多目标跟踪的多伯努利平滑方法

为提高基于滤波的多目标跟踪方法的性能,提出了一种多伯努利平滑方法.该方法由前向滤波和反向平滑两部分组成,前向滤波采用势平衡多目标多伯努利滤波,反向平滑利用多伯努利概率密度近似多目标平滑状态的概率密度,实现多目标平滑状态概率密度的反向递推计算.仿真结果表明,与滤波相比,多伯努利平滑对目标数量和目标状态的估计精度都有显著提高.     

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.     

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     

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.     

Estimation of noisy telegraph processes: Nonlinear filtering versus nonlinear smoothing (Corresp.)

In the estimation problem of a two-state stationary Markov process with Gaussian white noise added, the optimal smoother is a two-filter smoother. In a special case, the performance of the optimal nonlinear filter and smoother is evaluated analytically. Some asymptotic results are also derived.     

Nonlinear speed observer for high-performance induction motorcontrol

In this paper, we consider the problem of estimating the angular velocity of an induction motor using encoder measurements. Two methods are compared. In the first method, the speed is found by calculating the backward difference of the position measurement and low-pass filtering the result. In the second method, the velocity is estimated using a nonlinear observer constructed using the known dynamic model of the induction motor. The performance of the two methods is evaluated in the context of their use for velocity feedback in a high-performance field-oriented control law. Experimental results demonstrate that the speed observer leads to a smoother operation of the motor in closed-loop. With the estimator based on differentiation, either the delay imposed by the low-pass filter is too large to maintain high bandwidth feedback, or the fluctuations in the estimated speed are so large that much more energy ends up being dissipated to achieve the same control task     

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.     

Can the zero-lag filter be a good smoother?

The problem of constructing low complexity suboptimal fixed-lag estimators is discussed. First, it is shown that any optimal fixed-lag estimator structure generally performs better if more delay is accepted than the designed lag. As this holds for any design lag including zero-lag, it is demonstrated that the zero-lag filter treated as a suboptimal fixed-lag smoother has an error considerably lower than the conventional zero-lag error. A near optimal fixed-lag smoother is then found by a straightforward extention of the zero-lag filter. Several examples are considered. Finally, the usefulness of the conventional fixed-lag mmse criterion is discussed.     

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     

Spectral design of weighted median Filters:A general iterative approach

A new design strategy for weighted median (WM) filters admitting real and complex valued weights is presented. The algorithms are derived from Mallows theory for nonlinear selection type smoothers, which states that the closest linear filter to a selection type smoother in the mean square error sense is the one having as coefficients the sample selection probabilities (SSPs) of the smoother. The new design method overcomes the severe limitations of previous approaches that require the construction of high order polynomial functions and high dimensional matrices. As such, previous approaches could only provide solutions for filters of very small sizes. The proposed method is based on a new closed-form function used to derive the SSPs of any WM smoother. This function allows for an iterative approach to WM filter design from the spectral profile of a linear filter. This method is initially applied to solve the median filter design problem in the real domain, and then, it is extended to the complex domain. The final optimization algorithm allows the design of robust weighted median filters of arbitrary size based on linear filters having arbitrary spectral characteristics.     

Practical Kalman Filter Software Performance Testing & Validation

Several tests are described which can be used for any Kalman-type filter/smoother computer program. These tests are demonstrated by a case history on a large dimensional Kalman filter/smoother program which implements a 34-state inertial navigation system dynamic error model. The execution of a large dimensional Kalman filter/smoother (KFS) on real measurement data does not represent a software test of the KFS since the right answer (the correct underlying state vector) is unknown; only ``reasonableness checks' are actually possible. Simulated test data were used to exercise the KFS program in a Monte Carlo sense and its outputs evaluated using heuristic plot comparisons as well as rigorous statistical tests. Direct tests on the accuracy of the transition matrix, discrete process noise matrix, and covariance matrix calculations have been derived and demonstrated. Methods for testing properties of the Kalman filter innovations sequence are also covered. The approach and required auxiliary software that generates the test data can be employed to perform suboptimal modeling sensitivity studies and for evaluating analysis methods that depend on KFS estimates.     

