A Single-Step Method for Over-the-Horizon Geolocation Using Importance Sampling

This paper investigates the geolocation for an over-the-horizon (OTH) transmitter observed by widely separated arrays. We propose a maximum likelihood (ML) based direct position determination (DPD) method to directly locate the transmitter in a single step by exploiting the position information embedded in azimuth angles. The Monte Carlo importance sampling (IS) technique is employed to find an approximate global solution to this DPD problem, where the importance function analogous to Gaussian distribution is derived. This enables the transmitter to be precisely located with low complexity in a noniterative manner. Additionally, we derive the Cramér–Rao bound (CRB) expression for the investigated problem. The simulation results corroborate the superior localization performance of the proposed method with respect to the conventional two-step approaches and the iterative DPD method.

Fundamental sensitivity bounds for quantum enhanced optical resonance sensors based on transmission and phase estimation

Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit (SNL). In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramér-Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity but a smaller degree of quantum enhancement than the transmission-based scheme. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions, probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.

Optimal Experimental Design for Inverse Identification of Conductive and Radiative Properties of Participating Medium

The conductive and radiative properties of participating medium can be estimated by solving an inverse problem that combines transient temperature measurements and a forward model to predict the coupled conductive and radiative heat transfer. The procedure, as well as the estimates of parameters, are not only affected by the measurement noise that intrinsically exists in the experiment, but are also influenced by the known model parameters that are used as necessary inputs to solve the forward problem. In the present study, a stochastic Cramér–Rao bound (sCRB)-based error analysis method was employed for estimation of the errors of the retrieved conductive and radiative properties in an inverse identification process. The method took into account both the uncertainties of the experimental noise and the uncertain model parameter errors. Moreover, we applied the method to design the optimal location of the temperature probe, and to predict the relative error contribution of different error sources for combined conductive and radiative inverse problems. The results show that the proposed methodology is able to determine, a priori, the errors of the retrieved parameters, and that the accuracy of the retrieved parameters can be improved by setting the temperature probe at an optimal sensor position.

Phase sensitivity of an $\operatorname{SU}(1,1)$ interferometer via product detection

We theoretically analyze the phase sensitivity of an $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.

Conditional and Unconditional Deterministic Bounds on the MSE of the Non-Uniform Linear Co-centered Orthogonal Loop and Dipole Array

The co-centered orthogonal loop and dipole (COLD) array exhibits some interesting properties, which makes it ubiquitous in the context of polarized source localization. In the literature, one can find a plethora of estimation schemes adapted to the COLD array. Nevertheless, their ultimate performance in terms the so-called threshold region of mean square error (MSE), have not been fully investigated. In order to fill this lack, we focus, in this paper, on conditional and unconditional bounds that are tighter than the well known Cramér-Rao Bound (CRB). More precisely, we give some closed form expressions of the McAulay-Hofstetter, the Hammersley-Chapman-Robbins, the McAulaySeidman bounds and the recent Todros-Tabrikian bound, for both the conditional and unconditional observation model. Finally, numerical examples are provided to corroborate the theoretical analysis and to reveal a number of insightful properties.

Hybrid Cramer-Rao Bound On Carrier And Sampling Frequency Offset Estimation For OFDM Systems In Rayleigh Fading Channels

For carrier frequency offset (CFO) and sampling (clock) frequency offset (SFO) estimation, the hybrid Cramer-Rao bound (HCRB) is developed when the CFO, SFO, information-bearing symbols are deterministic (non-random) and channel coefficients are random. Both noise and channel coefficients are complex Gaussian. For the HCRB to be applicable, it is necessary for deterministic parameters to be identifiable (uniquely determined). Some necessary identifiability conditions of some deterministic parameters are found and presented. The HCRB is dependent on the initial time instant. The HCRB is compared with some existing methods via simulation. Our results demonstrate that this bound is not tight enough. Further effort is needed to develop a tighter bound.

Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements

Finding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.