Unimodal Noise Research Articles

Auditory, tactile, and multimodal noise reduce balance variability

Auditory and somatosensory white noise can stabilize standing balance. However, the differential effects of auditory and tactile noise stimulation on balance are unknown. Prior work on unimodal noise stimulation showed gains in balance with white noise through the auditory and tactile modalities separately. The current study aims to examine whether multimodal noise elicits similar responses to unimodal noise. We recorded the postural sway of healthy young adults who were presented with continuous white noise through the auditory or tactile modalities and through a combination of both (multimodal condition) using a wearable device. Our results replicate previous work that showed that auditory or tactile noise reduces sway variability with and without vision. Additionally, we show that multimodal noise also reduces the variability of sway. Analysis of different frequency bands of sway is typically used to separate open-loop exploratory (< 0.3 Hz) and feedback-driven (> 0.3 Hz) sway. We performed this analysis and showed that unimodal and multimodal white noise affected postural sway variability similarly in both timescales. These results support that the sensory noise effects on balance are robust across unimodal and multimodal conditions and can affect both mechanisms of sway represented in the frequency spectrum. In future work, the parameters of acoustic/tactile manipulation should be optimized for the most effective balance stabilization, and multimodal therapies should be explored for older adults with typical age-related balance instabilities.

On GLRT-Based Detection of One-Sided Composite Signal in Unimodal Noise

Convexity properties of detection probability are investigated in generalized likelihood ratio test-based detection of one-sided composite signal corrupted by additive unimodal noise. It is shown that the detection probability of the corresponding threshold detector is a concave function of normalized signal power at low and high signal-to-noise ratio (SNR). For intermediate values of SNR, the behavior can be explicitly characterized based on the derivative of the logarithm of the channel noise density and the detector threshold. Optimal time-sharing strategies of average power-limited transmitters and jammers are established. Numerical examples are provided for Gaussian, Laplace, and Cauchy densities.

Can you hear/see me? Multisensory integration of signals does not always facilitate mate choice

Abstract Females of many species choose mates using multiple sensory modalities. Multimodal noise may arise, however, in dense aggregations of animals communicating via multiple sensory modalities. Some evidence suggests multimodal signals may not always improve receiver decision-making performance. When sensory systems process input from multimodal signal sources, multimodal noise may arise and potentially complicate decision-making due to the demands on cognitive integration tasks. We tested female túngara frog, Physalaemus (=Engystomops) pustulosus, responses to male mating signals in noise from multiple sensory modalities (acoustic and visual). Noise treatments were partitioned into three categories: acoustic, visual, and multimodal. We used natural calls from conspecifics and heterospecifics for acoustic noise. Robotic frogs were employed as either visual signal components (synchronous vocal sac inflation with call) or visual noise (asynchronous vocal sac inflation with call). Females expressed a preference for the typically more attractive call in the presence of unimodal noise. However, during multimodal signal and noise treatments (robofrogs employed with background noise), females failed to express a preference for the typically attractive call in the presence of conspecific chorus noise. We found that social context and temporal synchrony of multimodal signaling components are important for multimodal communication. Our results demonstrate that multimodal signals have the potential to increase the complexity of the sensory scene and reduce the efficacy of female decision making.

Multi-Bit &amp; Sequential Decentralized Detection of a Noncooperative Moving Target Through a Generalized Rao Test

We consider decentralized detection (DD) of an uncooperative moving target via wireless sensor networks (WSNs), measured in zero-mean unimodal noise. To address energy and bandwidth limitations, the sensors use multi-level quantizers. The encoded bits are then reported to a fusion center (FC) via binary symmetric channels. Herein, we propose a generalized Rao (G-Rao) test as a simpler alternative to the generalized likelihood ratio test (GLRT). Then, at the FC, a truncated one-sided sequential (TOS) test rule is considered in addition to the fixed-sample-size (FSS) manner. Further, the asymptotic performance of a trajectory-clairvoyant (multi-bit) Rao test is leveraged to develop an offline and per-sensor quantizer design. Detection gain measures are also introduced to assess resolution improvements. Simulations show the appeal of G-Rao test with respect to the GLRT, and the gain in detection by using multiple bits for quantization, as well as the advantage of the sequential detection approach.

