Optimal and robust noncausal filter formulations

The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H/sub /spl infin// predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar /spl gamma/ in the H/sub /spl infin// filter and smoother design. The results of simulation studies are presented, which demonstrate that optimal, robust, and extended Kalman smoothers can provide performance benefits.     

Iterative and sequential algorithms for multisensor signalenhancement

In problems of enhancing a desired signal in the presence of noise, multiple sensor measurements will typically have components from both the signal and the noise sources. When the systems that couple the signal and the noise to the sensors are unknown, the problem becomes one of joint signal estimation and system identification. The authors specifically consider the two-sensor signal enhancement problem in which the desired signal is modeled as a Gaussian autoregressive (AR) process, the noise is modeled as a white Gaussian process, and the coupling systems are modeled as linear time-invariant finite impulse response (FIR) filters. The main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system, and the authors apply the estimate-maximize (EM) algorithm for jointly estimating the desired signal, the coupling systems, and the unknown signal and noise spectral parameters. The resulting algorithm can be viewed as the time-domain version of the frequency-domain approach of Feder et al. (1989), where instead of the noncausal frequency-domain Wiener filter, the Kalman smoother is used. This approach leads naturally to a sequential/adaptive algorithm by replacing the Kalman smoother with the Kalman filter, and in place of successive iterations on each data block, the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data. A computationally efficient implementation of the algorithm is developed. An expression for the log-likelihood gradient based on the Kalman smoother/filter output is also developed and used to incorporate efficient gradient-based algorithms in the estimation process     

Parallel and sequential block Kalman filtering and theirimplementations using systolic arrays

Two sets of block Kalman filtering equations that differ in the manner of generating the initial and updated estimates are derived. Parallel and sequential schemes for generating these estimates are adopted. It is shown that the parallel implementation inherently leads to a block Kalman estimator which provides filtered estimates at the vector (block) level and fixed-lag smoother estimates at the sample level. The sequential implementation scheme, on the other hand, generates the estimates of each sample recursively, leading naturally to a scalar (filter) estimator. These scalar estimates are arranged in a vector form, resulting in a block estimator which solely generates filtered estimates both at the vector and sample levels. Simulation results on a speech signal are presented which indicate the advantages of the sequential block Kalman filter. An algorithm for iterative calculation of Kalman gain and error covariance matrices is given which does not require any matrix inversion operation. The implementation of this algorithm using available systolic array processors is presented. A ring systolic array which can be used to implement the state update part of the block Kalman filter is suggested     

Impact of Multiresolution Active and Passive Microwave Measurements on Soil Moisture Estimation Using the Ensemble Kalman Smoother

An observing system simulation experiment is developed to test tradeoffs in resolution and accuracy for soil moisture estimation using active and passive L-band remote sensing. Concepts for combined radar and radiometer missions include designs that will provide multiresolution measurements. In this paper, the scientific impacts of instrument performance are analyzed to determine the measurement requirements for the mission concept. The ensemble Kalman smoother (EnKS) is used to merge these multiresolution observations with modeled soil moisture from a land surface model to estimate surface and subsurface soil moisture at 6-km resolution. The model used for assimilation is different from that used to generate "truth." Consequently, this experiment simulates how data assimilation performs in real applications when the model is not a perfect representation of reality. The EnKS is an extension of the ensemble Kalman filter (EnKF) in which observations are used to update states at previous times. Previous work demonstrated that it provides a computationally inexpensive means to improve the results from the EnKF, and that the limited memory in soil moisture can be exploited by employing it as a fixed lag smoother. Here, it is shown that the EnKS can be used in large problems with spatially distributed state vectors and spatially distributed multiresolution observations. The EnKS-based data assimilation framework is used to study the synergy between passive and active observations that have different resolutions and measurement error distributions. The extent to which the design parameters of the EnKS vary depending on the combination of observations assimilated is investigated     

Estimation of nonstationary EEG with Kalman smoother approach: an application to event-related synchronization (ERS)

An adaptive spectrum estimation method for nonstationary electroencephalogram by means of time-varying autoregressive moving average modeling is presented. The time-varying parameter estimation problem is solved by Kalman filtering along with a fixed-interval smoothing procedure. Kalman filter is an optimal filter in the mean square sense and it is a generalization of other adaptive filters such as recursive least squares or least mean square. Furthermore, by using the smoother the unavoidable tracking lag of adaptive filters can be avoided. Due to the properties of Kalman filter and benefits of the smoothing the time-frequency resolution of the presented Kalman smoother spectra is extremely high. The presented approach is applied to estimation of event-related synchronization/desynchronization (ERS/ERD) dynamics of occipital alpha rhythm measured from three healthy subjects. With the Kalman smoother approach detailed spectral information can be extracted from single ERS/ERD samples.     

