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Jason F. Ralph

Publications and source records attributed to Jason F. Ralph.

At least 19 recordsLinked to original sources
arXiv2026

Time-dependent multiparameter estimation for quantum experiments via online-offline sequential Monte-Carlo method

While typical online estimation methods can estimate the multiparameter dynamics of many systems, they may not be sufficient for a system with highly noisy measurement and rapid detection rate. In this paper, we create a hybrid estimation method by augmenting the sequential Monte Carlo (SMC) sampler, an online estimation method with an offline technique known as the time-batch estimation technique. By continuously monitoring the system, we may divide signals into batches and average them into an averaged trajectory. The system dynamics is then evolved with batch-averaged Kraus maps, for which we derive a highly efficient approximation. To facilitate the adoption of our algorithm, we present a modular derivation of the SMC methods and showcase our algorithm as an explicit example. We then implement our algorithm on the measurement signals obtained from superconducting-qubit experiments under two types of measurement setting: a fluorescence measurement and a dispersive $z$-measurement. The algorithm's hyperparameter values are chosen from independent numerical simulation, while the accuracy of our estimation is validated by a signal reconstruction method. Our results show that, for the fluorescence case, our algorithm can estimate the system's parameters better than the standard calibration method, and, for the dispersive case, our estimation is capable of finding an unexpected jump in parameter values that the standard calibration method could not find.

quant-ph↗
arXiv2024

Bayesian Wideband Signal Detection via Source Signal Marginalization and RJMCMC

Consider an array receiving unknown wideband signals from an unknown number of sources $k$. Wideband signals can occupy arbitrarily wide bandwidths, rendering demodulation-based approaches inapplicable, a common situation in settings involving acoustic signals. Here, we aim to determine $k$ given $N$ noisy array-valued measurements, a task known as the "detection problem," for which Bayesian model comparison is a common approach. To render Bayesian inference tractable, it is typically necessary to marginalize the source signals. Unfortunately, for wideband signals, naive marginalization has an unaffordable time complexity of $\mathcal{O}(N^3 k^3)$. As a result, fully Bayesian signal detection has yet to be demonstrated in wideband settings. In this work, we propose a wideband signal model that allows for computationally tractable marginalization of the source signals. We begin from the canonical model of linear time-invariant (LTI) signal propagation, which is then augmented into a circular convolution, all without loss of generality. This allows for efficient computation in the frequency domain, where the resulting linear system admits a decomposition into a sparse matrix we refer to as a \textit{stripe matrix decomposition}. Exploiting this sparsity pattern reduces the time complexity of computing the marginal likelihood to $\mathcal{O}(N k^3)$. These computational improvements enable efficient posterior inference via reversible-jump Markov chain Monte Carlo (RJMCMC). In this work, we use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than RJMCMC. Detection of the latent source signals can then be performed in a fully Bayesian manner using samples drawn by NRJMCMC. We evaluate our procedure by comparing it against generalized likelihood ratio testing (GLRT) and information criteria.

eess.SP↗
arXiv2023

Bayesian Estimation for Bell State Rotations

This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements and we demonstrate that the resultant improvement over the optimal single qubit case approaches the $\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also demonstrate how the accuracy of the estimation method is a function of the purity of mixed states.

quant-ph↗
arXiv2022

Adaptive Bayesian Beamforming for Imaging by Marginalizing the Speed of Sound

Imaging methods based on array signal processing often require a fixed propagation speed of the medium, or speed of sound (SoS) for methods based on acoustic signals. The resolution of the images formed using these methods is strongly affected by the assumed SoS, which, due to multipath, nonlinear propagation, and non-uniform mediums, is challenging at best to select. In this letter, we propose a Bayesian approach to marginalize the influence of the SoS on beamformers for imaging. We adapt Bayesian direction-of-arrival estimation to an imaging setting and integrate a popular minimum variance beamformer over the posterior of the SoS. To solve the Bayesian integral efficiently, we use numerical Gauss quadrature. We apply our beamforming approach to shallow water sonar imaging where multipath and nonlinear propagation is abundant. We compare against the minimum variance distortionless response (MVDR) beamformer and demonstrate that its Bayesian counterpart achieves improved range and azimuthal resolution while effectively suppressing multipath artifacts.

