Time-varying Filter Research Articles

Event-Based State Estimation With Variance-Based Triggering

An event-based state estimation scenario is considered where a sensor sporadically transmits observations of a scalar linear process to a remote estimator. The remote estimator is a time-varying Kalman filter. The triggering decision is based on the estimation variance: the sensor runs a copy of the remote estimator and transmits a measurement if the associated measurement prediction variance exceeds a tolerable threshold. The resulting variance iteration is a new type of Riccati equation with switching that corresponds to the availability or unavailability of a measurement and depends on the variance at the previous step. We study asymptotic properties of the variance iteration and, in particular, asymptotic convergence to a periodic solution.

Simultaneous Optimization of Acoustic Echo Reduction, Speech Dereverberation, and Noise Reduction against Mutual Interference

We propose an optimized speech enhancement method that combines acoustic echo reduction, speech dereverberation, and noise reduction in a unified framework. Normally, partial optimization of acoustic echo reduction, speech dereverberation, and noise reduction does not lead to total optimization. A cascade method of multiple functions causes mutual interference between these functions and degrades eventual speech enhancement performance. Unlike cascade methods, the proposed method combines all functions to optimize eventual speech enhancement performance based on a unified framework, which is also robust against the mutual interference problem. With the proposed method, in addition to time-invariant linear filters, time-varying filters are used to reduce residual reverberation, residual acoustic echo signal, and background noise signal which cannot be reduced using time-invariant filters. These time-invariant filters and time-varying filters are also optimized based on a unified likelihood function to avoid the mutual interference problem. By combining the time-invariant linear filters and the time-varying filters, the proposed method uses a local Gaussian model with a full-rank covariance matrix and a non-zero average vector as a probabilistic model of the microphone input signal. In the local Gaussian model, non-stationary characteristics of speech sources are considered to effectively enhance speech sources. Under this probabilistic model, all the parameters are optimized simultaneously based on the expectation-maximization algorithm and calculates a minimum mean squared error estimate of a desired signal. The experimental results show that the proposed method is superior to the cascade methods.

Parameter identification of a discretized biased noisy sinusoidal signal

A discrete time, on-line approach is proposed for the simultaneous identification of the frequency, the amplitude and the phase parameters in continuous noisy sinusoidal signals. The proposed technique takes the exact discretization of a continuous sinusoidal signal and generates exact computation formulas for the frequency, bias, amplitude and phase parameters, calculated in terms of quotients involving functions of the output and of some of its delayed values. The formula yields exact parameter calculations in the noiseless case, and it can be synthesized by means of time-varying filters whose outputs are obtained on-line. When the treated signal is affected by additive noises, a least squares-based “invariant filtering” is proposed, resulting in an enhancement of the signal to noise ratio of the factors conforming the basic algorithm. The scheme is proven and analysed by means of a laboratory experiment, a noise analysis and a comparison against other existing methods, where the proposed method shows accurate results with fast convergence rates.

Mode identification and extraction of broadband ultrasonic guided waves

Lamb waves have dispersion and multimodal characteristics, which are the major reasons for the complexity of their signals. A signal processing technique is established to extract individual dispersive waveforms from raw received Lamb wave signals, even when they interfere with each other in the time-frequency domain. In this technique, the prior knowledge of the dispersion characteristic is utilized for mode identification. On this basis, the propagation distances of concerned modes are estimated and ridge tracking is completed in the interfered neighboring area. Subsequently, an effective time-varying filter, the Vold-Kalman filter, is introduced to isolate these interfered wave modes. When each mode is extracted from the overall Lamb wave signal, accurate quantitative data on propagation characteristics such as energy, attenuation, amplitude, and reflection coefficients can be accurately estimated. The results illustrate a strategy for optimal design of Lamb wave inspections in either a pulse-echo or pitch-catch configuration.

Dynamic Signal Phase Distortion Using Coefficient-Modulated Allpass Filters

Recent work has shown that if the coefficients of a first-order allpass filter are modulated over time, it behaves as a dynamic Phase Distortion (PD) device. A key advantage of this arrangement is that the filter input and the modulation signal can, within stability constraints, be arbitrary. Furthermore, no heterodyning or interpolation, as used for the techniques of Adaptive PD and Adaptive FM, respectively, is required. This now broadens the palette of sound effects that allpass filters are capable of generating and opens up a new perspective through which they can be configured for sonic modification purposes. However, a rigorous analysis of this dynamic device is not available and the purpose of this paper is to draw on the theory of time-varying filters to thoroughly understand its properties in the time and frequency domains. The significant influence of filter topology on the transient behavior of the output is also investigated. Finally, a procedure for mapping from a desired PD function to a modulation signal is also illustrated. This can be applied to derive modulation functions that impart particular timbral properties to the input, and it is used to create examples demonstrating the capabilities of this new technique.

