Direct, prediction- and smoothing-based Kalman and particle filter algorithms

We address the recursive computation of the filtering probability density function (pdf) p_n|n in a hidden Markov chain (HMC) model. We first observe that the classical path p_n−1|n−1→p_n|n−1→p_n|n is not the only possible one that enables to compute p_n|n recursively, and we explore the direct, prediction-based (P-based) and smoothing-based (S-based) recursive loops for computing p_n|n. We next propose a common methodology for computing these equations in practice. Since each path can be decomposed into an updating step and a propagation step, in the linear Gaussian case these two steps are implemented by Gaussian transforms, and in the general case by elementary simulation techniques. By proceeding this way we routinely obtain in parallel, for each filtering path, one set of Kalman filter (KF) equations and one generic sequential Monte Carlo (SMC) algorithm. Finally we classify in a common framework four KF (two of which are original), which themselves can be associated to four generic SMC algorithms (two of which are original). We finally compare our algorithms via simulations. S-based filters behave better than P-based ones, and within each class of filters better results are obtained when updating precedes propagation.     

Real-time implementation of a narrow-band Kalman filter with afloating-point processor DSP32

The author presents experimental results from two studies. First, a real-time narrowband Kalman filter is implemented with a floating-point digital processor DSP32. The real-time capability of this narrowband filter is investigated by varying parameters Q and R. The covariance matrices Q and R of the dynamic and measurement noise sequences are found to exhibit duality in the real-time tuning process and have a direct effect on system stability. If the value of Q used is smaller (with fixed R ), the tracking time and the narrower tracking bandwidth of the filter will be longer. In addition, if the value of R used (with fixed Q) is smaller, the tracking time will be smaller, and the tracking bandwidth of the filter will be larger. The results are tabulated. Second, two optimal codes (in the sense of the execution speed), straight-line code and general matrix-based code, have been developed for implementing the narrowband Kalman filter. These two codes are compared in terms of program memory size, data memory size, and speed of execution. With the matrix-based code, the DSP32 performance is evaluated in terms of speed and memory size by varying the number of states of a Kalman filter. The results are also tabulated     

遗忘因子在卡尔曼滤波自适应波束形成的应用

使用卡尔曼滤波控制的自适应波束形成,具有高收敛速率,低失调量,可用于非平稳过程等优点。系统建模是卡尔曼滤波的基础,系统模型不准确带来的验前数据误差,使滤波器精度降低,可能造成发散,本文提出的带遗忘因子卡尔曼滤波算法能补偿模型误差。通过计算机模拟,其模拟结果表明了该方法是有效的。     

Failure monitoring in a high performance hydrostatic actuation system using the extended Kalman filter

This paper describes the development and evaluation of a fault detection strategy for a high performance hydrostatic actuation system, the electrohydraulic actuator (EHA). The approach makes use of the extended Kalman filter (EKF) technique for parameter estimation purposes and changes in the estimated system parameters were related to faults in the EHA. The hydrostatic system has potential applications in the aerospace industry, in robotics, in machining and as such, failures in the EHA can pose a safety hazard as well as result in costly downtime and unscheduled maintenance. Monitoring failures in the hydrostatic system is achieved by estimating two parameters of interest, namely the viscous friction coefficient and the effective bulk modulus. Changes in the viscous friction coefficient in the actuator indicate deterioration of the hydraulic oil or wear in the seals. Lowering of the effective bulk modulus affects the response of the closed loop system, reduces system bandwidth and may cause instability. A simulation study was conducted to investigate the feasibility of the approach as well as the level of accuracy to be expected. The methodology was then verified using experimental results.     

基于无线层析成像和卡尔曼滤波的定位追踪

无线传感网的无源定位问题对现实社会有着重要意义,通过对局域范围内的RSSI进行捕捉,并根据RSSI的变化在区域内的衰减,再依据线型模型进行计算,从而得到局域范围内的位置坐标。将每次采样得到的位置坐标信息进行预处理,再通过卡尔曼滤波进行优化,从而形成物体运动的轨迹。     

Adaptive synchronization and channel parameter estimation using anextended Kalman filter

Unified modeling and estimation of the MD (multiplicative distortion) in finite-alphabet digital communication systems is presented. A simple form of MD is the carrier phase exp(j&thetas;), which has to be estimated and compensated for in a coherent receiver. A more general case with fading must, however, allow for amplitude as well as phase variations of the MD. The authors assume a state-variable model for the MD and generally obtain a nonlinear estimation problem with additional randomly varying system parameters such as received signal power, frequency offset, and Doppler spread. An extended Kalman filter is then applied as a near-optimal solution to the adaptive MD and channel parameter estimation problem. Examples are given to show the use and some advantages of this scheme     

