Tracking noisy limit cycle oscillation with nonlinear filters

For engineering systems, the dynamic state estimates provide valuable information for the detection and prediction of failure due to noise and vibration. From this perspective, nonlinear filtering techniques are applied to the problem of state estimation of dynamical systems undergoing noisy limit cycle oscillation. Specifically, the extended Kalman filter, ensemble Kalman filter and particle filter are used to track the limit cycle oscillations of a Duffing oscillator using noisy observational data. The noisy limit cycle oscillations feature highly non-Gaussian trends. The efficiency and limitations of the extended Kalman filter, ensemble Kalman filter and particle filter in tracking limit cycle oscillations are examined with respect to the model and measurement noise and sparsity of measurement data. For the limit cycle oscillations considered here, it is demonstrated that the ensemble Kalman filter and particle filter outperform the extended Kalman filter in the presence of sparse observational data or strong measurement noise. For moderate measurement noise and frequent measurement data, the ensemble Kalman filter and particle filter perform equally well in comparison to the extended Kalman filter.     

A new microphone system for near whispering

A new microphone system was developed to monitor the human voice near the microphone in a noisy environment. The system is equipped with two special functions in addition to the usual microphone functions: reduction of air-blow effects by the mouth and focused reception to a sound source. A wind filter was developed to reduce the air-blow effects from the mouth during speaking. This filter is a plate perforated by an array of small holes; the method used to design the filter is also presented. To achieve focused reception, four microphones were used in conjunction with a new signal-processing method. The proposed signal-processing method effectively increases the directivity in the desired direction. Additionally, it provides the system with focusing on the source since the source is located adjacent to the system. A prototype of the proposed system was fabricated and subjected to performance tests. The results showed that air-blow effects can be reduced by up to 20 dB and the directional gain is more than 4 dB. The proposed microphone system shows such good performance that it can be used in mobile phones for whispering communication.     

A survey of numerical methods for nonlinear filtering problems

The main goal of filtering is to obtain, recursively in time, good estimates of the state of a stochastic dynamical system based on noisy partial observations of the same. In settings where the signal/observation dynamics are significantly nonlinear or the noise intensities are high, an extended Kalman filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, can perform quite poorly: it may require very frequent re-initializations and in some situations may even diverge. The theory of nonlinear filtering addresses these difficulties by considering the evolution of the conditional distribution of the state of the system given all the available observations, in the space of probability measures. We survey a variety of numerical schemes that have been developed in the literature for approximating the conditional distribution described by such stochastic evolution equations; with a special emphasis on an important family of schemes known as the particle filters. A numerical study is presented to illustrate that in settings where the signal/observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended Kalman filter.     

Evaluation of a noise reduction system for the assessment of click-evoked otoacoustic emissions

A recently proposed noise reduction system intended to facilitate the assessment of click-evoked otoacoustic emission (CEOAE) in noisy environments [Comput. Biol. Med. 30, 341 (2000)] is evaluated using 13 normally hearing ears and 9 ears with a sensorineural hearing loss. The noise reduction system is based on an adaptive noise canceller design using an additional noise-only reference microphone and intended to reduce externally generated noise. The system is tested in quiet and at different levels of white noise. The three main design parameters of the noise reduction system (adaptation time constant, length of the adaptive filter, and position of the noise reference microphone) are varied systematically in different experiments. With the noise reduction system active, CEOAE can be assessed correctly at noise levels which are 5 to 9 dB higher than without the noise reduction system. For the range of adaptation time constants considered (65.6 to 656 ms), no statistically significant effect on the amount of noise reduction is observed. Noise reduction is highest when the reference microphone is positioned close to the ear probe. Using this reference microphone position and adaptive filters of 6.56 ms in length, average noise reductions of 7.17 to 8.50 dB are achieved.     

Control of epileptiform spikes based on nonlinear unscented Kalman filter

A new control strategy based on nonlinear unscented Kalman filter(UKF) is proposed for a neural mass model that serves as a model for simulating real epileptiform stereo-electroencephalographic (SEEG) signals. The UKF is used as an observer to estimate the state from the noisy measurement because it has been proved to be effective for state estimation of nonlinear systems. A UKF controller is constructed via the estimated state and is illustrated to be effective for epileptiform spikes suppression of aforementioned model by numerical simulations.     