High-Purity Germanium Spectroscopy at Rates in Excess of <formula formulatype="inline"><tex Notation="TeX">$10^{6}$</tex></formula> Events/s

In gamma spectroscopy, a compromise must be made between energy resolution and event-rate capability. Some foreseen nuclear material safeguards applications require a spectrometer with energy resolution typical of high purity germanium (HPGe) detectors, operated at event rates up to and exceeding ${10^6}$ per second. We report the performance of an HPGe spectrometer system adapted to run under such conditions. Our system consists of a commercial semi-coaxial HPGe detector, a modified high-voltage-rail, resistive-feedback, charge-sensitive preamplifier and a continuous waveform digitizer. Digitized waveforms are analyzed offline with a novel time-variant trapezoidal filter algorithm. Several time-invariant trapezoidal filters are run in parallel and the slowest one not rejected by instantaneous pileup conditions is used to measure each pulse height. We have attained full-width-at-half-maximum energy resolution approximately 8 keV measured at 662 keV with $1.03 \times {10^6}$ per second incoming event rate and 39% throughput. An additional constraint on the width of the fast trigger filter removes a significant amount of rising edge pileup that passes the first pileup cut, reducing throughput to 25%. While better resolution has been reported by other authors, our throughput is an order of magnitude higher than any other reported HPGe system operated at such an event rate.

Robust time-varying filtering and separation of some nonstationary signals in low SNR environments

Conventional time-varying filtering is inefficient for severely spoiled signals because it requires discernible spectral content of the signal in time–frequency domain. Motivated by the time–frequency peak filtering (TFPF) algorithm, a robust time-varying filtering (RTVF) algorithm is proposed in this paper for the objectives of filtering and separating some nonstationary signals that contain strong noise. The performance of the TFPF based on windowed Wigner–Ville distribution is intrinsically limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time–frequency distribution, which allows a sinusoidal constraint on the signal׳s waveform. The bias analysis of the RTVF is presented for some nonstationary signals with time-varying amplitude. Based on derived bias expressions, a criterion of optimal window size selection for implementation purpose is obtained. The RTVF can successfully decompose some multi-component signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the initial IF estimate. Computer simulations verify the theoretical analysis and demonstrate that the RTVF algorithm can achieve desirable performance of filtering and separation in low SNR environments.

Robust Centralized Fusion Kalman Filters with Uncertain Noise Variances

This paper studies the problem of the designing the robust local and centralized fusion Kalman filters for multisensor system with uncertain noise variances. Using the minimax robust estimation principle, the centralized fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bound of noise variances. A Lyapunov approach is proposed for the robustness analysis and their robust accuracy relations are proved. It is proved that the robust accuracy of robust centralized fuser is higher than those of robust local Kalman filters. Specially, the corresponding steady-state robust local and centralized fusion Kalman filters are also proposed and the convergence in a realization between time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A Monte-Carlo simulation example shows the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5490 Full Text: PDF

The Realization of Time-Varying Filtering for Physiological Signals

Purpose: We do it to eliminate the influence of clutters to the whole of system, improve identification for waveform, and then make ready for the next analysis. Method: We recommend time-varying filtering theory, make this theory as the basis to delimit experimental indicators for the specific requirements, then used LabVIEW2011`s paramount means packet for programming. Result: We have successfully used the varying filtering method to carry out clutters, improved the accuracy of the signal waveforms. Conclusion: Using the method described above can achieve the goal for the optimization on the heart sound signal processing, and also provide the reliable indemnification for analysis from the root.

Periodically Time-Varying ${\cal H}_{\infty}$ Memory Filter Design for Discrete-Time LTI Systems With Polytopic Uncertainty

This technical note focuses on the development of a general periodically time-varying memory filter (PTVMF) to improve the robust <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\cal H}_{\infty}$</tex></formula> filtering performance for discrete-time linear time-invariant (LTI) systems with polytopic parameter uncertainties. A sufficient condition to design the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\cal H}_{\infty}$</tex></formula> -PTVMF is given in terms of convex optimizations expressed as linear matrix inequalities (LMIs). Finally, examples demonstrate its potential less conservatism.

