Gaussian particle filtering

Sequential Bayesian estimation for nonlinear dynamic state-space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters.     

Design of Sigma-Point Kalman Filter with Recursive Updated Measurement

In this study, the authors focus on improving measurement update of existing nonlinear Kalman approximation filter and propose a new sigma-point Kalman filter with recursive measurement update. Statistical linearization technique based on sigma transformation is utilized in the proposed filter to linearize the nonlinear measurement function, and linear measurement update is applied gradually and repeatedly based on the statistically linearized measurement equation. The total measurement update of the proposed filter is nonlinear, and the proposed filter can extract state information from nonlinear measurement better than existing nonlinear filters. Simulation results show that the proposed method has higher estimation accuracy than existing methods.     

A sequential Monte Carlo filter for joint linear/nonlinear state estimation with application to DS-CDMA

A sequential Monte Carlo filter is considered which combines previously developed sequential importance sampling (SIS) techniques for conditional linear Gaussian models with measurement linearization for construction of approximate simulation densities. The resulting sequential Monte Carlo Kalman filter (SMC-KF) consists of a bank of conventional Kalman filters individually tuned to sampled trajectories of the nonlinear state variables. Sampling is according to a Gaussian distribution, with mean and covariance determined by extended Kalman filter-type equations. The SMC-KF is then applied to joint delay and multipath channel estimation in direct-sequence code-division multiple access (DS-CDMA). A combined analytical/simulation technique is employed to compare performance of the SMC-KF and a previously derived extended Kalman filter (EKF)-based DS-CDMA channel estimator.     

Cubature Information Filters Using High-Degree and Embedded Cubature Rules

The information form of the Kalman filter (KF) is preferred over standard covariance filters in multiple sensor fusion problems. Aiming at this issue, two types of cubature information filters (CIF) for nonlinear systems are presented in this article. The two approaches, which we have named the embedded cubature information filter (ECIF) and the fifth-degree cubature information filter (FCIF), are developed from a fifth-degree cubature Kalman filter and a newly proposed embedded cubature KF. Theoretical analysis shows that the proposed filters can achieve higher level estimation accuracy than conventional information filters, such as the CIF and the extended information filter (EIF). Performance comparisons of the proposed information filters with the conventional CIF are demonstrated via two independent multisensor tracking problems. The experimental results, presented herein, demonstrate that the proposed algorithms are more reliable and accurate than the CIF.     

Multirate modeling of AR/MA stochastic signals and its applicationto the combined estimation-interpolation problem

The use of the Kalman filter is investigated in this work for interpolating and estimating values of an AR or MA stochastic signal when only a noisy, down-sampled version of the signal can be measured. A multirate modeling theory of the AR/MA stochastic signals is first derived from a block state-space viewpoint. The missing samples are embedded in the state vector so that missing signal reconstruction problem becomes a state estimation scheme. Next, Kalman state estimation theory is introduced to treat the combined estimation-interpolation problem. Some extensions are also discussed for variations of the original basic problem. The proposed Kalman reconstruction filter can be also applied toward recovering missing speech packets in a packet switching network with packet interleaving configuration. By analysis of state estimation theory, the proposed Kalman reconstruction filters produce minimum-variance estimates of the original signals. Simulation results indicate that the multirate Kalman reconstruction filters possess better estimation/interpolation performances than a Wiener reconstruction filter under adequate numerical complexity     

Nonlinear filtering methods for harmonic retrieval and model orderselection in Gaussian and non-Gaussian noise

This paper addresses the problem of high-resolution parameter estimation (harmonic retrieval) and model-order selection for superimposed sinusoids. The harmonic retrieval problem is analyzed using a nonlinear parameter estimation approach. Estimation is performed using several nonlinear estimators with signals embedded in white and colored Gaussian noise. Simulation results demonstrate that the nonlinear filters perform close to the Cramer-Rao bound. Model order selection is performed in Gaussian and non-Gaussian noise. The problem is formulated using a multiple hypothesis testing approach with assumed known a priori probabilities for each hypothesis. Parameter estimation is performed using the extended Kalman filter when the noise is Gaussian. The extended high-order filter (EHOF) is implemented in non-Gaussian noise. Simulation results demonstrate excellent performance in selecting the correct model order and estimating the signal parameters     