Estimating the state of large spatio-temporally chaotic systems

We consider the estimation of the state of a large spatio-temporally chaotic system from noisy observations and knowledge of a system model. Standard state estimation techniques using the Kalman filter approach are not computationally feasible for systems with very many effective degrees of freedom. We present and test a new technique (called a Local Ensemble Kalman Filter), generally applicable to large spatio-temporally chaotic systems for which correlations between system variables evaluated at different points become small at large separation between the points.     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

Passive tracking of a moving source by a single observer in shallow water

Tracking of a moving source (MS) in shallow water is analyzed. The noisy observations of bearing, β, and any two time delays, τ₁ and τ₂, are made by a single observer, as opposed to spatially separated observers. Here, the time delays, τ₁ and τ₂, are, respectively, the differences in arrival times between the surface reflected path and direct path signals, and between the bottom reflected path and direct path signals [1]. The estimation process of MS kinematics is greatly aided by the two time delay measurements. These measurements impart consistency to the observation equations at each instant of time. In contrast to noisy bearings-only motion analysis, tracking is performed in a three-dimensional frame with concomitant advantages. Principally, the unwieldy requirement for a velocity change, anterior to convergence of the Kalman filter, is eliminated. The convergence time for the filter is greatly diminished. Furthermore, the filter displays a low operational threshold. Its stability is maintained when mismodeling exists, either in the observation or in the kinematical models.     

基于音视频信息融合的目标检测与跟踪算法

针对单一视觉跟踪算法易受遮挡影响的缺陷,提出一种基于音视频信息融合的目标检测与跟踪算法。整个算法框架包括视频检测与跟踪、声源定位、音视频信息融合跟踪3个模块。视频检测与跟踪模块采用YOLOv5m算法作为视觉检测的框架,使用无迹卡尔曼滤波和匈牙利算法实现多目标的跟踪与匹配;声源定位模块采用十字型麦克风阵列获取音频信息,结合各麦克风接收信号的时延计算声源方位;音视频信息融合跟踪模块构建音视频似然函数和音视频重要性采样函数,采用重要性粒子滤波作为音视频融合跟踪的算法,实现对目标的跟踪。在室内复杂环境下对算法性能进行测试,结果表明该算法跟踪准确率达到90.68%,相较于单一模态算法具有更好的性能。     

A Nonlinear Maximum Correntropy Information Filter for High-Dimensional Neural Decoding

Neural signal decoding is a critical technology in brain machine interface (BMI) to interpret movement intention from multi-neural activity collected from paralyzed patients. As a commonly-used decoding algorithm, the Kalman filter is often applied to derive the movement states from high-dimensional neural firing observation. However, its performance is limited and less effective for noisy nonlinear neural systems with high-dimensional measurements. In this paper, we propose a nonlinear maximum correntropy information filter, aiming at better state estimation in the filtering process for a noisy high-dimensional measurement system. We reconstruct the measurement model between the high-dimensional measurements and low-dimensional states using the neural network, and derive the state estimation using the correntropy criterion to cope with the non-Gaussian noise and eliminate large initial uncertainty. Moreover, analyses of convergence and robustness are given. The effectiveness of the proposed algorithm is evaluated by applying it on multiple segments of neural spiking data from two rats to interpret the movement states when the subjects perform a two-lever discrimination task. Our results demonstrate better and more robust state estimation performance when compared with other filters.     

Kalman filtering for reliable estimation of BBB permeability

INTRODUCTION: The blood-brain barrier (BBB) plays an important role in the pathophysiology of a number of central nervous system disorders. In the past, a number of laboratory techniques have been proposed to quantify permeability coefficient ki, an important index of barrier function. Recently, magnetic resonance imaging (MRI) has been used to estimate ki based on graphical plot technique. The MR technique was found to be in good agreement with the gold standard, quantitative autoradiography (QAR). However, a reduced image signal-to-noise ratio, among other factors such as partial volume effects, did not allow reliable estimation of permeability coefficients. This proof-of-principle study proposes the use of Kalman filter as a filtering technique for a reliable estimation of permeability coefficients. The results are compared to those obtained using the Wiener filter technique. MATERIALS AND METHODS: MRI experiments were performed in Wistar rats (N=2) using a 4.7-T Bruker Biospec MR system (Bruker Biospin, Billerica, MA). After acquiring localizer images, T2-weighted diffusion-weighted imaging images were acquired. Finally, a rapid T1 mapping protocol was implemented to acquire one pre-gadolinium diethylenetriamine pentaacetic acid baseline data set followed by postinjection data sets at 3-min intervals for 45 min. Data were postprocessed with and without the application of Kalman and Wiener filters to obtain an estimate of ki. RESULTS AND DISCUSSION: Comparing T1 maps, Patlak plots and permeability maps with and without the Kalman filtering presented several interesting observations. Kalman-filtered Patlak plots, compared to nonfiltered plots, showed that discrete data points on the plot were closer to the line fit. The number of time points used for the construction of the graphical plot had no effect on permeability coefficient estimates when the Kalman filter was used. A box-and-whiskers plot showed longer Y-error bars for nonfiltered and Wiener data compared to Kalman-filtered data. These observations suggest that it may be possible to obtain reliable permeability coefficient estimates in a short study time by applying the Kalman filter to the data. Future work involves investigating the application of this filter on a large-sample-size animal study and evaluating the role of partial volume effects on BBB permeability estimation.     