Quantification of signal and noise in two-way transmitted wavefields to improve well ties in Cooper Basin, Australia

Permian coal beds at 2400–2900 m depth in Cooper Basin, Australia have normal-incident reflection coefficient values as large as [Formula: see text]. If internal multiples are included in synthetic seismograms, excellent correlations exist between the synthetic seismogram and seismic, even when more than 50 coal beds are present. However, neither the synthetic seismogram nor the seismic tie the well-log lithologic boundaries because the incident wavefield that strikes a lithologic boundary and returns to the surface contains a signal wavelet followed by high-amplitude noise, which are interbed multiple reflections. Because the spectra of the signal and noise coda at a given two-way time normally do not overlap, time-varying Gaussian filters applied to the near-offset stack enhance the signal and suppress the noise coda. After filtering, the apparent time delay of reflections introduced by the coal beds is removed with variable time shifts (time compression), based on the estimated time-varying signal wavelets. The two-step process of low-pass filtering and compression yields seismic events that successfully tie the lithologic boundaries in the borehole, although with limited resolution. Our preliminary tests on a seismic line indicate that the horizon event associated with the base of a 500-m-thick coal sequence is more coherently imaged with our processing than with conventional processing.

Frequency Locking of an Optical Cavity Using a Time-Varying Kalman Filtering Approach

The cavity frequency locking problem, which arises in the field of quantum optics, involves matching the resonant frequency of an optical cavity to that of an incoming laser. Although this problem is investigated using linear control techniques for small perturbations, in this brief, we address the nonlinear control problem of frequency locking an optical cavity. Models of the measurement nonlinearities inherent in optical cavities are derived using a singular perturbation approach and instantaneous bounds are placed on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is then determined at each time step by solving two high-order polynomial equations. Based on a reduced-order model of the cavity, a time-varying Kalman filter is designed and simulation results are presented to validate our controller on a full-model of the cavity in the nonlinear region of operation.

Dynamic mass measurement in checkweighers using a discrete time-variant low-pass filter

Conveyor belt type checkweighers are complex mechanical systems consisting of a weighing sensor (strain gauge load cell, electrodynamically compensated load cell), packages (of different shapes, made of different materials) and a transport system (motors, gears, rollers). Disturbances generated by the vibrating parts of such a system are reflected in the signal power spectra in a form of strong spectral peaks, located usually in the lower frequency range. Such low frequency components overlap in the frequency domain with the useful signal and it is very difficult to eliminate them. The conventional way of suppressing disturbances is via low-pass filtering of the signal obtained from the load cell. However, if the speed of the conveyor belt is high, the response of the applied filter may not settle fast enough to enable accurate weighing of objects in motion, i.e., without stopping them on the weighing conveyor. Since attempts to overcome this problem using classical linear time-invariant low-pass filtering fail for high belt speeds, the paper presents and verifies experimentally a new approach, based on time-variant low-pass filtering. It is shown that, when properly tuned, the proposed time-variant filter fulfills the measurement accuracy requirements for a wide range of operating conditions.

Finite-horizon H∞ filtering for time-varying delay systems with randomly varying nonlinearities and sensor saturations

This paper mainly focuses on the H∞ filtering problem for a class of discrete time-varying systems with delays and randomly varying nonlinearities and sensor saturations. Two sets of binary switching sequences taking values of 1 and 0 are introduced to account for the stochastic phenomena of nonlinearities and sensor saturations which occur and influence the dynamics of the system in a probabilistic way. To further reflect the realities of transmission failure in the measurement, missing observation case is also considered simultaneously. By appropriately constructing a time-varying Lyapunov function and utilizing the stochastic analysis technique, sufficient criteria are presented in terms of a set of recursive linear matrix inequalities (RLMIs) under which the filtering error dynamics achieves the prescribed H∞ performance over a finite horizon. Moreover, at each time point k, the time-varying filter parameters can be solved iteratively according to the explicit solutions of the RLMIs. Finally, a numerical simulation is exploited to demonstrate the effectiveness of the proposed filter design scheme.