Recursive estimation from discrete-time point processes

The paper presents models for discrete-time point processes (DTPP) and schemes for recursive estimation of signals randomly influencing their rates. Although the models are similar to the better known models of signals in additive Gaussian noise, DTPP differ from these in that it is possible for DTPP's to find recursive representations for the nonlinear filters. If the signal can be modeled as a finite state Markov process, then these representations reduce to explicit recursive finite-dimensional filters. The derivation of the estimation schemes, as well as the filters themselves, present a surprising similarity to the Kalman filters for signals in Gaussian noise. We present finally an application of the estimation schemes derived in the paper to the estimation of the state of a random time-division multiple access (ALOHA-type) computer network.     

Kalman滤波下的多信号单通道盲源分离

窄带物联网环境中,接收机收到的信号通常为多路混合信号,对单通道接收来说,利用常规盲源分离方法很难实现混合信号的分离和源信号提取。针对这一问题,本文提出了一种利用Kalman滤波算法进行信号估计,解决单通道盲源分离的方法。该方法利用信号间的时序结构,通过Kalman滤波算法对多信号混合中的源信号不断估计并迭代更新,最终得到分离信号。仿真实验结果表明,该方法能有效估计并分离出源信号。      

基于数值积分卡尔曼-概率假设密度滤波的多说话人跟踪方法

针对多说话人跟踪的非线性系统模型,提出了一种基于数值积分卡尔曼-概率假设密度滤波的多说话人跟踪方法。该方法采用麦克风阵列的时间延迟估计作为观测数据,利用具有三次代数精度的球面-径向数值积分准则计算非线性系统贝叶斯滤波器中的多维积分,通过数值积分卡尔曼滤波和概率假设密度滤波对后验多说话人状态的一阶统计量进行估计,并通过递推更新得到说话人状态信息,实现非线性高斯系统的多说话人跟踪。该方法无需求解非线性系统函数的雅克比矩阵,且计算量较小。仿真实验分析了检测概率、虚警点数目、采样周期、信噪比以及混响时间变化时跟踪算法的性能。实验结果表明,该方法降低了系统模型非线性对滤波算法的影响,增强了跟踪算法的鲁棒性,提高了说话人状态和数目的估计精度。      

高斯和高阶无迹卡尔曼滤波算法

为了提高非线性变换的近似精度,提出了一种高阶无迹变换（High order Unscented Transform,HUT）机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波（High-order Unscented Kalman Filter,HUKF）算法.进一步的为了解决非线性、非高斯系统的状态估计问题,将HUKF与高斯和滤波（Gaussian Sum Filter,GSF）相结合,提出了一种高斯和高阶无迹卡尔曼滤波算法（Gaussian Sum High order Unscented Kalman filter,GS-HUKF）,该算法的核心思想是利用一组高斯分布的和去近似状态的后验概率密度,同时针对每一个高斯分布采用高阶无迹卡尔曼滤波算法进行估计.数值仿真实验结果表明,提出的HUT机制与普通的无迹变换（Unscented Transform,UT）相比,具有更高的近似精度;提出的GS-HUKF与传统的GSF以及高斯和粒子滤波器（Gaussian Sum Particle Filter,GS-PF）相比,兼容了二者的优点,即具有计算复杂度低和估计精度高的特性.     

