Performance Analysis of Gibbs Sampling for Bayesian Extracting Sinusoids

This paper involves problems of estimating parameters of sinusoids from white noisy data by using Gibbs sampling (GS) in a Bayesian framework. Modifications of its algorithm is tested on data generated from synthetic signals and its performance is compared with conventional estimators such as Maximum Likelihood(ML) and Discrete Fourier Transform (DFT) under a variety of signal to noise ratio (SNR) and different length of data sampling (N), regarding to Cramér-Rao lower bound (CRLB). All simulation results show its effectiveness in frequency and amplitude estimation of sinusoids.

Kalman Filter Implementation of Subglottal Impedance-Based Inverse Filtering to Estimate Glottal Airflow during Phonation

Subglottal Impedance-Based Inverse Filtering (IBIF) allows for the continuous, non-invasive estimation of glottal airflow from a surface accelerometer placed over the anterior neck skin below the larynx, which has been shown to be advantageous for the ambulatory monitoring of vocal function. However, during long-term ambulatory recordings over several days, conditions may drift from the laboratory environment where the IBIF parameters were initially estimated due to sensor positioning, skin attachment, and temperature, among other factors. Observation uncertainties and model mismatch may result in significant deviations in the glottal airflow estimates, but are very difficult to quantify in ambulatory conditions due to a lack of a reference signal. To address this issue, we propose a Kalman filter implementation of the IBIF filter, which allows for both estimating the model uncertainty and adapting the airflow estimates to correct for signal deviations. One-way ANOVA results from laboratory experiments using the Rainbow Passage indicate a an improvement on amplitude-based measures for PVH subjects compared to IBIF which shows a statistically difference with respect to the reference oral airflow (p=0.02,F=4.1). MFDR from PVH subjects is slightly different to the oral airflow when compared to IBIF (p=0.04, F=3.3). Other measures did not have significant differences with either Kalman or IBIF, with the exception of H1H2, whose performance deteriorates for both methods. Overall, both methods show similar flottal airflow measures, with the advantage of Kalman by improving amplitude estimation. Moreover, Kalman filter deviations from the IBIF output airflow might suggest a better representation of some fine details in the ground-truth glottal airflow signal. Other applications may take more advantage from the adaptation offered by the Kalman filter implementation.

Coherent demodulation of the two-level APSK signals with the symbol amplitude estimation

The study focuses on the algorithms for the coherent demodulation of the two-level amplitude phase-shift keyed signals with an estimate of the received symbol amplitude carried out by its relative comparison with the preceding symbol amplitude. Determining calibrated values of the symbol amplitudes in order to compare them with the preset threshold values is considered unnecessary in this case. Phase demodulation is implemented based on the phase detector of the multi-level phase-shift keyed signals. Symbol amplitudes are determined by the quadrature channels responses. Both analog and digital demodulation algorithms are considered. Simulation of the demodulation algorithm is carried out.

Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algorithms make assumptions that make them unsuitable for this 'coherent' setting, leaving only the textbook approach. We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint. They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates. Instead, they use block-encoding techniques to compute the estimate one bit at a time, performing all amplification via singular value transformation. These improved subroutines accelerate the performance of quantum Metropolis sampling and quantum Bayesian inference.

Amplitude estimation via maximum likelihood on noisy quantum computer

Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assuming the depolarization noise. We then formulate the problem as a two-parameters estimation problem with respect to the target amplitude parameter and the noise parameter. In particular we show that there exist anomalous target values, where the Fisher information matrix becomes degenerate and consequently the estimation error cannot be improved even by increasing the number of amplitude amplifications. The experimental demonstration shows that the proposed maximum likelihood estimator achieves quantum speedup in the number of queries, though the estimation error saturates due to the noise. This saturated value of estimation error is consistent to the theory, which implies the validity of the depolarization noise model and thereby enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.