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In signal processing, frequency estimation is one of the most important tasks for enormous number of applications. Particle filtering has been implemented intensively for the purpose of frequency estimation and the results were found to be excellent for many cases, under different time-frequency representation of the signal and different particle filter implementations. This work presents an enhancement of frequency estimation by using a particle smoother (backward particle filter) to enhance the frequency estimates as compared to the forward particle filter (PF). Calculated from the short-time Fourier transforms (STFTs), the signal was analyzed in the frequency domain, acting as a measurement model of the PF framework. Simulation results exhibit the advantage of the particle smoother over the forward PF. Demonstrated via the frequency estimates from both filters, particle smoother delivers better tracking results than the forward PF under low noise levels.

This paper presents a new algorithm for adaptive resampling, called percentile-based resampling (PBR) in a sequential Bayesian filtering, i.e., particle filter (PF) in particular, to improve tracking quality of the frequency trajectories under noisy environments. Since the conventional resampling scheme used in the PF suffers from computational burden, resulting in less efficiency in terms of computation time and complexity as well as the real time applications of the PF. The strategy to remedy this issue is proposed in this work. After state updating, important high particle weights are used to formulate the pre-set percentile in each sequential iteration to create a new set of high quality particles for the next filtering stage. The number of particles after PBR remains the same as the original. To verify the effectiveness of the proposed method, we first evaluated the performance of the method via numerical examples to a complex and highly nonlinear benchmark system. Then, the proposed method was implemented for frequency estimation for two time-varying signals. From the experimental results, via three measurement metrics, our approach delivered better performance than the others. Frequency estimates obtained by our method were excellent as compared to the conventional resampling method when number of particles were identical. In addition, the computation time of the proposed work was faster than those recent adaptive resampling schemes in literature, emphasizing the superior performance to the existing ones., Frequency tracking; Frequency estimation; Bayesian filtering; Adaptive resampling; Particle filter; Markov chain Monte Carlo; Signal processing; Electrical engineering; Computer engineering

This paper is concerned with the improvement of the Dual Tone Multi Frequency (DTMF) identification where the signals were transmitted via real communication channels. The frequencies of the DTMF signals are tracked using particle filtering method, a method that rely on the numerical computation in approximating the posterior probability density function (PDF) of the underlying state parameters, to identify which pad was pressed at the transmitter end. We propose and implement the adaptive resampling to improve the performance of the DTMF identification. The method enhances the quality of resampling stage generating a better set of particles which will be used for posterior PDF of the tones of the DTMF signals. Results reveal the advantage of using the proposed method in comparison to the conventional resampling scheme.

Window functions are typically used in time-frequency (TF) signal analysis, especially in spectrogram calculation. In frequency estimation problems, most methods for solving such tasks rely on the spectrogram-based approach where the time-series of the signal is considered in the frequency domain via the short-time Fourier transform (STFT). Sequential Bayesian filtering h as b een o ne o f t he m ost p owerful methods for sequential estimation of time-varying parameters where the signal model and observation data are complicated in terms of nonliear/non-Gaussian assumptions. The method integrates mathematical and statistical properties of the signal in order to construct a posterior probability density functions of the interesting parameters. Therefore, when window function is applied in STFT, the statistical property of the transformed domain may be destroy, resulting in the movement of the frequency estimates according to the window type used in spectrogram calculation. Therefore, we investigate in this work the effect of windows on the accuracy of the sequential Bayesian filtering based frequency estimation. Simulation results show that window has some effect only when the noise level is high.

This work considers the estimation of the seismic events using a Bayesian filtering method, a multiple model particle filtering (MMPF) framework, in particular, from the noisy seismic records. According to the nonlinearity of the seismic signals, the nonlinear dynamical system can be used for the modelling of the signal. In geological studies, it is very important to accurately estimate the events from the recorded seismic signals, under noisy environment in particular since the signal is usually acquired usually under noisy conditions resulting in the difficulty in information extraction. This work proposes the MMPF, an effective filter in a sequential Monte Carlo method, in cooperated with the seismic wavelet model for the estimation of the seismic events under the noisy environments. To evaluate the performance of the method, a set of synthetic noisy signals with different numbers of events, noise levels, was created and used in the simulations. Results illustrates that the proposed MMPF can provide the excellent seismic event estimates under noisy environment.

Sequential Bayesian filtering methods have been previously used in dispersion curve tracking for long range sound propagation in the ocean. Modal frequency probability density functions were extracted for sound speed inversion. Here, we calculate modal arrival time densities, instead, and employ them for inversion for sediment sound speed and thickness and water column depth. Bayesian mode identification is performed to this end. We investigate two methods for describing the statistical errors in power spectra, which we use in the arrival time density calculation using normal modes. We then link these densities to the parameters of interest. The approaches are tested with synthetic data as well as data collected in the Gulf of Mexico. [Work supported by ONR.]

Iterative and sequential Bayesian filtering methods have been previously used in dispersion tracking for long range sound propagation in oceanic environments. In this work we combine previous approaches to develop an improved tracking methods, which will then be used to link the extracted time-frequency information to geoacoustic inversion. The main idea is that probability density functions and Maximum a Posteriori estimates computed for frequencies and arrival times via filtering are propagated "backwards" through sound propagation models for geoacoustic inversion and quantification of the uncertainty in the estimation process.

The goal of this work is to improve our knowledge of the ocean medium using physics of sound propagation and statistical signal processing. Two of the approaches we discuss are based on global and local optimization combined with sequential filtering. A third one falls under the category of direct (“exact”) methods. The first two approaches are based on the extraction and the association between paths/modes and detected arrivals and also produce posterior probability density functions, characterizing the uncertainty structure of modal/multipath arrivals. These are then propagated backwards through an acoustic model for posterior probability density function calculation of environmental parameters. A third method extends Stickler’s exact inverse approach, employing measurements of a reflection coefficient at low frequencies to obtain the sediment sound speed profile. We develop an approximation based on interpolation and a regularization approach. The former improves on results of a previous method for sol...

Bayesian methods provide a wealth of information on acoustic features of a propagation medium and the uncertainty surrounding their estimation. In previous work, we showed how sequential Bayesian (particle) filtering can be used to extract dispersion characteristics of a waveguide. Here, we utilize these characteristics for the estimation of geoacoustic properties of sediments. As expected, the method relies on accurate identification of modes. The effect of correct/erroneous mode identification on geoacoustic estimates is quantified and approaches are developed for robust modal recognition in conjunction with the particle filter. Additionally, the statistical behavior of the noise present in the data measurements is further investigated with more complex noise modeling leading to improved results. The approaches are validated with both synthetic and real data collected during the Gulf of Mexico Experiment. [Work supported by ONR.]

Iterative and sequential Bayesian filtering methods have been previously used in dispersion tracking for long range sound propagation in oceanic environments. The methods rely on accurate modeling of (i) the acoustic field in the frequency domain as a function of time and (ii) the statistical model governing the behavior of errors in the measured data. Normal distributions are typically used for the latter but may not necessarily be the most accurate models for the description of the data. We investigate alternative methods for describing the statistical errors in power spectra, which we then use for linking the extracted time-frequency information to geoacoustic inversion. Probability density functions computed for frequencies and arrival times via filtering are propagated “backwards” through sound propagation models for quantification of the uncertainty in the estimation process. [Work supported by ONR].