State and parameter estimation in stochastic dynamical models

This paper derives generalized maximum likelihood estimates of state and model parameters of a stochastic dynamical model. In contrast to previous studies, the change in background distribution due to changes in model parameters is taken into account. An ensemble approach to solving the maximum likelihood estimates is proposed. An exact solution for the ensemble update based on a square root Kalman Filter is derived. This solution involves a two step procedure in which an ensemble is first produced by a standard ensemble Kalman Filter, and then “corrected” to account for parameter estimation, thereby allowing a user to take advantage of an existing ensemble filter. The solution is illustrated with simple, low-dimensional stochastic dynamical models and shown to work well and outperform augmentation methods for estimating stochastic parameters.     

A speech enhancement method based on Kalman filtering

I.IntroductionKa1manfilteringisjustamethodtoestimatestatistica1lythestateoftheobservedsystemfromthecorruptedsigna1s,andthiskindofcstimationisarecurrcneeestimationbasedon1inear,nonbiasandminimumvariance.Moreover,Ka1manfilteringisapplicabletonon-sta-honarysignalsandtime-variantdynamicsystem.Therefore,Kalmanfilteringisveryapplica-bletoenhancingthespeechsigna1sthatarecorruptedbynoise.ThispaperreportStheconcretcmethodofenhanccmentofnoisyspccchanditscxperimentresults.Experimentsindicate:Afterthes…     

Tracking individual fish from a moving platform using a split-beam transducer

Tracking of individual fish targets using a split-beam echosounder is a common method for investigating fish behavior. When mounted on a floating platform like a ship or a buoy, the transducer movement often complicates the process. This paper presents a framework for tracking single targets from such a platform. A filter based on the correlated fish movements between pings is developed to estimate the platform movement, and an extended Kalman filter is used to combine the split-beam measurements and the platform-position estimates. Different methods for gating and data association are implemented and tested with respect to data-association errors, using manually tracked data from a free-floating buoy as a reference. The data association was improved by utilizing the estimated velocity for each track to predict the location of the next observation. The data association was more robust when estimates of platform tilt/roll were used. Other techniques to estimate position and velocity, like linear regression and smoothing splines, were implemented and tested on a simulated data set. The platform-state estimation improved the estimates for methods like the Kalman filter and a smoothing spline with cross validation, but not for robust methods like linear regression and smoothing spline with a fixed degree of smoothing.     

Time-reversal processing for an acoustic communications experiment in a highly reverberant environment

Time-reversal (T/R) communications is a new application area motivated by the recent advances in T/R theory. Although perceived by many in signal processing as simply an application of matched-filter theory, a T/R receiver offers an interesting solution to the communications problem for a reverberant channel. In this paper, the performance of various realizations of the T/R receiver for an acoustic communications experiment in air is described along with its associated processing. The experiment is developed to evaluate the performance of point-to-point T/R receivers designed to extract a transmitted information sequence propagating in a highly reverberant environment. It is demonstrated that T/R receivers are capable of extracting the transmitted coded sequence from noisy microphone sensor measurements with zero-symbol error. The processing required to validate these experimental results is discussed. These results are also compared with those produced by an equivalent linear equalizer or inverse filter, which provides the optimal solution when it incorporates all of the reverberations.     

