Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The convergence of the proposed algorithm is proved in two main steps: noise statistics is estimated, where each agent only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.     

Robust adaptive algorithm for nonlinear systems with unknown measurement noise and uncertain parameters by variational Bayesian inference

This paper studies an adaptive algorithm for the estimation problem of nonlinear systems with unknown or missing measurement noise and uncertain parameters using variational Bayesian (VB) inference. We combine VB inference with the Monte Carlo sampling technique to settle this problem. There are many cases of missing information, and because of the difficulty in obtaining the analytical results, the existing control methods for uncertain systems lack generality. We present a set of nonlinear recursive adaptive filtering algorithms that address the unknown parameters and probability density function. The proposed algorithms yield a separable variational approximation of the joint posterior distribution of noise parameters with uncertain parameters and states on each step separately. Estimation convergence and robustness against disturbances are guaranteed. A convergence result for VB inference is presented. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms.     

An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

This paper investigates the simultaneous state and noise covariance estimation for linear systems with inaccurate noise statistics. An enhanced adaptive Kalman filtering (EAKF) based on dynamic recursive nominal covariance estimation (DNRCE) and modified variational Bayesian (VB) inference is presented. The EAKF realizes the concurrently estimation of state and noise covariance matrices by introducing a nominal parameter in the traditional recursive covariance estimation and designing a new adaptive forgotten factor for the dynamic model of the estimated information propagation. The simulation of a target tracking example shows that, compared with the existing filters, the proposed filter has good adaptive performance for inaccurate and time-varying noise covariance matrices.     

基于不确定模型误差系统的变分贝叶斯STCKF

强跟踪容积卡尔曼滤波器在对含有模型误差和时变噪声的非线性系统进行滤波时, 容易出现性能降低甚至发散. 鉴于此, 提出一种基于变分贝叶斯的强跟踪容积卡尔曼滤波算法. 该算法运用虚拟噪声法补偿模型误差, 假设虚拟噪声均值非零, 且满足高斯分布, 虚拟噪声方差服从逆gamma分布, 在强跟踪容积卡尔曼滤波器估计状态的同时, 采用变分贝叶斯推理估计虚拟噪声参数. 仿真结果表明, 所提出算法对含模型误差与时变噪声的非线性系统具有较好的估计精度, 相比于自适应算法具有更强的鲁棒性.     

基于RLS与EKF算法的锂电池SOC估计

准确估计荷电状态是电池管理系统高效和安全运行的关键因素之一.以Thevenin模型为基础,运用递推最小二乘法,对模型参数进行估计并且定期更新.采用扩展卡尔曼滤波算法实现了对锂电池荷电状态的估算.仿真结果表明,该估算策略能保持很高的精度,并对观测噪声有很强的抑制作用.     

具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.     

Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises

In this paper, the problem of distributed weighted robust Kalman filter fusion is studied for a class of uncertain systems with autocorrelated and cross-correlated noises. The system under consideration is subject to stochastic uncertainties or multiplicative noises. The process noise is assumed to be one-step autocorrelated. For each subsystem, the measurement noise is one-step autocorrelated, and the process noise and the measurement noise are two-step cross-correlated. An optimal robust Kalman-type recursive filter is first designed for each subsystem. Then, based on the newly obtained optimal robust Kalman-type recursive filter, a distributed weighted robust Kalman filter fusion algorithm is derived for uncertain systems with multiple sensors. The distributed fusion algorithm involves a recursive computation of the filtering error cross-covariance matrix between any two subsystems. Compared with the centralized Kalman filter, the distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.     

多算法结合的汽车参数和状态估计方法研究

为实时准确获取汽车参数及状态信息以提高汽车主动安全性能,提出了一种多算法结合的自适应估计算法。该算法将递推最小二乘算法、蚁群优化算法及容积卡尔曼滤波算法进行有效结合,同时将含有不准确模型参数及未知时变噪声的三自由度非线性整车模型作为标称模型。采用递推最小二乘算法实时估计汽车参数,引入蚁群优化算法实时跟踪容积卡尔曼滤波器的过程噪声及量测噪声,根据目标函数对噪声协方差进行寻优,以解决系统的噪声时变问题,从而获取汽车状态的准确估计。基于CarSim/Simulink的仿真实验结果表明,该算法的状态估计精度高,且具备汽车模型参数校正能力,可以满足系统的控制需要。     

A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise

A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least-squares or Panuska's method. Convergence properties of the proposed algorithm are studied, and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed, and an extension to an estimator for randomly varying parameters is outlined.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.     

State estimation and parameter identification method for dual-rate system based on improved Kalman prediction

For the dual-rate system, such as the process of space teleoperation whose control signals is partly determined by delayed feedback states, the state values and system parameters are coupled and influenced each other, which are hard to be estimated simultaneously. In this paper, we propose a novel method for this problem. Firstly, considering the asynchronism of the input and output sampling signals, an auxiliary model is modeled as a medium to the state and output functions. Secondly, the Kalman prediction algorithm is improved to estimate the state values at output signals of the dual-rate system. The general step is using the output estimated errors in original and auxiliary systems to modify the estimated state values of the auxiliary model, and then the unknown state values in original system is defined by the ones in auxiliary model. Based on improved Kalman algorithm and hierarchical identification algorithm, we present the detailed procedures of state estimation and parameter identification method for the dual-rate system. The processes of state estimation and parameter identification are calculated and modified alternately. Finally, the simulation results reveal that the state and parameters both approach to the real values and the state values converge faster than the parameters.     