Mobile Location Estimator in a Rough Wireless Environment Using Extended Kalman-Based IMM and Data Fusion

An extended Kalman-based interacting multiple model (EK-IMM) smoother is proposed for mobile location estimation with the data fusion of the time of arrival (TOA) and the received signal strength (RSS) measurements in a rough wireless environment. The extended Kalman filter is used for nonlinear estimation. The IMM is employed as a switch between the line-of-sight (LOS) and non-LOS (NLOS) states, which are considered to be a Markov process with two interactive modes. Combining extended Kalman filtering with the IMM scheme for accurately smooth range estimation between the corresponding base station (BS) and mobile station (MS) in the rough wireless environment, the proposed robust mobile location estimator, in association with data fusion, can efficiently mitigate the NLOS effects on the measurement range error. Simulation results illustrate that the performance of the proposed method has been significantly improved in the LOS/NLOS transition case. Moreover, the performance of the EK-IMM smoother with data fusion is also better than that with a single measurement used alone.      

Processing performance of two Kalman filter algorithms with aDSP32C by using assembly and C languages

Two Kalman filter algorithms are implemented with a DSP32C processor. These two Kalman filters use conventional matrix operation and U-D factorization algorithms, respectively. The real-time processing performance of each algorithm is evaluated in terms of throughput, program and data memory sizes. Both DSP32C assembly and high-level C language programs of these two algorithms are developed (a total of four programs) for evaluating the coding efficiency. It is observed that both algorithms can be more efficiently programmed by using assembly language, a matrix-based algorithm enjoys its simple and regular operations so that less program memory is required in both assembly and in C languages, the U-D factorization algorithm involves fewer multiply-accumulate operations and provides a fast throughput in C language only, and the advantage of less multiply-accumulate operations in U-D factorization algorithm no longer exists in assembly language when the number of states of a Kalman filter is large     

Monte Carlo smoothing with application to audio signal enhancement

We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao-Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. All the algorithms suggested are tested with real speech and audio data, and the results are shown and compared with those generated using the generic particle smoother and the extended Kalman filter (EKF). It is found that the proposed Rao-Blackwellized particle smoother improves on the standard particle smoother and the extended Kalman smoother. In addition, the proposed block-based smoother algorithm enhances the efficiency of the proposed Rao-Blackwellized smoother by significantly reducing the storage capacity required for the particle information     

基于REKF的异类传感器异步数据融合算法研究

提出了一种基于异类传感器(R和IR)的数据融合目标跟踪算法,两种传感器具有不同的测量维数,量测数据异步采样并以不同的速率传输到融合中心站点.通过时间匹配技术,完成两种异步数据的融合,然后实现滤波器的状态更新.同时文中讨论了一种REKF(旋转推广卡尔曼滤波:Rotation Extended Kalman Filter)算法,可以有效地解决量测非线性和降低计算量的问题.     

BPNN辅助KF的MEMS陀螺仪数据处理方法

针对微机电系统(MEMS)陀螺仪数据误差建模不精确或无法给出模型的情况,提出了误差反馈（BP）神经网络辅助卡尔曼滤波对陀螺仪数据进行降噪处理的方法。分析卡尔曼滤波器的系统噪声方差Q矩阵可知,当模型不精确时可通过Q补偿。基于BP神经网络优化Q值原理,首先把采集到的MEMS陀螺仪数据输入卡尔曼滤波器得到Q;再把新息、滤波增益、量测噪声方差输入神经网络,把Q作为神经网络的输出,神经网络优化系统噪声协方差矩阵得到Q*;最后将Q*作为卡尔曼滤波算法系统噪声方差矩阵。实验结果表明,在建模不精确的情况下该方法也能有效提高陀螺仪的精度。     

多通道ARMA信号信息融合Wiener滤波器

应用Kalman滤波方法,基于白噪声估计理论,在线性最小方差最优信息融合准则下,提出了多通道ARMA信号的两传感器信息融合稳态最优Wiener滤波器、平滑器和预报器;给出了最优加权阵和最小融合误差方差阵.与单传感器情形相比,可提高滤波精度.一个雷达跟踪系统的仿真例子说明了其有效性.     

基于LabVIEW的某导航设备卡尔曼滤波方位解算修正技术

某导航设备信号常使用卡尔曼滤波算法进行方位解算。为改良卡尔曼滤波噪声系数，确保算法在较短的时间内准确解算设备信号方位值，提出一种基于LabVIEW 的卡尔曼滤波方位解算修正技术，通过LabVIEW 快速构建信号模型和卡尔曼滤波方位解算模型，完成对卡尔曼滤波初始参数的修正。经测试，该技术有效缩短卡尔曼滤波噪声系数修正时间，可应用于实装工程。     

基于滤波方法的OFDM信道估计研究

维纳滤波和卡尔曼滤波都是基于最小均方误差准则的滤波方法,本文主要研究这两种滤波方法在OFDM信道估计中的应用。为了跟踪频率选择性信道的变化,采用在OFDM系统中易于实现的梳状导频进行研究。传统的MMSE在统计意义上是最好的线性估计器,但是需要对矩阵求逆,是一种计算量较大,算法较复杂的方法。LMMSE是频域维纳滤波方法,其减小了MMSE的复杂度,但只适用于慢衰落信道,针对时变信道,本文提出卡尔曼滤波的信道估计方法,仿真结果表明,卡尔曼滤波的信道估计方法在时变信道中具有良好的性能。     

