PCA-aided calibration of systems comprising multiple unbiased sensors

The calibration of sensors comprising inertial measurement units is crucial for reliable and accurate navigation. Such calibration is usually performed with specialized expensive rotary tables or requires sophisticated signal processing based on iterative minimization of nonlinear functions, which is prone to get stuck at local minima. We propose a novel calibration algorithm based on principal component analysis. The algorithm results in a closed-form formula for the sensor sensitivity axes and scale factors. We illustrate the proposed algorithm with simulation experiments, in which we assess the calibration accuracy in the case of calibration of a system consisting of 12 single-axis gyroscopes.

Statistical reconstruction of pulse shapes from pulse streams

A short sample sequence of a finite-length pulse signal allows for its reconstruction only if the signal has a sparse representation in some basis. The recurrence of the pulse allows for a statistical approach to its reconstruction. We propose a novel method for this task. It is based on the distribution of short sample sequences treated as points which lie along a curve in a low-dimensional Euclidean space. We prove that the probability distribution of the points along this curve determines the underlying pulse signal uniquely. Based on this discovery, we propose an algorithm for pulse estimation from a finite number of short sequences of pulse-stream samples.