Minimax Linear Estimation with the Probability Criterion under Unimodal Noise and Bounded Parameters

We consider a linear regression model with a vector of bounded parameters and a centered noise vector that has an uncertain unimodal distribution but known covariance matrix. We pose the minimax estimation problem for a linear combination of unknown parameters with the use of the probability criterion. The minimax estimate is determined as a result of minimizing a probability bound over the region of possible values of the variance and squared bias for all possible linear estimates. We establish that the resulting robust solution is less conservative in comparison with wider classes of distributions.

Confidence Analysis of Linear Unbiased Estimates under Uncertain Unimodal Noise Distributions

The estimation problem for a linear parametric function in a linear regression model with uncertain symmetric unimodal noise distributions and given noise covariances is solved. The quality of estimation is determined by the probability that the error exceeds specified limits. For taking the uncertainty into account, a minimax optimization problem is formulated. The main result of this paper is that the Gauss inequality defines a tight upper bound of the error probability for any linear unbiased estimate. The worst-case distribution of the noise vector is constructed by using a linear transformation of a Gaussian random vector and a uniform random variable. The estimate that is minimax with respect to the probability criterion coincides with the least-squares estimate. The obtained solution is illustrated by the example of estimating motion parameters for several hypotheses about noise distributions.

Multibit Decentralized Detection Through Fusing Smart and Dumb Sensors Based on Rao Test

We consider decentralized detection of an unknown signal corrupted by zero-mean unimodal noise via wireless sensor networks. We assume the presence of both smart and dumb sensors: the former transmit unquantized measurements, whereas the latter employ multilevel quantizations (before transmission through binary symmetric channels) in order to cope with energy and/or bandwidth constraints. The data are received by a fusion center, which relies on a proposed Rao test, as a simpler alternative to the generalized likelihood ratio test (GLRT). The asymptotic performance analysis of the multibit Rao test is provided and exploited to propose a (signal-independent) quantizer design approach by maximizing the noncentrality parameter of the test-statistic distribution. Since the latter is a nonlinear and nonconvex function of the quantization thresholds, we employ the particle swarm optimization algorithm for its maximization. Numerical results are provided to show the effectiveness of the Rao test in comparison to the GLRT and the boost in performance obtained by (multiple) threshold optimization. Asymptotic performance is also exploited to define detection gain measures allowing to assess gain arising from use of dumb sensors and increasing their quantization resolution.

The quaternion minimum error entropy algorithm with fiducial point for nonlinear adaptive systems

In this paper, we develop a kernel adaptive filter for quaternion domain data, based on information theoretic learning cost function which could be useful for quaternion based kernel applications of nonlinear filtering. The new algorithm is based on error entropy function with Fiducial point and is referred to as the quaternion minimum error entropy with fiducial point (QKMEEF) algorithm. In our previous work we developed quaternion kernel adaptive filter based on minimum error entropy referred to as the quaternion KMEE (QKMEE) algorithm [1]. Since entropy does not change with the mean of the distribution, the algorithm may converge to a set of optimal weights without having zero mean error. Traditionally, to make the zero mean output error, the output during testing session was biased with the mean of errors of training session. However, for non-symmetric or heavy tails error PDF the estimation of error mean is problematic. The minimum error entropy criterion, minimizes Renyi’s quadratic entropy of the error between the filter output and desired response or indirectly maximizing the error information potential. Here, the approach is applied to quaternions. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the Quaternion Minimum Error Entropy Algorithm with Fiducial points. Simulation results are used to show the behavior of the new algorithm (QKMEEF) when signal is non-Gaussian in presence of unimodal noise versus bi-modal noise distributions. Simulation results also show that the new algorithm Quat-KMEEF can track and predict the 4-Dimensional non-stationary process signals where there are correlations between components better than quadruple real-valued KMEEF and Quat-KLMS algorithms.

