A spherical simplex unscented Kalman filter with smart sigma-point processing for estimations in CT ΣΔ modulators

In this paper, a spherical simplex unscented Kalman filter with reduced mathematical complexity for concurrent estimations of nonidealities in continuous-time sigma-delta modulators is investigated. Sigma-Delta modulators are known to suffer from nonidealities during run-time. To restore the ideal behavior, observation of the system with subsequent correction is desirable. Earlier publications show several methods to correct for different nonidealities. But commonly only a single parameter is considered per technique, while the rest is assumed ideal. Recently, an unscented Kalman filter was presented to be able to estimate DAC and major loop-filter nonidealities concurrently with high precision and robustness. However, due to the huge amount of mathematics required, a hardware implementation of the method seems more than challenging. Therefore, a novel adaption of the estimator is presented, reducing mathematics such that the algorithm is accelerated by approximately a factor of 4 compared to the previous publication.