Noise covariances estimation for systems with bias states

This paper presents a new approach to noise covariances estimation for a linear, time-invariant, stochastic system with constant but unknown bias states. The system is supposed to satisfy controllable/observable conditions without bias states. Based on a restructured data representation, the covariance of a new variable that consists of measurement vectors is expressed as a linear combination of unknown parameters. Noise covariances are then estimated by employing a recursive least-squares algorithm. The proposed method requires no a priori estimates of noise covariances, provides consistent estimates, and can also be applied when the relationship between bias states and other states is unknown. The method has been applied to strapdown inertial navigation system initial alignment. Simulation results indicate a satisfactory performance of the proposed method     

Estimating Noise Variances by Using Multiple Observers

Unknown variances of the noises that excite a time-invariant, linear dynamic system and/or in the observation of its output can be estimated by use of multiple observers. One observer is needed, in general, for each unknown variance. Each observer is time invariant and has different gains from the others. It is shown that each unknown variance is a linear combination of the variances of the residuals of the observers. The required estimates of the noise variances are obtained by using the measured variances of the residuals. The method presented in this paper is illustrated by an application to determining noise parameters in a ring laser gyro.     

Parameterization and adaptive control of space robot systems

In space application, robot system are subject to unknown or unmodeled dynamics, for example, in the tasks of transporting an unknown payload or catching an unmodeled moving object. We discuss the parameterization problem in dynamic structure and adaptive control of a space robot system with an attitude-controlled base to which the robot is attached. We first derive the system kinematic and dynamic equations based on Lagrangian dynamics and the linear momentum conservation law. Based on the dynamic model developed, we discuss the problem of linear parameterization in term of dynamic parameters, and find that in joint space, the dynamics can be linearized by a set of combined dynamic parameters; however, in inertial space linear parameterization is impossible in general. Then we propose an adaptive control scheme in joint space, and present a simulation study to demonstrate its effectiveness and computational procedure. Because most takes are specified in inertial space instead of joint space, we discuss the issues associated to adaptive control in inertial space and identify two potential problem: unavailability of joint trajectory because the mapping from inertial space trajectory is dynamic-dependent and subject to uncertainty; and nonlinear parameterization in inertial space. We approach the problem by making use of the proposed joint space adaptive controller and updating the joint trajectory by the estimated dynamic parameters and given trajectory in inertial space     

Event-triggered adaptive control for attitude tracking of spacecraft

Plug-and-play technology is an important direction for future development of spacecraft and how to design controllers with less communication burden and satisfactory performance is of great importance for plug-and-play spacecraft. Considering attitude tracking of such spacecraft with unknown inertial parameters and unknown disturbances, an event-triggered adaptive backstepping controller is designed in this paper. Particularly, a switching threshold strategy is employed to design the event-triggering mechanism. By introducing a new linear time-varying model, a smooth function, an integrable auxiliary signal and a bound estimation approach, the impacts of the network-induced error and the disturbances are effectively compensated for and Zeno phenomenon is successfully avoided. It is shown that all signals of the closed-loop system are globally uniformly bounded and both the attitude tracking error and the angular velocity tracking error converge to zero. Compared with conventional control schemes, the proposed scheme significantly reduces the communication burden while providing stable and accurate response for attitude maneuvers. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bi?s is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.     

基于未知输入观测器的非线性动态系统故障估计

针对一类受扰非线性动态系统的执行器故障估计问题,提出一种未知输入观测器来实现故障估计。首先,通过坐标变换将原系统转化为合适的形式;其次,采用线性矩阵不等式与Lyapunov泛函分别设计H_∞输出反馈控制器和未知输入观测器,在此基础上实现对系统中执行器故障的渐近估计;最后,通过机械臂系统仿真分析并验证了所提方法的有效性。与已有方法相比,所提方法不要求故障可导,也不要求故障或干扰上界已知,因此易于在工程实际中实现对非线性系统执行器故障的估计。     

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

Artificial excitation is the most employedtype,but it is not suitable for some large- scalestructures such as platforms,bridges and build-ings,because a sufficient amount of excitation en-ergy can be needed to vibrate these structures,andthat impliesthe dangerofdamaging them locally orglobally.So natural excitation ( such as wind,wave,and traffic excitation) can be used in thesecases.However,a measure of the input force be-ing applied to the systems is not available and onlythe response can be…     

A Discrete Method for Parameter Identification in Linear Systems with Transport Lags

Linear dynamical systems with transport lags are characterized by linear differential-difference equations. The task of identifying unknown parameters in such systems from the input-output data is difficult due to mathematical complications associated with differentialdifference equations. This paper presents a method which solves the identification problem. The method is digitally oriented and shows how a continuous-time system can be identified by discrete techniques. The solution is based on Kalman's least square method. The identification procedure essentially involves two steps: 1) discretizing the continuous system via finite difference approximation, and 2) estimating the parameters through the identification of the resulting discrete model. Experimental results have verified the validity of the proposed method.     

