并行卡尔曼滤波及其心动阵列实现综述

本文综述了基于心动(Systolic)阵列结构的并行卡尔曼滤波各种算法及其心动阵列实现,对各种阵列滤波算法在处理单元数,计算时间和效率等方面进行了比较,并对进一步的研究工作提出一些展望。     

Square-root Bryson-Frazier smoothing algorithms

Some new square-root algorithms for Bryson-Frazier smoothing formulas are suggested: square-root algorithms and a fast square-root (or so-called Chandrasekhar type) algorithm. The new square-root algorithms use square-root arrays composed of smoothed estimates and their error covariances. These algorithms provide many advantages over the conventional algorithms with respect to systolic array and parallel implementations as well as numerical stability and conditioning. For the case of constant-parameter systems, a fast square-root algorithm is suggested, which requires less computation than others     

Sequential square root filtering and smoothing of discrete linear systems

Square-root information estimation algorithms are immensely important estimation analysis tools that are not sufficiently well understood nor adequately exploited. In an endeavor to rectify this state of affairs an expository derivation of the square-root information filter/smoother is given. It is based on the recursive least-squares method and is easier to grasp, interpret and generalize than are the dynamic programming arguments previously used. Backward smoothing algorithms, both square-root and covariance recursions, are derived as direct and consequences of the method. A comparison of smoothing algorithms indicates that those presented in this paper are the most efficient. Partitioning the results to separate bias parameters provides further computational economies and reduction of storage requirements.The principal objective of this paper is to inspire greater utilization of square-root estimation algorithms. Arguments supporting this thesis are the new least-squares filter/smoother derivations, enhanced numerical accuracy, reduced computation, and lower storage requirements.     

New square-root algorithms for Kalman filtering

Presents some new square-root algorithms that allow more reliable computation of the state estimates, using, as far as possible, quantities obtained via orthogonal operations. New algorithms are given for covariance quantities and information quantities, and a new combined algorithm is also presented     

Cubature Kalman smoothers

The cubature Kalman filter (CKF) is a relatively new addition to derivative-free approximate Bayesian filters built under the Gaussian assumption. This paper extends the CKF theory to address nonlinear smoothing problems; the resulting state estimator is named the fixed-interval cubature Kalman smoother (FI-CKS). Moreover, the FI-CKS is reformulated to propagate the square-root error covariances. Although algebraically equivalent to the FI-CKS, the square-root variant ensures reliable implementation when committed to embedded systems with fixed precision or when the inference problem itself is ill-conditioned. Finally, to validate the formulation, the square-root FI-CKS is applied to track a ballistic target on reentry.     

Multisensor fusion for linear control systems with asynchronous, Out-Of-Sequence and erroneous data

This paper presents a set of new centralized algorithms for estimating the state of linear dynamic Multiple-Input Multiple-Output (MIMO) control systems with asynchronous, non-systematically delayed and corrupted measurements provided by a set of sensors. The delays, which make the data available Out-Of-Sequence (OOS), appear when using physically distributed sensors, communication networks and pre-processing algorithms. The potentially corrupted measurements can be generated by malfunctioning sensors or communication errors. Our algorithms, designed to work with real-time control systems, handle these problems with a streamlined memory and computational efficient reorganization of the basic operations of the Kalman and Information Filters (KF & IF). The two versions designed to deal only with valid measurements are optimal solutions of the OOS problem, while the other two remaining are suboptimal algorithms able to handle corrupted data.     

An algorithm for propagating the square-root covariance matrix in triangular form

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the convential sequential estimation algorithm with regard to computation time.     

Estimation of urban air pollution

The problem of real-time estimation of air pollutant concentrations in an urban atmosphere based on concentration measurements made intermittently at a set of monitoring stations is considered. A square-root distributed parameter filter for a general class of dynamic urban air pollution models is developed. The filter is tested by application to a hypothetical urban area, and the effect of the number of monitoring stations on the estimated concentrations is studied.     

Uncertainties for recursive estimators in nonlinear state-space models, with applications to epidemiology

Consider a nonlinear dynamic system where one wishes to estimate a state vector using noisy measurements. Many algorithms have been proposed to address this problem, among them the extended Kalman filter (and its variants) and constant-gain stochastic approximation. To quantify the efficacy of these algorithms, it is necessary to describe the distribution of the state estimation error. Typically, performance has been measured by the estimation error covariance alone, which does not provide enough information to probabilistically quantify the estimation accuracy. By casting the estimation error in an autoregressive-type form, this paper addresses the broader question of the distribution of the error for a general class of recursive algorithms. We illustrate the distributional results in an epidemiological problem of disease monitoring.     

A general approach to constructing parameter identification algorithms in the class of square root filters with orthogonal and J-orthogonal tranformations

We study modern implementations of the discrete Kalman filter, namely array square-root algorithms. An important feature of such algorithms is the use of orthogonal and J-orthogonal transformations on each filtering step. For the first time, we develop for this class of algorithms a simple universal approach that lets us generalize any numerically stable implementation of this type to the case of updates in sensitivity equations of the filter with respect to unknown system model parameters. An advantage of the resulting adaptive schemes is their numerical stability with respect to machine rounding errors. Estimation of the noisy state vector of the system and identification of unknown system parameters occur simultaneously. The proposed approach can be used for parameter identification problems, adaptive control problems, experiment planning, and others.     