3-D tracking and motion estimation using hierarchical Kalman filter

The authors present a novel approach to the problem of tracking and reconstructing articulated objects in 3-D space. The newly conceived computational process and its supporting data structure, the hierarchical Kalman filter (HKF) and the adaptive hierarchical structure (AHS). Allow the problem to be treated in a singlet unified framework. There are three novelties in the authors' formulation: reducing the 3-D tracking problem to 2-D tracking; incorporating the kinematic and the dynamic properties of object; and tracking nonrigid objects. To demonstrate the appropriateness of the proposed method, the authors present some of the experimental results on both synthetic and real images     

Design and optimization of IIR filter structure using hierarchicalgenetic algorithms

A new genetic algorithm (GA) is proposed for digital filter design. This scheme utilizes a new hierarchical multilayer gene structure for the chromosome formulation. This is a unique structure, which retains the conventional genetic operations, while the genes may take various forms to represent the system characteristics. As a result, both the system structure and the parametric variables can be optimized in a simultaneous manner, without extra computational cost and effort. It has been demonstrated that this technique not only fulfils all types of filter performance requirements, but that the lowest order of the filter can also be found     

ECG denoising and compression using a modified extended Kalman filter structure

This paper presents efficient denoising and lossy compression schemes for electrocardiogram (ECG) signals based on a modified extended Kalman filter (EKF) structure. We have used a previously introduced two-dimensional EKF structure and modified its governing equations to be extended to a 17-dimensional case. The new EKF structure is used not only for denoising, but also for compression, since it provides estimation for each of the new 15 model parameters. Using these specific parameters, the signal is reconstructed with regard to the dynamical equations of the model. The performances of the proposed method are evaluated using standard denoising and compression efficiency measures. For denosing, the SNR improvement criterion is used, while for compression, we have considered the compression ratio (CR), the percentage area difference (PAD), and the weighted diagnostic distortion (WDD) measure. Several Massachusetts Institute of Technology–Beth Israel Deaconess Medical Center (MIT–BIH) ECG databases are used for performance evaluation. Simulation results illustrate that both applications can contribute to and enhance the clinical ECG data denoising and compression performance. For denoising, an average SNR improvement of 10.16 dB was achieved, which is 1.8 dB more than the next benchmark methods such as MABWT or EKF2. For compression, the algorithm was extended to include more than five Gaussian kernels. Results show a typical average CR of 11.37:1 with WDD ≪ 1.73%. Consequently, the proposed framework is suitable for a hybrid system that integrates these algorithmic approaches for clean ECG data storage or transmission scenarios with high output SNRs, high CRs, and low distortions.      

Fast converging and low complexity adaptive filtering using anaveraged Kalman filter

Kalman filtering is applied to obtain a fast converging, low complexity adaptive filter that is of the matrix stepsize normalized least mean square (NLMS) type. By replacing certain variables with averages, the solution of an averaged diagonal Riccati equation allows optimal time varying adaptation gains to be precomputed or computed online with a small number of scalar Riccati equations. The adaptation gains are computed from prior assumptions on impulse response power and shape. This fact results in a systematic procedure for adaptation gain tuning in the time-varying matrix stepsize case. Simulations using music as input, show significant performance improvements as compared with the NLMS algorithm     

Modeling and decoding motor cortical activity using a switching Kalman filter

We present a switching Kalman filter model for the real-time inference of hand kinematics from a population of motor cortical neurons. Firing rates are modeled as a Gaussian mixture where the mean of each Gaussian component is a linear function of hand kinematics. A "hidden state" models the probability of each mixture component and evolves over time in a Markov chain. The model generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.     

High efficiency control of synchronous reluctance motors using extended Kalman filter

High-efficiency control of synchronous reluctance motors (SynRMs) is very important in the sense of energy saving and conservation of the natural environment because the efficiency of the SynRM is generally lower than that of other types of AC motors. This paper presents a high-efficiency control strategy for the SynRMs. In this strategy, the d- and q-axes currents are controlled instantaneously. Since the control performance mainly depends on the accuracy of the machine parameters, online parameter estimation using the extended Kalman filter is incorporated into the control strategy. This control strategy improved the drive efficiency and robust performance against machine parameter variations. The validity of the proposed scheme is demonstrated through experimental results.     

Detection and extraction of periodic noises in audio and biomedical signals using Kalman filter

This paper studies the subject of adaptive noise cancelation using the Kalman filtering technique to achieve high precision and fast convergence. It is shown that the Kalman filter can successfully be designed to detect and extract periodic noises which may be constituted of different sinusoidal components with possibly unknown and/or time-varying frequencies. This highlights the feature of Kalman filter in synthesizing periodic noises in the time-domain which is not possible using Fourier-based methods such as DFT. Usefulness of the method is discussed in the context of two examples: active cancelation of periodic noises from audio waveforms and filtering of electrocardiogram measurements.     