Identification of rational transfer function from frequencyresponse sample

A method for identifying a transfer function, H(z)=A(z)/B(z), from its frequency response values is presented. Identifying the transfer function involves determining the unknown degrees and coefficients of the polynomials A(z) and B( z), given the frequency response samples. The method for finding the parameters of the transfer function involves solving linear simultaneous equations only. An important aspect of the method is the decoupled manner in which the polynomials A(z) and B(z) are determined. The author presents two slightly different derivations of the linear equations involved, one based on the properties of divided differences and the other using Vandermonde matrices or, equivalently, Lagrange interpolation. A matrix synthesized from the given frequency response samples is shown to have a rank equal to the number of poles in the system     

传递矩阵-直接积分法及其应用

本文提出了借传递矩阵法建立“特征盘”的运动方程,然后借直接积分法求解,用以求转子-支承系统的临界转速、振型、不平衡响应、及稳定性分析的方法。导出了在考虑其本身的转动惯量、质量、剪切应力影响下的轴段传递矩阵。以实例说明了借传递矩阵法建立“特征”微分方程组的过程。计算与实测了一个模型转子-支承系统的不平衡响应、临界转速及振型,二者基本吻合。     

Radar target identification using the bispectrum: a comparativestudy

Radar target identification is performed using time-domain bispectral features. The classification performance is compared with the performance of other classifiers that use either the impulse response or frequency domain response of the unknown target. The classification algorithms developed here are based on the spectral or the bispectral energy of the received backscatter signal. Classification results are obtained using simulated radar returns derived from measured scattering data from real radar targets. The performance of classifiers in the presence of additive Gaussian (colored or white), exponential noise, and Weibull noise are considered, along with cases where the azimuth position of the target is unknown. Finally, the effect on classification performance of responses horn extraneous point scatterers is investigated     

Optimal Inputs for Nonlinear Process Parameter Estimation

The sensitivity of observed data to an unknown parameter is enhanced by utilizing optimal inputs. The derivation is given for the optimal input of an nth-order nonlinear differential equation. To obtain the optimal input, the solution of 4n two-point boundary value equations is required. Numerical resutis are given for a second order linear example. The optimal return is compared with the return obtained for a step input. The existence of a critical time length is demonstrated.     

一种线性辨识系统动态模型的自寻优算法

基于静态特性已知的线性时变系统,通过对其动态响应数据的分析,建立了随时间跳变的动态参数模型,提出了一种新的线性自寻优辨识算法。该算法在静态特性约束条件下,可估计模型的跳变时刻及结构参数。经对某航空发动机电子综合调节器燃油通道动态过程参数模型辨识的实例,验证了该算法精确快速。      

翼伞系统在未知风场中的归航控制

翼伞系统在未知风场中执行归航任务时,需获得风场的大小和方向信息,以便在归航过程中利用或者消除风场的影响。为实现翼伞系统在未知风场中精确归航与逆风雀降着陆,首先提出一种利用全球定位系统(GPS)定位数据和最小二乘法在线辨识风向和风速的方法,然后将风场中平均风的影响在轨迹规划中予以考虑,设计分段归航路径;将突风作为外界干扰,在轨迹跟踪过程中由线性自抗扰控制(LADRC)器进行观测和补偿。最后通过仿真实验验证了本文所提出的归航控制方法对于提高翼伞系统在未知风场中的归航精度和抗风能力有重要意义。     

A Stratified Statistical Filter with Nonlinear Application

This paper introduces a statistical filter (or, more strictly, a filtering algorithm) which has intended application in the area of nonlinear systems. Within this context, the filter enables one to investigate the convergence effects produced by varying the initial estimates associated with the respective state variables, together with the various system parameters. The present algorithm is not intended to replace the more powerful optimal statistical filters used in linear theory, but rather to provide a simulation tool which can readily be applied to a given nonlinear system. The application considered in this paper bears a similarity to a tracking problem which might be encountered by an optical device, where angular information is the primary observable quanity. In this particular application, angular observations are available, and statistical estimates are desired for a position variable, together with an unknown parameter. The application is introduced primarily for the purpose of demonstrating the behavior of the filter when applied to a relatively simple nonlinear system.     

A modified adaptive Kalman filter for real-time applications

A modified adaptive Kalman filtering algorithm is derived for the standard linear problem under an irregular environment where all variances of the zero-mean Gaussian white (system and observation) noises are unknown a priori. This algorithm has certain merits over various existing adaptive schemes in that it is simple, efficient, and suitable for real-time applications. An illustrative numerical example is presented     

JTIDS relative navigation and data registration

The Joint Tactical Information Distribution System (JTIDS), an integrated communication, navigation, and identification system, provides a solution to the critical data registration problem facing the joint US military services today, namely, the establishment, in real-time, of accurately correlated positions and tracks for all friendly, unknown, and hostile targets in an operational area, thus providing the total situation awareness required for tactical and C² operations. The fundamental relationships of JTIDS navigation and the error analysis for target registration and target hand-off in both geodetic and relative grid coordinates are presented. Simulation results are provided for two scenarios to demonstrate the level of improvement that JTIDS navigation can have on situation awareness, target acquisition, and weapon delivery. Specifically, it is shown that accurate data registration can be achieved by as few as two JTIDS members, with or without accurate knowledge of geodetic position     

Statistically Optimum Optical Data Processing with Automatic Focus Estimation

The problem of optimally processing data with unknown focus is investigated. Optimum data processors are found by the method of maximum likelihood under a variety of assumptions that apply to most of the situations arising in practice. The unknown focus may be either an unknown parameter or an unknown random variable; the signal may be of known form or a random function; it is further assumed that the signal is received in additive, white, Gaussian noise. The problems of jointly estimating other unknown parameters and, in the case of a random signal, jointly estimating the signal, are also treated. The asymptotic variance and correlation of the estimators is discussed. Electrooptical realizations of the maximum likelihood computers are given. An iterative method of solution of the likelihood equation is also discussed. The discussion and results are directly applicable to the processing of synthetic aperture radar data.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.