Sequential joint signal detection and signal-to-noise ratio estimation

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.Comment: 5 pages, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 201

A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements

Multipath propagation causes major impairments to Global Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step

Covariate-assisted ranking and screening for large-scale two-sample inference

Two-sample multiple testing has a wide range of applications. The conventionalpractice first reduces the original observations to a vector of p-values and then chooses a cutoffto adjust for multiplicity. However, this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures.We introduce a new framework fortwo-sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power. A data-driven multiple-testing procedure is developed by employinga covariate-assisted ranking and screening (CARS) approach that optimally combines the informationfrom both the primary and the auxiliary variables. The proposed CARS procedureis shown to be asymptotically valid and optimal for false discovery rate control. The procedureis implemented in the R package CARS. Numerical results confirm the effectiveness of CARSin false discovery rate control and show that it achieves substantial power gain over existingmethods. CARS is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

Multisensor Poisson Multi-Bernoulli Filter for Joint Target-Sensor State Tracking

In a typical multitarget tracking (MTT) scenario, the sensor state is either assumed known, or tracking is performed in the sensor's (relative) coordinate frame. This assumption does not hold when the sensor, e.g., an automotive radar, is mounted on a vehicle, and the target state should be represented in a global (absolute) coordinate frame. Then it is important to consider the uncertain location of the vehicle on which the sensor is mounted for MTT. In this paper, we present a multisensor low complexity Poisson multi-Bernoulli MTT filter, which jointly tracks the uncertain vehicle state and target states. Measurements collected by different sensors mounted on multiple vehicles with varying location uncertainty are incorporated sequentially based on the arrival of new sensor measurements. In doing so, targets observed from a sensor mounted on a well-localized vehicle reduce the state uncertainty of other poorly localized vehicles, provided that a common non-empty subset of targets is observed. A low complexity filter is obtained by approximations of the joint sensor-feature state density minimizing the Kullback-Leibler divergence (KLD). Results from synthetic as well as experimental measurement data, collected in a vehicle driving scenario, demonstrate the performance benefits of joint vehicle-target state tracking.Comment: 13 pages, 7 figure

Polarization-based Tests of Gravity with the Stochastic Gravitational-Wave Background

The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-field, highly dynamical regimes. One such opportunity is the measurement of gravitational-wave polarizations. While general relativity predicts only two tensor gravitational-wave polarizations, general metric theories of gravity allow for up to four additional vector and scalar modes. The detection of these alternative polarizations would represent a clear violation of general relativity. The LIGO-Virgo detection of the binary black hole merger GW170814 has recently offered the first direct constraints on the polarization of gravitational waves. The current generation of ground-based detectors, however, is limited in its ability to sensitively determine the polarization content of transient gravitational-wave signals. Observation of the stochastic gravitational-wave background, in contrast, offers a means of directly measuring generic gravitational-wave polarizations. The stochastic background, arising from the superposition of many individually unresolvable gravitational-wave signals, may be detectable by Advanced LIGO at design-sensitivity. In this paper, we present a Bayesian method with which to detect and characterize the polarization of the stochastic background. We explore prospects for estimating parameters of the background, and quantify the limits that Advanced LIGO can place on vector and scalar polarizations in the absence of a detection. Finally, we investigate how the introduction of new terrestrial detectors like Advanced Virgo aid in our ability to detect or constrain alternative polarizations in the stochastic background. We find that, although the addition of Advanced Virgo does not notably improve detection prospects, it may dramatically improve our ability to estimate the parameters of backgrounds of mixed polarization.Comment: 24 pages, 20 figures; Accepted by PRX. This version includes major changes in response to referee comments and corrects an error in Eq. E