基于代价参考粒子滤波器组的检测前跟踪算法

基于粒子滤波的检测前跟踪方法是检测和估计非线性调频信号的有效方法之一。但此类方法运算量大,难以并行执行。此外,由于粒子滤波算法收敛较慢,基于粒子滤波的检测前跟踪方法的检测和状态估计能力有待提高。针对上述问题,该文首先提出一种代价参考粒子滤波器组。该滤波器组收敛快速,具有完全的并行结构,可快速准确地估计非线性调频信号的瞬时频率。其次,提出基于代价参考滤波器组的检测前跟踪算法,可在给定虚警率下,在各个时刻检测目标和估计目标状态。两类非线性调频信号检测和估计的仿真结果表明,基于代价参考粒子滤波器组的检测前跟踪算法的检测性能、估计性能和运行速率均优于类似的方法,如基于粒子滤波的检测前跟踪方法,基于Rutten粒子滤波的检测前跟踪方法等。     

结合匈牙利指派和改进粒子滤波的多目标跟踪算法

使用汽车雷达进行多目标跟踪时,为了提高航迹关联效率并改善非线性场景跟踪效果,提出了结合匈牙利指派和卡尔曼重要性采样的粒子滤波(Particle Filter with Kalman Importance Sampling,PF-KIS)算法。首先,将航迹关联分解为聚类和指派,通过密度聚类筛选并整合有效目标,经过匈牙利指派得到目标和航迹的最佳匹配关系,避免产生多余联合事件,提高关联效率;其次,以卡尔曼滤波的结果作为粒子滤波的先验,使采样粒子分布更合理,提高估计精度,进而改善非线性跟踪能力。实验表明,算法平均航迹关联正确率约为95%;非线性场景误差约为卡尔曼滤波的1/2,有效地改善了非线性场景跟踪能力。     

Optimal signal reconstruction in noisy filter bank systems:multirate Kalman synthesis filtering approach

A multirate Kalman synthesis filter is proposed in this paper to replace the conventional synthesis filters in a noisy filter bank system to achieve optimal reconstruction of the input signal. Based on an equivalent block representation of subband signals, a state-space model is introduced for an M-band filter bank system with subband noises. The composite effect of the input signal, analysis filter bank, decimators, and interpolators is represented by a multirate state-space model. The input signal is embedded in the state vector, and the corrupting noises in subband paths are generally considered as additive noises. Hence, the signal reconstruction problem in the M-band filter bank systems with subband noises becomes a state estimation procedure in the resultant multirate state-space model. The multirate Kalman filtering algorithm is then derived according to the multirate state-space model to achieve optimal signal reconstruction in noisy filter bank systems. Based on the optimal state estimation theory, the proposed multirate Kalman synthesis filter provides the minimum-variance reconstruction of the input signal. Two numerical examples are also included. The simulation results indicate that the performance improvement of signal reconstruction in noisy filter bank systems is remarkable     

IMM-based Kalman filter for channel estimation in UWB OFDM systems

Ultra-wide band (UWB) communication is one of the most promising technologies for high-data rate wireless networks for short-range applications. This paper proposes a blind channel estimation method namely Interactive Multiple Model (IMM)-based Kalman algorithm for UWB OFDM systems. IMM-based Kalman filter is proposed to estimate frequency selective time-varying channel. In the proposed method, two Kalman filters are concurrently estimating channel parameters. The first Kalman filter, namely the Static Model Filter (SMF) gives an accurate result when the user is static while the second Kalman filter namely the Dynamic Model Filter (DMF) gives an accurate result when the receiver is in moving state. The static transition matrix in SMF is assumed as an Identity matrix where as in DMF, it is computed using Yule–Walker equations. The resultant filter estimate is computed as a weighted sum of individual filter estimates. The proposed method is compared with other existing channel estimation methods.     

高斯-厄米特粒子滤波器

针对非线性、非高斯系统状态的在线估计问题,本文提出一种新的基于序贯重要性抽样的粒子滤波算法.在滤波算法中,我们用一簇高斯-厄米特滤波器(GHF)来产生重要性概率密度函数.此概率密度在系统状态的转移概率的基础上融入最新的观测数据,因此更接近于系统状态的后验概率.理论分析与实验结果表明:在观测模型具有高精度的场合或似然函数位于系统状态转移概率的尾部时,用GHF产生重要性概率密度函数的粒子滤波即高斯-厄米特粒子滤波(GHPF)的性能要明显地优于标准的粒子滤波、扩展的卡尔曼滤波、GHF.     