Design of Gaussian Approximate Filter and Smoother for Nonlinear Systems with Correlated Noises at One Epoch Apart

In this study, the authors investigate the filtering and smoothing problems of nonlinear systems with correlated noises at one epoch apart. A pseudomeasurement equation is firstly reconstructed with a corresponding pseudomeasurement noise, which is no longer correlated with the process noise. Based on the reconstructed measurement model, new Gaussian approximate (GA) filter and smoother are derived, from which Kalman filter and smoother can be obtained for linear systems. For nonlinear systems, different GA filters and smoothers can be developed through utilizing different numerical methods for computing Gaussian-weighted integrals involved in the proposed solution. Numerical examples concerning univariate nonstationary growth model, passive ranging problem, and target tracking show the efficiency of the proposed filtering and smoothing methods for nonlinear systems with correlated noises at one epoch apart.     

基于无穷单应阵的动态天基弱小目标检测

提出了一种基于无穷单应矩阵抑制动态天基背景的方法,为动态天基背景下的弱小运动目标检测提供了新思路。与以往方法不同,对于由成像卫星运动而造成运动的高频恒星背景,该方法首先利用惯性坐标系下成像卫星姿态及位置的变化,确定卫星平台运动对恒星成像的影响;然后,根据相机对无穷远点的成像原理,计算出不同时刻图像之间的单应矩阵以补偿背景恒星的运动;利用改进的中值滤波抑制低频地球背景,并结合三维时空方向滤波和卡尔曼预测实现对弱小目标的检测与稳定跟踪。实验结果表明,算法能对背景恒星运动准确补偿,抑制背景的效果(图像信噪比增益和背景抑制因子)为传统方法两倍以上,在背景抑制后对弱小目标进行有效检测,定位误差可稳定在半个像素以内。     

基于扩展卡尔曼滤波的水下目标测量系统

为实时、准确获取水下目标的航迹,设计采用运动通信平台获取目标的相对位置,进而推算目标航速和位置。采用扩展卡尔曼滤波方法对测量数据进行处理,推导了卡尔曼滤波算法,建立了目标状态方程和测量方程。针对系统的非线性测量方程,采用雅克比矩阵进行线性化处理,进而建立了扩展卡尔曼滤波算法。通过实例仿真分析,结果表明,该算法收敛速度和估计精度能够满足系统的应用要求,是有效、可行的。     

无人机导航系统的探索与研究

文中提出了无人机GPS/INS组合导航系统的解决方案。首先介绍导航系统的算法和原理,根据任务需求,给出硬件构成及软件核心程序流程。通过仿真结果证明,在组合系统中,采取PID控制以及卡尔曼滤波算法,大大提高了导航的精度。     

Derivation of a sawtooth iterated extended Kalman smoother via theAECM algorithm

The iterated extended Kalman smoother (IEKS) is derived under expectation-maximization (EM) algorithm formalism, providing insight into the behavior of the suboptimal extended Kalman filter (EKF) and smoother (EKS). Through an investigation of smoothing algorithms that result from variants of the EM algorithm, the sawtooth iterated extended Kalman smoother (SIEKS) and its computationally inexpensive counterparts are proposed via the alternating expectation conditional maximization (AECM) algorithm. The SIEKS is guaranteed to produce a sequence estimate that moves up the likelihood surface. Numerical simulations including frequency tracking examples display the superior performance of the sawtooth EKF over the standard EKF for a range of nonlinear signal models     

Kalman filter with hypothesis testing: A tool for estimating uncertain parameters

In this paper we present a simple and practical algorithm for the estimation of uncertain parameters of linear systems. The uncertainty is twofold, involving random observation noise, and possible jumps in the parameter values. The jumps may occur at unknown points in time, and are of unknown magnitudes and directions. The algorithm is based on the Kalman filter, with a single-sample hypothesis test, which is used to employ a three-state decision rule (yes, no, maybe). The maybe choice invokes a fading memory Kalman filter. The overall algorithm contains the constant parameter filter, fading memory filter, and the set of tests and rules that enable it to switch back and forth between the two filters. Application examples are presented.     

Inference life-models of electrical insulating materials by using aKalman filter

A Kalman filter is applied to life tests for characterizing electrical or thermal endurance of electrical insulating materials. This recursive estimator provides updated life model parameter values after each life test. The life models are: (1) inverse power law and the exponential law, used for electrical or multi-stress ageing; and (2) Arrhenius model, used for thermal ageing. The state, prediction, and updating equations of the Kalman filter algorithm are specified for insulation endurance inference. Insight into the definition of the state variables, which are directly related to the model parameters, and determination of system and observation errors are developed. A recursive breakdown test detects important changes in the prevailing ageing process. The range of validity of the life model, as well as information on electrical and thermal threshold are considered. A flow chart of the filtering algorithm is presented. Example experimental results relevant to insulating materials and systems subjected to electrical and thermal life tests are processed according to the algorithm