In GNSS-denied environments, aiding a vehicle's inertial navigation system (INS) is crucial to reducing the accumulated navigation drift caused by sensor errors (e.g. bias and noise). One potential solution is to use measurements of gravity as an aiding source. The measurements are matched to a geo-referenced map of Earth's gravity in order to estimate the vehicle's position. In this paper, we propose a novel formulation of the map matching problem using a hidden Markov model (HMM). Specifically, we treat the spatial cells of the map as the hidden states of the HMM and present a Viterbi style algorithm to estimate the most likely sequence of states, i.e. most likely sequence of vehicle positions, that results in the sequence of observed gravity measurements. Using a realistic gravity map, we demonstrate the accuracy of our Viterbi map matching algorithm in a navigation scenario and illustrate its robustness compared to existing methods.

Nonlinear optical processes are vital for fields including telecommunications, signal processing, data storage, spectroscopy, sensing, and imaging. As an independent research area, nonlinear optics began with the invention of the laser, because practical sources of intense light needed to generate optical nonlinearities were not previously available. However the high power requirements of many nonlinear optical systems limit their use, especially in portable or medical applications, and so there is a push to develop new materials and resonant structures capable of producing nonlinear optical phenomena with low-power light emitted by inexpensive and compact sources. Acoustic nonlinearities, especially giant acoustic nonlinear phenomena in gas bubbles and liquid droplets, are much stronger than their optical counterparts. Here, we suggest employing acoustic nonlinearities to generate new optical frequencies, thereby effectively reproducing nonlinear optical processes without the need for laser light. We critically survey the current literature dedicated to the interaction of light with nonlinear acoustic waves and highly-nonlinear oscillations of gas bubbles and liquid droplets. We show that the conversion of acoustic nonlinearities into optical signals is possible with low-cost incoherent light sources such as light-emitting diodes, which would usher new classes of low-power photonic devices that are more affordable for remote communities and developing nations, or where there are demanding requirements on size, weight and power.

The negatively charged nitrogen-vacancy (NV) center in diamond is a leading solid-state quantum emitter, offering spin-photon interfaces over a wide temperature range with applications from electromagnetic sensing to bioimaging. While NV centers in bulk diamond are well understood, embedding them in nanodiamonds (NDs) introduces complexities from size, geometry, and surface effects. NVs in NDs show altered fluorescence properties including longer lifetimes, lower quantum efficiency, and higher sensitivity to dielectric surroundings, which arise from radiative suppression, surface-induced non-radiative decay, and total internal reflection. Prior models typically addressed isolated aspects, such as dielectric contrast or surface quenching, without integrating full quantum-optical NV behavior with classical electrodynamics. We present a hybrid framework coupling rigorous electromagnetic simulations with a quantum-optical NV model including phonon sideband dynamics. NV emission is found to depend strongly on ND size, NV position, and surrounding refractive index. Our results explain observations such as shallow NVs in water-coated NDs appearing brighter than deeper ones in air and provide a unified framework for realistic emission scenarios. Unlike previous models, our approach predicts wavelength-dependent escape efficiencies and position-dependent variations. This integrated model informs the design of brighter NV-based sensors and quantum devices, advancing understanding of quantum emitter photophysics in nanoscale dielectrics.

The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modelling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T) and 1s(E) states, finding them to be 32 and 31 meV respectively. These results constitute the first ab initio confirmation of the s manifold energy levels for phosphorus donors in silicon.