On-line estimation of signal and noise parameters with application to adaptive Kalman filtering

This paper presents two algorithms for on-line estimation of the optimal gain of the Kalman filter applied to sensor signals when the signal-to-noise ratio is unknown. First-order spectra of a pure signal and colored measurement noise have been assumed. The proposed adaptive Kalman filtering algorithms have been tested for various spectra of the pure signal and noise, and for various signal-to-noise ratios. The effect of the length of an adaptation step and a sampling frequency on the mean square errors of the pure signal estimation has also been examined. Although the test have been performed for stationary signals, the algorithms presented can also be used successfully for time-varying sensor signals when the signal-to-noise ratios vary very slowly in comparison with the length of the adaptation step.The results are helpful for designers who synthesize optimal linear digital filters for sensor signals with first-order spectra and colored measurement noise. The estimation error curves presented enable designers to determine the noise reduction attainable for particular applications of the adaptive Kalman filtering algorithms.     

基于T-S模糊模型的非线性系统状态估计

现实世界中的动力系统大多是非线性的,而非线性系统的状态估计方法目前主要有扩展卡尔曼滤波,无味滤波,粒子滤波等,但它们对于非线性程度很高的系统滤波结果不是很理想。若用模糊规则模型去逼近非线性系统,基于规则理论去寻求状态的估计,则估计性能能够得到较大的改善。将模糊推理理论与Kalman滤波结合,用线性的方法逼近非线性模型,提出一种对非线性系统目标状态估计的新方法,给出了具体的处理过程,仿真实验支持理论结果     

基于最优导频的自适应Kalman滤波信道估计方法

针对时变信道中的子载波间干扰(ICI)和噪声的统计模型不准确引起的滤波发散问题,介绍了一种基于最优导频预滤波的自适应Kalman联合算法。该算法通过使用最优导频滤除ICI,获得理想信道初始状态,然后将其作为Kalman滤波初始信息在时域上进行自适应Kalman信道估计。最后仿真实验表明,和传统的基于导频的Kalman滤波(KF)算法相比,该方法能有效抑制KF发散和改善信道估计精度。     

Joint estimation of PN code delay and multipath using the extendedKalman filter

The problem of delay estimation in the presence of multipath is considered. It is shown that the extended Kalman filter (EKF) can be used to obtain joint estimates of time-of-arrival and multipath coefficients for deterministic signals when the channel can be modeled as a tapped-delay line. Simulation results are presented for the EKF joint estimator used for synchronization in a direct-sequence spread-spectrum system operating over a frequency-selective fading channel. A simplified model of the EKF joint estimator is considered for analysis purposes. The evolution in time of the tracking error probability density function and the nonlinear tracking error variance are examined through numerical solution of the Chapman-Kolmogorov equation. The nonlinear tracking error variance is compared to both the linear error variance estimate directly provided by the EKF and the Cramer-Rao lower bound     

New nonlinear algorithms for estimating and suppressing narrowbandinterference in DS spread spectrum systems

It has been shown that the narrowband (NB) interference suppression capability of a direct-sequence (DS) spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter. The conventional approach to this problem makes use of a linear filter. However, the binary DS signal, that acts as noise in the prediction process, is highly non-Gaussian. Thus, linear filtering is not optimal. Vijayan and Poor (1990) first proposed using a nonlinear approximate conditional mean (ACM) filter of the Masreliez (1975) type and obtained significant results. This paper proposes a number of new nonlinear algorithms. Our work consists of three parts. (1) We develop a decision-directed Kalman (DDK) filter, that has the same performance as the ACM filter but a simpler structure. (2) Using the nonlinear function in the ACM and the DDK filters, we develop other nonlinear least mean square (LMS) filters with improved performance. (3) We further use the nonlinear functions to develop nonlinear recursive least squares (RLS) filters that can be used independently as predictors or as interference identifiers so that the ACM or the DDK filter can be applied. Simulations show that our nonlinear algorithms outperform conventional ones