Generalized Rao Test for Decentralized Detection of an Uncooperative Target

We tackle distributed detection of a non-cooperative target with a Wireless Sensor Network (WSN). When the target is present, sensors observe an (unknown) deterministic signal with attenuation depending on the distance between the sensor and the (unknown) target positions, embedded in symmetricand unimodal noise. The Fusion Center (FC) receives quantized sensor observations through error-prone Binary Symmetric Channels (BSCs) and is in charge of performing a more-accurate global decision. The resulting problem is a two-sided parameter testing with nuisance parameters (i.e. the target position) present only under the alternative hypothesis. After introducing the Generalized Likelihood Ratio Test (GLRT) for the problem, we develop a novel fusion rule corresponding to a Generalized Rao (G-Rao) test, based on Davies' framework, to reduce the computational complexity. Also, a rationale for threshold-optimization is proposed and confirmed by simulations. Finally, the aforementioned rules are compared in terms of performance and computational complexity.

Cross-modal noise compensation in audiovisual words

Perceiving linguistic input is vital for human functioning, but the process is complicated by the fact that the incoming signal is often degraded. However, humans can compensate for unimodal noise by relying on simultaneous sensory input from another modality. Here, we investigated noise-compensation for spoken and printed words in two experiments. In the first behavioral experiment, we observed that accuracy was modulated by reaction time, bias and sensitivity, but noise compensation could nevertheless be explained via accuracy differences when controlling for RT, bias and sensitivity. In the second experiment, we also measured Event Related Potentials (ERPs) and observed robust electrophysiological correlates of noise compensation starting at around 350 ms after stimulus onset, indicating that noise compensation is most prominent at lexical/semantic processing levels.

Optimal Asymmetric Binary Quantization for Estimation Under Symmetrically Distributed Noise

Estimation of a location parameter based on noisy and binary quantized measurements is considered in this letter. We study the behavior of the Cramér-Rao bound as a function of the quantizer threshold for different symmetric unimodal noise distributions. We show that, in some cases, the intuitive choice of threshold position given by the symmetry of the problem, placing the threshold on the true parameter value, can lead to locally worst estimation performance.

One-Bit Decentralized Detection With a Rao Test for Multisensor Fusion

In this letter we propose the Rao test as a simpler alternative to the generalized likelihood ratio test (GLRT) for multisensor fusion. We consider sensors observing an unknown deterministic parameter with symmetric and unimodal noise. A decision fusion center (DFC) receives quantized sensor observations through error-prone binary symmetric channels and makes a global decision. We analyze the optimal quantizer thresholds and we study the performance of the Rao test in comparison to the GLRT. Also, a theoretical comparison is made and asymptotic performance is derived in a scenario with homogeneous sensors. All the results are confirmed through simulations.

Blind source estimation of FIR channels for binary sources: a grouping decision approach

This paper proposes a novel grouping decision approach for blind source estimation of FIR (finite impulse response) channels with binary sources. First, solvability is discussed for single-input systems and multi-input systems. Necessary and sufficient conditions for recoverability are derived. For single-input systems, a new deterministic algorithm based on grouping and decision is proposed to recover the source up to a delay. The algorithm is easy to implement and has several advantages. For instance, when the solvability conditions are satisfied, it can be applied to cases in which: (i) the channel has zeros on the unit circle or outside of the unit circle; (ii) there are fewer sensors than sources; (iii) the source is temporarily dependent. To improve noise tolerance and reduce computational cost, the algorithm is further elaborated for highly noisy channels and high-order FIR channels, respectively. For the channels with high unimodal noise, fewer peaks appear in the probability density function (pdf) of the outputs compared to the pdf of the outputs of channels with a higher SNR. After the peaks representing cluster centers are estimated using a maximum likelihood (ML) approach, the deterministic algorithm can be used. Similar to highly noisy channels, the algorithm is also effective for high-order, exponentially decaying channels after fewer cluster centers are estimated. Furthermore, blind source estimation for multi-input systems also can be carried out as with the case of single input systems. Two deflation algorithms are presented for temporarily dependent sources and i.i.d. sources. Based on the source estimation and deflation algorithms, the sources can be obtained one by one. Finally, the validity and performance of the algorithms are illustrated by several simulation examples.