Comparative Study of AC Signal Analysis Methods for Impedance Spectroscopy Implementation in Embedded Systems

For embedded impedance spectroscopy, a suitable method for analyzing AC signals needs to be carefully chosen to overcome limited processing capability and memory availability. This paper compares various methods, including the fast Fourier transform (FFT), the FFT with barycenter correction, the FFT with windowing, the Goertzel filter, the discrete-time Fourier transform (DTFT), and sine fitting using linear or nonlinear least squares, and cross-correlation, for analyzing AC signals in terms of speed, memory requirements, amplitude measurement accuracy, and phase measurement accuracy. These methods are implemented in reference systems with and without hardware acceleration for validation. The investigation results show that the Goertzel algorithm has the best overall performance when hardware acceleration is excluded or in the case of memory constraints. In implementations with hardware acceleration, the FFT with barycentre correction stands out. The linear sine fitting method provides the most accurate amplitude and phase determinations at the expense of speed and memory requirements.

The geoPebble System: Design and Implementation of a Wireless Sensor Network of GPS-Enabled Seismic Sensors for the Study of Glaciers and Ice Sheets

The geoPebble system is a network of wirelessly interconnected seismic and GPS sensor nodes with geophysical sensing capabilities for the study of ice sheets in Antarctica and Greenland, as well as mountain glaciers. We describe our design methodology, which has enabled us to develop these state-of-the art units using commercial-off-the-shelf hardware combined with custom-designed hardware and software. Each geoPebble node is a self-contained, wirelessly connected sensor for collecting seismic activity and position information. Each node is built around a three-component seismic recorder, which includes an amplifier, filter, and 24-bit analog-to-digital converter that can sample incoming seismic signals up to 10 kHz. The timing for each node is available from GPS measurements and a local precision oscillator that is conditioned by the GPS timing pulses. In addition, we record the carrier-phase measurement of the L1 GPS signal in order to determine location at sub-decimeter accuracy (relative to other geoPebble nodes within a radius of a few kilometers). Each geoPebble includes 32 GB of solid-state storage, wireless communications capability to a central supervisory unit, and auxiliary measurements capability (including tilt from accelerometers, absolute orientation from magnetometers, and temperature). The geoPebble system has been successfully validated in the field in Antarctica and Greenland.

Functional observability and target state estimation in large-scale networks

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

Persistent and enhanced spin-nematic squeezing in a spinor Bose-Einstein condensate

We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose-Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spinnematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.

Intracavity Measurement Sensitivity Enhancement without Runaway Noise

A method to increase the sensitivity of an intracavity differential phase measurement that is not made irrelevant by a larger increase of noise is explored. By introducing a phase velocity feedback by way of a resonant dispersive element in an active sensor in which two ultrashort pulses circulate, it is shown that the measurement sensitivity is elevated without significantly increasing the Petermann excess noise factor. This enhancement technique has considerable implications for any optical phase based measurement; from gyroscopes and accelerometers to magnetometers and optical index measurements. Here we describe the enhancement method in the context of past dispersion enhancement studies including the recent work surrounding non-Hermitian quantum mechanics, justify the method with a theoretical framework (including numerical simulations), and propose practical applications.

High precision phase estimation with controllable sensitivity and dynamic range

High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.