Robust weighted fusion Kalman filters for multisensor time-varying systems with uncertain noise variances

This paper addresses the design of robust weighted fusion Kalman filters for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the five robust weighted fusion time-varying Kalman filters are presented based on the worst-case conservative systems with the conservative upper bounds of noise variances. The actual filtering error variances or their traces of each fuser are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. A Lyapunov equation approach is presented to prove the robustness of the robust Kalman filters. The concept of robust accuracy is presented and the robust accuracy relations among the local and fused robust Kalman filters are proved. Specially, the corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization of the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Road Slope Estimation in Bicycles without Torque Measurements

Electrically Power Assisted Cycles (EPACs) have been gaining increasing attention worldwide during the past few years. The delivery of a good assistance during inclines makes or destroys an EPAC. This paper addresses the low-cost estimation of road slope on bicycle without pedaling torque measurement. Two estimation algorithms are discussed. A full 6 Degrees of Freedom kinematic Extended Kalman Filter and a simpler, more cost-effective 2 DoF Kalman filter based on the longitudinal kinematic model. The proposed reduced-sensor algorithm is shown to be very accurate during straight running; however it is affected by errors during cornering. This issue is addressed by augmenting the filter with a curve correction algorithm. The curve correction algorithm, based on a time-varying low pass filter is detailed and validated on experimental data, comparing the estimated road slope against cartographic data.

Estimation of Q factors from reflection seismic data for a band-limited and stabilized inverse Q filter driven by an average-Q model

Reliable Q estimation is desirable for model-based inverse Q filtering to improve seismic resolution. On the one hand, conventional methods estimate Q from the amplitude spectra or frequency variations of individual wavelets at different depth (or time) levels, which is vulnerable to the effects of spectral interference and ambient noise. On the other hand, most inverse Q filtering algorithms are sensitive to noise, in order not to boost them, sometimes at the expense of degrading compensation effect. In this paper, the average-Q values are obtained from reflection seismic data based on the Gabor transform spectrum of a seismic trace. We transform the 2-D time-variant frequency spectrum into the 1-D spectrum, and then estimate the average-Q values based on the amplitude attenuation and compensation functions, respectively. Driven by the estimated average-Q model, we also develop a modified inverse Q filtering algorithm by incorporating a time-variant bandpass filter (TVBF), whose high cut off frequency follows a hyperbola along the traveltime from a specified time. Finally, we test this modified inverse Q filtering algorithm on synthetic data and perform the Q estimation procedure on a real reflection seismic data, followed by applying the modified inverse Q filtering algorithm. The synthetic data test and the real data example demonstrate that the algorithm driven by average-Q model may enhance the seismic resolution, without degrading the signal-to-noise ratio.

Two empirical methods for improving the performance of statistical multirate high-resolution signal reconstruction

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition- and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the low-resolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.

Covariance Intersection Fusion Robust Time-Varying Kalman Filter for Two-Sensor System with Uncertain Noise Variances

This paper investigates the problem of designing covariance intersection fusion robust time-varying Kalman filter for two-sensor time-varying system with uncertain noise variances. Using the minimax robust estimation principle, the local and covariance intersection (CI) fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. Their robustness is proved based on the proposed Lyapunov equation, and the robust accuracy of time-varying CI fuser is higher than that of each local robust time-varying Kalman filter. A two-sensor tracking system simulation verifies the robustness and robust accuracy relations.

Closed-Loop Performance Analysis of Algebraic Estimators

The closed-loop behavior of algebraic estimators is studied in this work via the simulation of an example. The algebraic estimators can be implemented as time-varying filters that gives an estimation of derivatives of the input signal. One considers here the inverted pendulum over a car as a representant of a class of systems with state \(x= (y^{\top }, {\dot{y}}^{\top })^{\top }\), where \(y \in \mathbb {R}^m\) is the output and \(\dot{y} \in \mathbb {R}^m\) is its time derivative. For this class of systems, which includes several important mechanical systems, the estimation of the state relies on the determination of the derivative of the output. The case study that is presented in this paper indicates many interesting properties of those estimators and allows one to state many conjectures that can be considered in a future research. This work includes also a theoretical contribution that allows to compute a bound of the error of the second-order algebraic estimator. Furthermore, it is shown that all estimators that respects this bound will assure closed-loop stability in the context of the separation principle for this particular class of systems.