Speed estimation of an induction motor drive using an optimizedextended Kalman filter

This paper presents a novel method to achieve good performance of an extended Kalman filter (EKF) for speed estimation of an induction motor drive. A real-coded genetic algorithm (GA) is used to optimize the noise covariance and weight matrices of the EKF, thereby ensuring filter stability and accuracy in speed estimation. Simulation studies on a constant V/Hz controller and a field-oriented controller (FOC) under various operating conditions demonstrate the efficacy of the proposed method. The experimental system consists of a prototype digital-signal-processor-based FOC induction motor drive with hardware facilities for acquiring the speed, voltage, and current signals to a PC. Experiments comprising offline GA training and verification phases are presented to validate the performance of the optimized EKF     

结合扩展卡尔曼滤波的摄像机标定技术

摄像机标定是求解相机内参和外参的过程,是进行后续的计算机视觉相关工作的基础,在所有标定方法中传统摄像机标定法具有最高的标定精度。卡尔曼滤波器(KF)是一组可以有效地预测过程状态信息的数学方程,文中提出一个结合扩展卡尔曼滤波(EKF)的传统摄像机标定新算法。特征点的空间三维坐标和对应的像点坐标是滤波器的输入,输出则是被估计的相机内参与外参。实验结果表明,该方法可以获得更高的标定精度。     

Structural identification of pseudorandom sequences based on using the nonlinear Kalman filter

This study has shown the relevancy of investigating new techniques for notation and processing of signals built on pseudorandom sequences (PRS) of the maximum period. For the first time an arbitrary PRS was represented in the form of a multidimensional nonlinear finite-difference structure. On the basis of the above representation it was proposed to use a nonlinear suboptimal discrete algorithm of Kalman filtration for the problem of structural identification of received PRS. A numerical example of filtration of the sequence generated in accordance with the specified recurrent rule was considered and its efficiency was also shown.     

Pedestrian trajectory prediction in crossing scenario using fuzzy logic and switching Kalman filter

Pedestrian trajectory prediction plays an important role in bothadvanced driving assistance system (ADAS) and autonomous vehicles. An algorithm for pedestrian trajectory prediction in crossing scenario is proposed. To obtain features of pedestrian motion, we develop a method for data labelling and pedestrian body orientation regression. Using the hierarchical features as domain of discourse, fuzzy logic rules are built to describe the transition between different pedestrian states and motion models. With derived probability of each type of motion model we further predict the pedestrian trajectory in the next 1.5 s using switching Kalman filter (KF). The proposed algorithm is further verified in our dataset, and the result indicates that the proposed algorithm successfully predicts pedestrian' s crossing behavior 0.4 s earlier before pedestrian moves. Meanwhile, the precision of predicted trajectory surpasses other methods including interacting multi-model KF and dynamic Bayesian network (DBN).     

A family of adaptive filter algorithms with decorrelatingproperties

Although the normalized least mean square (NLMS) algorithm is robust, it suffers from low convergence speed if driven by highly correlated input signals. One method presented to overcome this problem is the Ozeki/Umeda (1984) affine projection (AP) algorithm. The algorithm applies update directions that are orthogonal to the last P input vectors and thus allows decorrelation of an AR(P) input process, speeding up the convergence. This article presents a simple approach to show this property, which furthermore leads to the construction of new algorithms that can handle other kinds of correlations such as MA and ARMA processes. A statistical analysis is presented for this family of algorithms. Similar to the AP algorithm, these algorithms also suffer a possible increase in the noise energy caused by their pre-whitening filters     

Influence of stochastic noise statistics on Kalman filter performance based on video target tracking

The system stochastic noises involved in Kalman filtering are preconditioned on being ideally white and Gaussian distributed. In this research, efforts are exerted on exploring the influence of the noise statistics on Kalman filtering from the perspective of video target tracking quality. The correlation of tracking precision to both the process and measurement noise covariance is investigated; the signal-to-noise power density ratio is defined; the contribution of predicted states and measured outputs to Kalman filter behavior is discussed; the tracking precision relative sensitivity is derived and applied in this study case. The findings are expected to pave the way for future study on how the actual noise statistics deviating from the assumed ones impacts on the Kalman filter optimality and degradation in the application of video tracking.     

The performance of two symbol timing recovery algorithms for PSKdemodulators

A statistical analysis of a decision-directed symbol timing algorithm for phase shift keyed modems is presented. The timing detector uses only one sample per symbol period and is suitable for high speed modems which employ discrete-time synchronization methods. Expressions for the timing detector's mean value and variance, as a function of timing offset, are derived and compared to simulation results. The analysis includes the effects of decision errors which occur at low signal-to-noise ratios and eventually limit the useful operating range of the decision-directed methods. A modification is described so that the need for prior phase recovery is avoided. These algorithms are compared to a popular two-sample-per-symbol nondecision-directed timing detector. A method of examining the relative performance of the various algorithms is presented and results are given for a range of signal-to-noise ratios and channel bandwidths