带有噪声递推估计的自适应集合卡尔曼滤波

卡尔曼滤波(KF)广泛应用于线性系统的状态估计问题.然而,它需要精确已知过程噪声的统计特性,这在实际应用中往往是不能满足的.在这个背景下,首先,根据协方差匹配原理建立一种带有过程噪声递推估计的自适应KF算法;然后,为了突破KF只能处理线性系统估计问题的局限,将过程噪声递推估计引入集合卡尔曼滤波(EnKF)中,提出一种自适应EnKF算法;最后,采用估计理论证明所提出算法的稳定性.与标准EnKF相比,该自适应算法在过程噪声统计特性未知的情况下滤波依然收敛,滤波精度及稳定性显著提升.仿真结果验证了所提出算法的有效性.     

An interlaced extended Kalman filter

An estimation algorithm for a class of discrete time nonlinear systems is proposed. The system structure we deal with is partitionable into in subsystems, each affine w.r.t. the corresponding part of the state vector. The algorithm consists of a bank of m interlaced Kalman filters, and each of them estimates a part of the state, considering the remaining parts as known time-varying parameters whose values are evaluated by the other filters at the previous step. The procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably “increasing” the noise covariance matrices. Comparisons through numerical simulations with the extended Kalman filter and its modified versions proposed in the literature illustrate the good trade-off provided by the algorithm between the reduction of the computational load and the estimation accuracy     

针对气动肌肉仿生肘关节抖振现象的Kalman-PID控制

本文为了抑制气动人工肌肉(PAM)抖振现象,首先利用PID控制律近似代替其数学模型,求得其离散状态方程并代入到离散卡尔曼递推公式中,进而提出基于PID控制参数的卡尔曼PID(Kalman-PID,KPID)控制算法.为了验证算法的有效性,以3自由度PAM仿生肘关节为控制对象,分别利用PID及KPID控制器对其进行位姿控制.由实验结果可知,该算法相较PID控制器拥有更高的控制精度,提升了系统的鲁棒性,能够有效抑制由系统过程误差及测量误差所引起的PAM抖振现象,从而使仿生肘关节运动更加平稳.此外,不同于传统卡尔曼滤波算法与控制算法相结合的方式,KPID控制算法无需事先知道被控对象精准的数学模型及噪音特性的先验知识,从而避免复杂的数学建模过程,扩大了卡尔曼滤波算法的应用范围.     

Recursive estimation of the parameters of linear multivariable systems

A recursive algorithm is proposed for the identification of linear multivariable systems. Utilization of a canonical state space model minimizes the number of parameters to be estimated. The problem of identification in the presence of noise is solved by using a recursive generalized least-squares method.     

基于递归工具变量卡尔曼滤波算法的纯方位水下目标跟踪

基于纯方位信息的水下目标跟踪中常用的伪线性卡尔曼滤波算法偏差较大、跟踪精度差,结合偏差补偿算法提出一种用于纯方位水下目标跟踪的递归工具变量卡尔曼滤波算法,并将过程噪声协方差的不确定性考虑在内.针对伪线性卡尔曼滤波算法的偏差问题,采用递归工具变量算法的工具变量矩阵来消除量测矩阵与伪线性噪声间的关联性,从而消除偏差.仿真结果表明,所提出的递归工具变量卡尔曼滤波算法在水下方位角噪声较大时也能保持稳定性和跟踪精度.     

广义系统信息融合稳态与自校正满阶Kalman滤波器

基于线性最小方差标量加权融合算法和射影理论,对带多个传感器和带相关噪声的广义系统,提出了分布式标量加权融合稳态满阶Kalman滤波器.推得了任两个传感器子系统之间的稳态满阶滤波误差互协方差阵,其解可任选初值离线迭代计算.所提出的稳态融合滤波器避免了每时刻计算协方差阵和融合权重,减小了在线计算负担.当系统含有未知模型参数时,基于递推增广最小二乘算法和标量加权融合算法,提出了一种两段融合自校正状态滤波器.其中第1段融合获得未知参数的融合估计;第2段融合获得分布式自校正融合状态滤波器.与局部估计和加权平均融合估计相比,所提出的标量加权融合参数估计和自校正状态估计都具有更高的精度.仿真研究验证了其有效性.     

An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

In this study, an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation. The mechanism of linear Kalman filter (LKF) with point data processing is adopted to develop a new recursive algorithm. The novelty of the enhanced linear Kalman filter (EnLKF in short and distinguished from extended Kalman filter (EKF)) is that it is not formulated from the routes of extended Kalman Filters (to approximate nonlinear models by linear approximation around operating points through Taylor expansion) and also it includes LKF as its subset while linear models have no correlated errors in regressor terms. No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure. The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research. Three simulated examples are selected to bench-test the performance of the algorithm. In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. It should be noted that this approach is fundamentally different from those using linearisation to approximate nonlinear models and then conduct state/parameter estimate.     

Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.     

Online Noise Estimation Using Stochastic-Gain HMM for Speech Enhancement

We propose a noise estimation algorithm for single-channel noise suppression in dynamic noisy environments. A stochastic-gain hidden Markov model (SG-HMM) is used to model the statistics of nonstationary noise with time-varying energy. The noise model is adaptive and the model parameters are estimated online from noisy observations using a recursive estimation algorithm. The parameter estimation is derived for the maximum-likelihood criterion and the algorithm is based on the recursive expectation maximization (EM) framework. The proposed method facilitates continuous adaptation to changes of both noise spectral shapes and noise energy levels, e.g., due to movement of the noise source. Using the estimated noise model, we also develop an estimator of the noise power spectral density (PSD) based on recursive averaging of estimated noise sample spectra. We demonstrate that the proposed scheme achieves more accurate estimates of the noise model and noise PSD, and as part of a speech enhancement system facilitates a lower level of residual noise.