Efficient recursive state estimator for dynamic systems withoutknowledge of noise covariances

An efficient recursive state estimator for dynamic systems without knowledge of noise covariances is suggested. The basic idea for this estimator is to incorporate the dynamic matrix and the forgetting factor into the least squares (LS) method to remedy the lack of knowledge of noises. We call it the extended forgetting factor recursive least squares (EFRLS) estimator. This estimator is shown to have similar asymptotic properties to a completely specified Kalman filter state estimator. More importantly, the performance of EFRLS greatly exceeds that of existing filtering techniques when the noise variance is misspecified. In addition, EFRLS also performs well when there is cross-correlation between the process and measurement noise streams or temporal dependencies within those streams. Some discussions and a number of simulations are made to provide practical guidance on the choice of an optimal forgetting factor and evaluate the performance of the EFRLS algorithms, which strongly dominates that of the standard forgetting factor recursive least squares (FRLS) and some misspecified Kalman filtering     

Optimal sensor selection strategy for discrete-time stateestimators

A novel sensor selection strategy is introduced, which can be implemented on-line in time-varying discrete-time system. We consider a case in which several measurement subsystem are available, each of which may be used to drive a state estimation algorithm. However, due to practical implementation constraints (such as the ability of the on-board computer to process the acquired data), only one of these subsystems can actually by utilized at a measurement update. An algorithm is needed, by which the optimal measurement subsystem to be used is selected at each sensor selection epoch. The approach described is based on using the square root V-Lambda information filter as the underlying state estimation algorithm. This algorithm continuously provides its user with the spectral factors of the estimation error covariance matrix, which are used in this work as the basis for an on-line decision procedure by which the optimal measurement strategy is derived. At each sensor selection epoch, a measurement subsystem is selected, which contributes the largest amount of information along the principal state space direction associated with the largest current estimation error. A numerical example is presented, which demonstrates the performance of the new algorithm. The state estimation problem is solved for a third-order time-varying system equipped with three measurement subsystem, only one of which can be used at a measurement update. It is shown that the optimal measurement strategy algorithm enhances the estimator by substantially reducing the maximal estimation error     

Optimum FFT-based frequency acquisition with application toCOSPAS-SARSAT

In the case of a single sinusoid or multiple well-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform followed by a fine estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described. It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors. This method achieves a frequency standard deviation and a bias in the order of only a few percent of a bin. In the case of short-time stationarity, for a moderate number of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, in contrast to the asymptotic result of 1.5 dB. The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts. The algorithm is analyzed theoretically, and good agreement is found with test results     

基于复合地标导航的动平台四旋翼飞行器自主优化降落技术

针对四旋翼飞行器在依靠地标导航完成动平台自主降落任务中存在的目标易丢失、地标定位死区大和降落可靠性差等问题,设计了一种基于复合地标导航的动平台四旋翼飞行器自主优化降落系统。该系统以圆环地标和二维码构成复合地标来解决仅用单一地标定位时存在的定位死区大和定位范围小等问题。针对地标识别丢失、动平台车轮打滑和码盘标定不精确等问题,建立动平台的精确运动模型同时考虑码盘包含未知测量偏差,基于扩展卡尔曼滤波器实现了对动平台连续位姿的在线估计。最终,基于动平台位姿估计结果以最小Jerk指标设计降落轨迹和降落策略,实现了四旋翼飞行器在动平台上高效平稳的降落。为验证所提系统的有效性,设计了仿真和实际降落实验,验证了所提复合地标实现摄像头距离在0.5~6.0 m内的综合完整定位;所设计的动平台状态估计器能在码盘存在未知测量偏差的情况下准确估计出平台的实时位姿,同时所提自主优化降落策略和轨迹规划算法保证了可靠的动平台降落。     

State Estimation for Discrete Systems with Switching Parameters

The problem of state estimation for discrete systems with parameters which may be switching within a finite set of values is considered. In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time. For the Markov parameter case, it is found that the optimal estimator requires only N2 elemental estimators where N is the number of possible parameter values.     

On Optimal Control of Linear Systems in the Presence of Multiplicative Noise

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an "enforced separation" solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

Time delay estimation at high signal-to-noise ratio

The estimation of the delay between two signals is examined in the limit of high signal-to-noise ratio (SNR). It is shown that for the case of white noise, cross correlation with no prefiltering approaches the optimal maximum-likelihood (ML) estimator as the SNR grows to infinity. In simulation experiments with SNRs greater than 1, it outperforms the approximate ML estimator, which is based on estimated spectra. Other algorithms, such as generalized cross correlation or parameter estimation algorithms, are shown to be suboptimal at high SNRs     

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

MMAE-Based Control with Space-Time Point Process Observations

A multiple model adaptive estimator (MMAE) has been formulated to estimate the state of a dynamic system modeled by a linear stochastic differential equation, from which measurements, described as a noise-corrupted space-time point process functionally related to that state, are extracted. Assumed certainty equivalence is used to combine such an estimator with the LQ full-state feedback controller to synthesize a practical, implementable controller. Performance of the estimator and resultant controller characteristics are investigated via simulation as a function of approximation method used to limit the full-scale estimator to finite dimensionality and also as a function of important parameters defining the dynamics and observation processes.     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Adaptive Estimation for a System with Unknown Measu rement Bias