eess.SP↗
arXiv2022

A Geometric Approach to Passive Localisation

In this paper, we present a geometric framework for the passive localisation of static emitters. The objective is to localise the position of the emitters in a given area by centralised coordination of mobile passive sensors. This framework uses only the geometry of the problem to minimise the maximal bounds of the emitters' locations without using a belief or probability distribution. This geometric approach provides effective boundaries on the emitters' position. It can also be useful in evaluating different decision-making strategies for coordinating mobile passive sensors and complementing statistical methods during the initialisation process. The effectiveness of the geometric approach is shown by designing and evaluating a greedy decision-making strategy, where a sensor selects its future position by minimising the maximum uncertainty on its next measurement using one of the global objective functions. Finally, we analyse and discuss the emergent behaviour and robustness of the proposed algorithms.

cs.MA↗
arXiv2022

Double Deep Q Networks for Sensor Management in Space Situational Awareness

We present a novel Double Deep Q Network (DDQN) application to a sensor management problem in space situational awareness (SSA). Frequent launches of satellites into Earth orbit pose a significant sensor management challenge, whereby a limited number of sensors are required to detect and track an increasing number of objects. In this paper, we demonstrate the use of reinforcement learning to develop a sensor management policy for SSA. We simulate a controllable Earth-based telescope, which is trained to maximise the number of satellites tracked using an extended Kalman filter. The estimated state covariance matrices for satellites observed under the DDQN policy are greatly reduced compared to those generated by an alternate (random) policy. This work provides the basis for further advancements and motivates the use of reinforcement learning for SSA.

cs.LG↗
arXiv2022

Position fixing with cold atom gravity gradiometers

This paper proposes a position fixing method for autonomous navigation using partial gravity gradient solutions from cold atom interferometers. Cold atom quantum sensors can provide ultra-precise measurements of inertial quantities, such as acceleration and rotation rates. However, we investigate the use of pairs of cold atom interferometers to measure the local gravity gradient and to provide position information by referencing these measurements against a suitable database. Simulating the motion of a vehicle, we use partial gravity gradient measurements to reduce the positional drift associated with inertial navigation systems. Using standard open source global gravity databases, we show stable navigation solutions for trajectories of over 1000km.

quant-ph↗
arXiv2018

Dynamical model selection near the quantum-classical boundary

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in post-selection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using a novel experiment in levitated optomechanical systems as an example.

quant-ph↗
arXiv2018

Real-Time Kalman Filter: Cooling of an Optically Levitated Nanoparticle

We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The translational centre of mass motion along the optical axis of the trapped nanoparticle has been cooled by three orders of magnitude, from a temperature of 300K to a temperature of 162 +/- 15mK.

quant-ph↗
arXiv2018

A System for the Generation of Synthetic Wide Area Aerial Surveillance Imagery

The development, benchmarking and validation of aerial Persistent Surveillance (PS) algorithms requires access to specialist Wide Area Aerial Surveillance (WAAS) datasets. Such datasets are difficult to obtain and are often extremely large both in spatial resolution and temporal duration. This paper outlines an approach to the simulation of complex urban environments and demonstrates the viability of using this approach for the generation of simulated sensor data, corresponding to the use of wide area imaging systems for surveillance and reconnaissance applications. This provides a cost-effective method to generate datasets for vehicle tracking algorithms and anomaly detection methods. The system fuses the Simulation of Urban Mobility (SUMO) traffic simulator with a MATLAB controller and an image generator to create scenes containing uninterrupted door-to-door journeys across large areas of the urban environment. This `pattern-of-life' approach provides three-dimensional visual information with natural movement and traffic flows. This can then be used to provide simulated sensor measurements (e.g. visual band and infrared video imagery) and automatic access to ground-truth data for the evaluation of multi-target tracking systems.