Sequential Bayesian geoacoustic inversion for mobile and compact source-receiver configuration

Geoacoustic characterization of wide areas through inversion requires easily deployable configurations including free-drifting platforms, underwater gliders and autonomous vehicles, typically performing repeated transmissions during their course. In this paper, the inverse problem is formulated as sequential Bayesian filtering to take advantage of repeated transmission measurements. Nonlinear Kalman filters implement a random-walk model for geometry and environment and an acoustic propagation code in the measurement model. Data from MREA/BP07 sea trials are tested consisting of multitone and frequency-modulated signals (bands: 0.25-0.8 and 0.8-1.6 kHz) received on a shallow vertical array of four hydrophones 5-m spaced drifting over 0.7-1.6 km range. Space- and time-coherent processing are applied to the respective signal types. Kalman filter outputs are compared to a sequence of global optimizations performed independently on each received signal. For both signal types, the sequential approach is more accurate but also more efficient. Due to frequency diversity, the processing of modulated signals produces a more stable tracking. Although an extended Kalman filter provides comparable estimates of the tracked parameters, the ensemble Kalman filter is necessary to properly assess uncertainty. In spite of mild range dependence and simplified bottom model, all tracked geoacoustic parameters are consistent with high-resolution seismic profiling, core logging P-wave velocity, and previous inversion results with fixed geometries.     

Unscented Kalman filter and its nonlinear application for tracking a moving target

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 40 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. To overcome these limitations, this paper proposes the unscented Kalman filter (UKF). And the algorithms of the FEKF, SEKF and UKF are given. Furthermore, the state models and measurement models of a target are set up. For comparison purpose, the three algorithms is simulated for the target tracking, and the algorithm performance is analyzed and compared by the simulation results of FEKF, SEKF and UKF. Numerical results demonstrate that FEKF and UKF give almost identical results while the estimates of SEKF are clearly worse. The UKF is easier to implement, avoiding Jacobian and Hessian matrices computation.     

Multi-parameter identification from scalar time series generated by a Malkus-Lorenz water wheel

We address the issue of multi-parameter estimation from scalar outputs of chaotic systems, using the dynamics of a Malkus water wheel and simulations of the corresponding Lorenz-equations model as an example. We discuss and compare two estimators: one is based on a globally convergent adaptive observer and the second is an extended Kalman filter (EKF). Both estimators can identify all three unknown parameters of the model. We find that the estimated parameter values are in agreement with those obtained from direct measurements on the experimental system. In addition, we explore the question of how to distinguish the impact of noise from those of model imperfections by investigating a model generalization and the use of uncertainty estimates provided by the extended Kalman filter. Although we are able to exclude asymmetric inflow as a possible unmodeled effect, our results indicate that the Lorenz-equations do not perfectly describe the water wheel dynamics.     

逼近积分点数下限的五阶容积卡尔曼滤波定轨算法

为了在保持滤波定轨精度不变的条件下提高定轨计算的实时性,提出一种新的逼近积分点个数下限的五阶容积卡尔曼滤波定轨算法.首先,采用一种数值容积准则对非线性函数的高斯加权积分进行近似,该准则所需的积分点个数仅比五阶代数精度容积准则积分点个数的理论下限多一个积分点,并在贝叶斯滤波算法框架下推导出本文算法的更新步骤.然后,给出实时定轨所需的状态方程和量测方程,在状态方程中考虑了J2项引力摄动和大气阻力摄动,在量测方程中利用坐标系转换推导了轨道状态与测量元素之间的非线性关系.仿真实验结果表明,本文所提算法在定轨精度方面与已有的五阶滤波算法相当,但所需的积分点个数最少,计算实时性最高,从而验证了本文算法的有效性.     

Towards the acoustical characterisation of an Intensive Care Unit

Intensive Care Units (ICUs) can be immensely noisy places, where high noise levels may have deleterious effects on patients, visitors and staff alike. Many studies have identified sound levels exceeding World Health Organisation’s recommendations, although very few measured for more than 24 h or concurrently in multiple locations, as normally done in outdoor studies. In order to assess the feasibility of installing a continuous monitoring system in the indoor environment of an 18 bedded general intensive care, a MEMS-based microphone was used to monitor the noise levels for 7 days. Results showed minimal variation between night and day, but changes in sound level could be correlated with regularly occurring activities. The impact of microphone-holding structure on the measurements and the possibility of inferring patient and visitor’ exposure from a fixed measurement position are also discussed. Laboratory analysis, confirmed by in situ testing, identified ideal microphone positioning, and led to a correction of −1 dB for the sound pressure level measured at the microphone to obtain the level experienced by the patient.