An adaptive state estimator for passive underwater tracking of maneuvering targets is developed. The state estimator is designed specifically for a system containing unknown or randomly switching biased measurements. In modeling the stochastic system, it is assumed that the bias sequence dynamics can be modeled by a semi-Markov process. By incorporating the semi-Markovian concept into a Bayesian estimation technique, an estimator consisting of a bank of parallel, adaptively weighted, Kalman filters has been developed. Despite the large and randomly varying measurement biases, the proposed estimator, provides an accurate estimate of the system states.     

基于普通分离原理的制导/估计综合设计方法

现有的先进制导律研究常常分离设计最优估计器和最优制导律,但是这种分离设计没有被证明是有效和最优的设计方法.本文基于普通分离原理(GST),提出一种制导/估计综合设计方法.首先,将拦截器反导作战模型考虑为一类非线性、非高斯追逃拦截问题,建立了噪声环境中追逐-逃逸对策模型;其次,引入追逃未达集概念,利用几何方法将估计器设计...     

高超声速飞行器组合导航鲁棒滤波算法

高超声速飞行器由于其飞行环境的影响,使得GPS和星敏感器的量测噪声表现出非高斯特性。针对常规基于Kalman滤波的组合导航在非高斯噪声下性能下降的问题,提出了基于鲁棒滤波的高超声速飞行器组合导航算法。方法在惯性／GPS／＆异步量测建模的基础上,通过随机去耦将量测更新转化为线性回归问题,并基于M估计获得状态量最优估计。仿真结果表明,方法对非高斯噪声具有更好的鲁棒性,有效提高了高超声速飞行器组合导航系统的性能。     

Estimating the Doppler centroid of SAR data

After reviewing frequency-domain techniques for estimating the Doppler centroid of synthetic-aperture radar (SAR) data, the author describes a time-domain method and highlights its advantages. In particular, a nonlinear time-domain algorithm called the sign-Doppler estimator (SDE) is shown to have attractive properties. An evaluation based on an existing SEASAT processor is reported. The time-domain algorithms are shown to be extremely efficient with respect to requirements on calculations and memory, and hence they are well suited to real-time systems where the Doppler estimation is based on raw SAR data. For offline processors where the Doppler estimation is performed on processed data, which removes the problem of partial coverage of bright targets, the ΔE estimator and the CDE (correlation Doppler estimator) algorithm give similar performance. However, for nonhomogeneous scenes it is found that the nonlinear SDE algorithm, which estimates the Doppler-shift on the basis of data signs alone, gives superior performance     

Total information processor for 121.5/243 MHz SARSAT signals

Search and rescue satellite-aided tracking (SARSAT) has certain shortcomings which could possibly be ameliorated by employing a more extensive signal processing strategy. The approach proposed is based on partially compensating for the Doppler shift, which then permits the data processing windows to be increased significantly. Incorporating a ranking technique with the conventional fast Fourier transform (FFT) processor and implementing an autoregressive moving-average estimator provides an optimal strategy that maximizes the probability of detecting the emergency signals     

State estimation using an approximate reduced statistics algorithm

The problem of state estimation using nonlinear additive Gaussian noise measurements is addressed. A geometric model for the posterior state density is assumed based on a multidimensional Haar basis representation. An approximate reduced statistics (ARS) algorithm, suggested by the parameter estimator of Kulhavy is then developed, using successive minimization of relative entropy between model densities and an approximate posterior density. The state estimator thus derived is applied to a bearings-only target tracking problem in a multiple sensor scenario     

IMM estimator versus optimal estimator for hybrid systems

The special feature of the interacting multiple model (TMM) estimator that distinguishes it from other suboptimal multiple model (MM) estimators is the "mixing/interaction" between its "mode-matched" base state filtering modules at the beginning of each cycle. This note shows that the same feature is exactly what it has in common with the optimal estimator for hybrid (MM) systems and this can be seen as the main reason for its success.     

考虑一阶环节和法向约束的最优导引律

前言 目前关于最优导引律的文献中,除文献讨论了将导引对象视为具有瞬时响应特性的质点,考虑了控制的法向约束而外,其他均未考虑控制的约束问题。为了大幅度地提高导引精度,在建立“导引对象--目标”的数学模型时,就必须考虑导引对象的动态响应。     

阵风缓和系统的组合控制规律

 本文给出具有阵风缓和和其他主动控制功能的组合控制规律。阵风缓和用测量阵风方法的开环控制。当缓和输出量时,闭环控制用以稳定阵风缓和系统并满足其他主动控制要求。本文用一组合的二次型性能指标,得到最优反馈控制规律与测量阵风的组合的控制规律。文末并附有算例。