cs.OH↗
arXiv2016

The role of entanglement in calibrating optical quantum gyroscopes

We consider the calibration of an optical quantum gyroscope by modeling two Sagnac interferometers, mounted approximately at right angles to each other. Reliable operation requires that we know the angle between the interferometers with high precision, and we show that a procedure akin to multi-position testing in inertial navigation systems can be generalized to the case of quantum interferometry. We find that while entanglement is a key resource within an individual Sagnac interferometer, its presence between the interferometers is a far more complicated story. The optimum level of entanglement depends strongly on the sought parameter values, and small but significant improvements may be gained from choosing states with the optimal amount of entanglement between the interferometers.

quant-ph↗
arXiv2016

Observing quantum chaos with noisy measurements and highly mixed states

A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\hbar$. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low purity states and to variations in the parameters of the system.

quant-ph↗
arXiv2016

Coupling rotational and translational motion via a continuous measurement in an optomechanical sphere

We consider a measurement of the position of a spot painted on the surface of a trapped nano-optomechanical sphere. The measurement extracts information about the position of the spot and in doing so measures a combination of the orientation and position of the sphere. The quantum back-action of the measurement entangles and correlates these two degrees of freedom. Such a measurement is not available for atoms or ions, and provides a mechanism to probe the quantum mechanical properties of trapped optomechanical spheres. In performing simulations of this measurement process we also test a numerical method introduced recently by Rouchon and collaborators for solving stochastic master equations. This method guarantees the positivity of the density matrix when the Lindblad operators for all simultaneous continuous measurements are mutually commuting. We show that it is both simpler and far more efficient than previous methods.

quant-ph↗
arXiv2016

Efficient estimation of probability of conflict between air traffic using Subset Simulation

This paper presents an efficient method for estimating the probability of conflict between air traffic within a block of airspace. Autonomous Sense-and-Avoid is an essential safety feature to enable Unmanned Air Systems to operate alongside other (manned or unmanned) air traffic. The ability to estimate probability of conflict between traffic is an essential part of Sense-and-Avoid. Such probabilities are typically very low. Evaluating low probabilities using naive Direct Monte Carlo generates a significant computational load. This paper applies a technique called Subset Simulation. The small failure probabilities are computed as a product of larger conditional failure probabilities, reducing the computational load whilst improving the accuracy of the probability estimates. The reduction in the number of samples required can be one or more orders of magnitude. The utility of the approach is demonstrated by modeling a series of conflicting and potentially conflicting scenarios based on the standard Rules of the Air.

eess.SY↗
arXiv2015

Efficient Quantum Filtering for Quantum Feedback Control

We discuss an efficient numerical scheme for the recursive filtering of diffusive quantum stochastic master equations. We show that the resultant quantum trajectory is robust and may be used for feedback based on inefficient measurements. The proposed numerical scheme is amenable to approximation, which can be used to further reduce the computational burden associated with calculating quantum trajectories and may allow real-time quantum filtering. We provide a two-qubit example where feedback control of entanglement may be within the scope of current experimental systems.

quant-ph↗
arXiv2013

Ideal gas behavior of a strongly-coupled complex (dusty) plasma

In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly-coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.

physics.plasm-ph↗
arXiv2011

Tracking shocked dust: state estimation for a complex plasma during a shock wave

We consider a two-dimensional complex (dusty) plasma crystal excited by an electrostatically-induced shock wave. Dust particle kinematics in such a system are usually determined using particle tracking velocimetry. In this work we present a particle tracking algorithm which determines the dust particle kinematics with significantly higher accuracy than particle tracking velocimetry. The algorithm uses multiple extended Kalman filters to estimate the particle states and an interacting multiple model to assign probabilities to the different filters. This enables the determination of relevant physical properties of the dust, such as kinetic energy and kinetic temperature, with high precision. We use a Hugoniot shock-jump relation to calculate a pressure-volume diagram from the shocked dust kinematics. Calculation of the full pressure-volume diagram was possible with our tracking algorithm, but not with particle tracking velocimetry.

physics.plasm-ph↗