The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches

The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95% confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1%), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black-hole binaries with circular orbits.Comment: Accepted for publication by the Monthly Notices of the Royal Astronomical Societ

Optimising magnetic resonance sampling patterns for parametric characterisation.

Sampling strategies are often central to experimental design. Choosing efficiently which data to acquire can improve the estimation of parameters and reduce the acquisition time. This work is focused on designing optimal sampling patterns for Nuclear Magnetic Resonance (NMR) applications, illustrated with respect to the best estimate of the parameters characterising a lognormal distribution. Lognormal distributions are commonly used as fitting models for distributions of spin-lattice relaxation time constants, spin-spin relaxation time constants and diffusion coefficients. A method for optimising the choice of points to be sampled is presented which is based on the Cramér-Rao Lower Bound (CRLB) theory. The method's capabilities are demonstrated experimentally by applying it to the problem of estimating the emulsion droplet size distribution from a pulsed field gradient (PFG) NMR diffusion experiment. A difference of <5% is observed between the predictions of CRLB theory and the PFG NMR experimental results. It is shown that CLRB theory is stable down to signal-to-noise ratios of ∼10. A sensitivity analysis for the CRLB theory is also performed. The method of optimizing sampling patterns is easily adapted to distributions other than lognormal and to other aspects of experimental design; case studies of optimising the sampling scheme for a fixed acquisition time and determining the potential for reduction in acquisition time for a fixed parameter estimation accuracy are presented. The experimental acquisition time is typically reduced by a factor of 3 using the proposed method compared to a constant gradient increment approach that would usually be used

Robust Power Allocation for Integrated Visible Light Positioning and Communication Networks

Integrated visible light positioning and communication (VLPC), capable of combining advantages of visible light communications (VLC) and visible light positioning (VLP), is a promising key technology for the future Internet of Things. In VLPC networks, positioning and communications are inherently coupled, which has not been sufficiently explored in the literature. We propose a robust power allocation scheme for integrated VLPC Networks by exploiting the intrinsic relationship between positioning and communications. Specifically, we derive explicit relationships between random positioning errors, following both a Gaussian distribution and an arbitrary distribution, and channel state information errors. Then, we minimize the Cramer-Rao lower bound (CRLB) of positioning errors, subject to the rate outage constraint and the power constraints, which is a chance-constrained optimization problem and generally computationally intractable. To circumvent the nonconvex challenge, we conservatively transform the chance constraints to deterministic forms by using the Bernstein-type inequality and the conditional value-at-risk for the Gaussian and arbitrary distributed positioning errors, respectively, and then approximate them as convex semidefinite programs. Finally, simulation results verify the robustness and effectiveness of our proposed integrated VLPC design schemes.Comment: 13 pages, 15 figures, accepted by IEEE Transactions on Communication

A Graph-based Algorithm for Robust Sequential Localization Exploiting Multipath for Obstructed-LOS-Bias Mitigation

This paper presents a factor graph formulation and particle-based sum-product algorithm (SPA) for robust sequential localization in multipath-prone environments. The proposed algorithm jointly performs data association, sequential estimation of a mobile agent position, and adapts all relevant model parameters. We derive a novel non-uniform false alarm (FA) model that captures the delay and amplitude statistics of the multipath radio channel. This model enables the algorithm to indirectly exploit position-related information contained in the MPCs for the estimation of the agent position. Using simulated and real measurements, we demonstrate that the algorithm can provide high-accuracy position estimates even in fully obstructed line-of-sight (OLOS) situations, significantly outperforming the conventional amplitude-information probabilistic data association (AIPDA) filter. We show that the performance of our algorithm constantly attains the posterior Cramer-Rao lower bound (PCRLB), or even succeeds it, due to the additional information contained in the presented FA model.Comment: corrected small errors, changed titl

The Recursive Form of Error Bounds for RFS State and Observation with Pd<1

In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework of the finite set statistics for the first time. The number of tracking algorithms with set-valued observations and state of targets is increased sharply recently. Nevertheless, the bound for these algorithms has not been fully discussed. Treating the measurement as set, this bound can be applied when the probability of detection is less than unity. Moreover, the state is treated as set, which is singleton or empty with certain probability and accounts for the appearance and the disappearance of the targets. When the existence of the target state is certain, our bound is as same as the most accurate results of the bound with probability of detection is less than unity in the framework of random vector statistics. When the uncertainty is taken into account, both linear and non-linear applications are presented to confirm the theory and reveal this bound is more general than previous bounds in the framework of random vector statistics.In fact, the collection of such measurements could be treated as a random finite set (RFS)

Simultaneous Target and Multipath Positioning

<p>In this work, we present the Simultaneous Target and Multipath Positioning (STAMP) technique to jointly estimate the unknown target position and uncertain multipath channel parameters. We illustrate the applications of STAMP for target tracking/geolocation problems using single-station hybrid TOA/AOA system, monostatic MIMO radar and multistatic range-based/AOA based localization systems. The STAMP algorithm is derived using a recursive Bayesian framework by including the target state and multipath channel parameters as a single random vector, and the unknown correspondence between observations and signal propagation channels is solved using the multi-scan multi-hypothesis data association. In the presence of the unknown time-varying number of multipath propagation modes, the STAMP algorithm is modified based on the single-cluster PHD filtering by modeling the multipath parameter state as a random finite set. In this case, the target state is defined as the parent process, which is updated by using a particle filter or multi-hypothesis Kalman filter. The multipath channel parameter is defined as the daughter process and updated based on an explicit Gaussian mixture PHD filter. Moreover, the idenfiability analysis of the joint estimation problem is provided in terms of Cramér-Rao lower bound (CRLB). The Fisher information contributed by each propagation mode is investigated, and the effect of Fisher information loss caused by the measurement origin uncertainty is also studied. The proposed STAMP algorithms are evaluated based on a set of illustrative numeric simulations and real data experiments with an indoor multi-channel radar testbed. Substantial improvement in target localization accuracy is observed.</p>Dissertatio