On-line identification and control of multivariablc discrete-time systems based on a transformed model

Recursive algorithms for on-line combined identification and control of linear discrete-time multivariable systems is presented. A variant of the observable canonical model with one-way coupling form of the state model is used to develop a solution of the problem. Exploiting the canonical structure of the model, the proposed solution turns out to be simpler than that obtained by El-Sherief (1983) and moreover, a combined decentralized state and parameter estimation based control scheme can be developed in three stages. In Stage I, the parameters of the system matrices are estimated by a recursive least-square algorithm or by a normalized stochastic approximation algorithm in decoupled manner. These parameters are then employed for state estimation in Stage 2 using a centralized conventional Kalman filter or by a decentralized adaptive Kalman filter which in turn reduces instrumentation and telemetry costs. Estimated parameters and states are then utilized in Stage 3 to implement the square-root based control law along with the good numerical behaviour of the control problem. The proposed algorithms are tested by considering an example of a third-order state-space model.     

Globally optimal flight path update with adding or removing out-of-sequence measurements

In a multisensor target tracking system, observations produced by sensors can arrive at a central processor out of sequence. There have been some state estimate update algorithms for out-of-sequence measurements (OOSMs). In this paper, we propose a flight path update algorithm for a sequence with arbitrary delayed OOSMs. The new algorithm has three advantages: (1) it is a globally optimal recursive algorithm; (2) it is an algorithm for arbitrary delayed OOSMs including the case of interlaced OOSMs with less storage, compared with the optimal state update algorithm in Zhang, Li, and Zhu (2005); (3) it can update the current whole flight path in addition to the current single state with less computation, i.e., the dimension of the matrices which need to be inverted is not more than that of the state in the process of updating the past ? (lag steps) estimates and corresponding error covariances. Besides, this algorithm can be easily modified to derive a globally optimal flight path update with removing an earlier (incorrectly associated) measurement.     

Array algorithms for H∞ estimation

We develop array algorithms for H^∞ filtering. These algorithms can be regarded as the Krein space generalizations of H ² array algorithms, which are currently the preferred method fur implementing H² filters. The array algorithms considered include two main families: square-root array algorithms, which are typically numerically more stable than conventional ones, and fast array algorithms which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters, as these conditions are built into the algorithms themselves. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H² case, further investigation is needed to determine the numerical behavior of such algorithms     

基于扩散卡尔曼滤波算法的目标跟踪估计

针对节点网络上的目标跟踪,提出一种基于扩散Kalman滤波算法的分布式跟踪估计.假设该节点网络系统按照线性状态空间模型演进,网络中的每个节点获取与未观察到的状态线性相关的测量值;对于每个测量值和每个节点,采用来自邻近区域的数据计算出一个局部状态估计值;采用一个基于扩散矩阵和连接矩阵的扩散步骤,将前面计算得到的邻域估计值...     

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

The presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez–Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez‐Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez–Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non‐Gaussian distributions, is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Hybrid state estimation: a target tracking application

In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related to the continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross-section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.     

LQ优化的并行化方法

本文提出了两种有效的并行ＬＱ优化算法，分别用于求解多输入及单输入情况下控制参数合成。这两种算法都可以用脉动阵列结构并行实现，通过对数据流时序以及控制器利用率的分析，说明了并行的有效性。     

A comparative analysis of various least-squares identification algorithms

The purpose of this paper is to clarify the relations and to provide some selection guides among several time-series identification algorithms that appear in the literature under different names but which are essentially least-squares identification algorithms where only the numerical solution of the least-squares estimation problem is different. Such algorithms are, apart from the batch and the sequential forms of direct least-squares, the PARCOR (partial correlation) algorithm, (which may be in the Durbin, the Levinson or the autocorrelation form), the lattice or the ladder algorithm, also known as the Markel-Gray algorithm, the square-root algorithm, the equation-error algorithm, and related algorithms.Further to the above, we shall discuss why certain such algorithms differ in performance from the direct least-squares forms, in terms of convergence, convergence-rate, computational effort (speed) per iteration, and in terms of robustness to computational errors, such as arise when using short word-length computers.     

基于高精度导航设备的海上多传感器配准算法

对海上多平台多传感器误差配准问题,利用平台的高精度导航信息将各传感器的量测数据转换到地心坐标系下,构建关于传感器偏差和舰艇姿态误差的伪测量模型,采用卡尔曼滤波对配准误差进行在线估计和补偿.算法较好地解决了传统的基于球极投影误差配准技术受地球曲率影响的不足,并突破了离线配准算法假定配准误差恒定的限制.仿真实验结果验证了算法的正确性和有效性.     

Learning algorithms for neural networks with the Kalman filters

Based on various approaches, several different learing algorithms have been given in the literature for neural networks. Almost all algorithms have constant learning rates or constant accelerative parameters, though they have been shown to be effective for some practical applications. The learning procedure of neural networks can be regarded as a problem of estimating (or identifying) constant parameters (i.e. connection weights of network) with a nonlinear or linear observation equation. Making use of the Kalman filtering, we derive a new back-propagation algorithm whose learning rate is computed by a time-varying Riccati difference equation. Perceptron-like and correlational learning algorithms are also obtained as special cases. Furthermore, a self-organising algorithm of feature maps is constructed within a similar framework.