision of the DriftLessTMbias estimation method under certain circumstances. The increase in accuracy and precision is higher as the cross correlation of the measurand and the bias signals decreases, the power of the noise increases, the misalignments are greater and there is more time available for the computations of the algorithm.