Higher order asymptotic inference in remote sensing of oceanic and planetary environments

Thesis (Ph. D. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 223-230).An inference method based on higher order asymptotic expansions of the bias and covariance of the Maximum Likelihood Estimate (MLE) is used to investigate the accuracy of parameter estimates obtained from remote sensing measurements in oceanic and planetary environments. We consider the problems of (1) planetary terrain surface slope estimation, (2) Lambertian surface orientation and albedo resolution and (3) passive source localization in a fluctuating waveguide containing random internal waves. In these and other applications, measurements are typically corrupted by signal-independent ambient noise, as well as signal-dependent noise arising from fluctuations in the propagation medium, relative motion between source and receiver, scattering from rough surfaces, propagation through random inhomogeneities, and source incoherence. We provide a methodology for incorporating such uncertainties, quantifying their effects and ensuring that statistical biases and errors meet desired thresholds. The method employed here was developed by Naftali and Makris[84] to determine necessary conditions on sample size or Signal to Noise Ratio (SNR) to obtain estimates that attain minimum variance, the Cramer-Rao Lower Bound (CRLB), as well as practical design thresholds. These conditions are derived by first expanding the bias and covariance of the MLE in inverse orders of sample size or SNR, where the firstorder covariance term is the CRLB. The necessary sample sizes and SNRs are then computed by requiring that (i) the first-order bias and second-order covariance terms are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. Analytical expressions have been derived for the asymptotic orders of the bias and covariance of the MLE obtained from general complex Gaussian vectors,[68, 109] which can then be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) they allow for both the mean and variance of the measurement to be functions of the estimation parameters, as is the case in the presence of signal-dependent noise. In the first part of this thesis, we investigate the problem of planetary terrain surface slope estimation from satellite images. For this case, we consider the probability distribution of the measured photo count of natural sunlight through a Charge- Coupled Device (CCD) and also include small-scale albedo fluctuation and atmospheric haze, besides signal-dependent (or camera shot) noise and signal-independent (or camera read) noise. We determine the theoretically exact biases and errors inherent in photoclinometric surface slope and show when they may be approximated by asymptotic expressions for sufficiently high sample size. We then determine the sample sizes necessary to yield surface slope estimates that have tolerable errors. We show how small-scale albedo variability often dominates biases and errors, which may become an order of magnitude larger than surface slopes when surface reflectance has a weak dependence on surface tilt. The method described above is also used to determine the errors of Lambertian surface orientation and albedo estimates obtained from remote multi-static acoustic, optical, radar or laser measurements of fluctuating radiance. Such measurements are typically corrupted by signal-dependent noise, known as speckle, which arises from complex Gaussian field fluctuations. We find that single-sample orientation estimates have biases and errors that vary dramatically depending on illumination direction measurement diversity due to the signal-dependent nature of speckle noise and the nonlinear relationship between surface orientation, illumination direction and fluctuating radiance. We also provide the sample sizes necessary to obtain surface orientation and albedo estimates that attain desired error thresholds. Next, we consider the problem of source localization in a fluctuating ocean waveguide containing random internal waves. Propagation through such a fluctuating environment leads to both the mean and covariance of the received acoustic field being parameter-dependent, which is typically the case in practice. We again make use of the new expression for the second-order covariance of the multivariate Gaussian MLE,[68 which allows us to take advantage of the parameter dependence in both the mean and the variance to obtain more accurate estimates. The degradation in localization accuracy due to scattering by internal waves is quantified by computing the asymptotic biases and variances of source localization estimates. We show that the sample sizes and SNRs necessary to attain practical localization thresholds can become prohibitively large compared to a static waveguide. The results presented here can be used to quantify the effects of environmental uncertainties on passive source localization techniques, such as matched-field processing (MFP) and focalization. Finally, a method is developed for simultaneously estimating the instantaneous mean velocity and position of a group of randomly moving targets as well as the respective standard deviations across the group by Doppler analysis of acoustic remote sensing measurements in free space and in a stratified ocean waveguide. It is shown that the variance of the field scattered from the swarm typically dominates the rangevelocity ambiguity function, but cross-spectral coherence remains and enables high resolution Doppler velocity and position estimation. It is shown that if pseudo-random signals are used, the mean and variance of the swarms' velocity and position can be expressed in terms of the first two moments of the measured range-velocity ambiguity function. This is shown analytically for free space and with Monte-Carlo simulations for an ocean waveguide. It is shown that these expressions can be used to obtain accurate, with less than 10% error, of a large swarm's instantaneous velocity and position means and standard deviations for long-range remote sensing applications.by loannis Bertsatos.Ph.D.in Ocean Engineerin