容积Rauch-Tung-Striebel平滑器

针对离散非线性系统的状态平滑问题,基于Rauch-Tung-Striebel(RTS)理论设计了一种容积卡尔曼平滑器(Cubature Kalman Smoother,CKS),即容积Rauch-Tung-Striebel平滑器(RTSCKS)。首先,基于经典贝叶斯状态估计理论框架,推导了状态概率密度分布形式的非线性系统最优平滑算法;其次,基于Rauch-Tung-Striebel理论,建立了相应的最优平滑递推算法;然后,将其与容积卡尔曼滤波算法相结合,建立了递推形式的RTS-CKS平滑器;最后,通过典型的纯方位跟踪模型验证了该平滑器的可行性和有效性。该平滑器为非线性系统的状态估计提供了新的估计算法。     

一种基于优化的动态补偿滤波器的设计方法

将动态补偿滤波器的设计问题转化为一个多变量的优化问题，本文描述了这种方法的构思、步骤，给出的算例和进一步的讨论说明了这种方法的特点。     

Schur type algorithms for spatial LS estimation with highlypipelined architectures

A family of Schur-type spatial least-squares algorithms is presented for solving the spatial LS estimation problem, in which the correlation matrix is neither Toeplitz nor near-Toeplitz, by order recursion. Normalized spatial Levinson- and Schur-type algorithms are also derived. Highly pipelined architectures are designed to realize these recursions. The reflection coefficients are first computed using the spatial Schur type recursions. Then, the forward and backward filter parameters are calculated by the spatial Levinson-type recursions. A pyramid systolic array is demonstrated to calculate not only the filter parameters but also the LDU decomposition of the inverse cross-correlation matrix at every clock phase. This pyramid array can be mapped onto a two-dimensional systolic array which has a simpler structure. A square systolic array is developed to implement the Levinson- and Schur-type temporal recursive LS (RLS) algorithms. A highly concurrent architecture which exploits the parallelism of the spatial Schur-type recursions is illustrated to perform the LDU decomposition of the cross-correlation matrix     

Application of Kalman filtering to real-time preprocessing ofgeophysical data

An algorithm for automatic preprocessing of multiple data sequences in real-time is proposed. Based on a fixed-lag Kalman filter approach, it models the signal using a state vector that consists of the signal, its first three differences, and a special variable used to implement data editing functions. The smoothed output lessens some of the noise problems encountered in practice, and the method provides mechanisms for identification and removal of spikes, identification and measurement of steps, and filling of data gaps. Two versions of the algorithm are developed, one based on the conventional form of the Kalman filter, and one using a sequential processing technique. The computational requirements of each are analyzed and compared. An alternate approach for fixed-lag smoothing based on a one-step forward predictor and an L-step backward sweep, with L being the fixed lag, is also considered. It is shown that despite the greater complexity of the model used in the algorithms proposed, for L>30 the computational requirements are very similar to those of the alternate method     

Locally monotonic regression

The concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal. The median filter is a suboptimal smoother under this measure of smoothness, since a filter pass does necessarily yield a locally monotonic output; even if a locally monotonic output does result, there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal. Locally monotonic regression is a technique for the optimal smoothing of finite-length discrete real signals under such a criterion. A theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given. Regression is considered as an approximation problem in R_n , the criterion of approximation is derived from a semimetric, and the approximating set is the collection of signals sharing the property of being locally monotonic     

非中心平滑算法及其在无人直升机 遥测数据处理中的应用

在一般多项式拟合移动平滑滤波的基础上,推导出位置多项式滤波非中心平滑的数学公式,建立并实现了位置多项式滤波的非中心平滑算法,结果表明滤波方差比得到了降低.本算法已应用于某型无人直升机遥测数据的处理中,实践证明,该方法有效地滤出了遥测数据中的随机误差,为分析无人直升机的飞行性能和进行可靠地监控奠定了基础.     

H2 inferential filtering, prediction, and smoothing withapplication to rolling mill gauge estimation

A new minimum mean square error optimal linear estimation problem is considered where no direct measurement of the output to be estimated is available. The optimal filter, predictor, and smoother are derived for this case where outputs must be inferred from available measurements. The results cover the usual Wiener or Kalman filtering problems and also optimal deconvolution estimation problems. However, they also apply to the situation, often found in industry, where estimates of signals are required that can only be determined from secondary measurements. A weighted H₂ cost-function is minimized where the weighting function can be chosen to improve the robustness of the solution. The optimal estimators are derived both for stable and for unstable signal source models. A signal-processing application is considered in detail to demonstrate the use of the optimal filter. The gauge control problem in metal rolling mills is discussed where only force measurements are available     

A low delay 16 kb/s speech coder

A code tree generated by a stochastically populated innovations tree with a backward adaptive gain and backward adaptive synthesis filters is considered. The synthesis configuration uses a cascade of two all-pole filters: a pitch (long time delay) filter followed by a formant (short time delay) filter. Both filters are updated using backward adaptation. The formant predictor is updated using an adaptive lattice algorithm. The multipath (M, L) search algorithm is used to encode the speech. A frequency-weighted error measure is used to reduce the perceptual loudness of the quantization noise. The addition of the pitch filter gives 2-10-dB increase in segSNR (segmental signal-to-noise ratio) in the voiced segments. Subjective testing has shown that the coder attains a subjective quality equivalent to 7 b/sample log-PCM (pulse code modulation) with an encoding delay of eight samples (1 ms with an 8-kHz sampling rate)