Discrete-time min-max tracking

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.     

Numerical Results on the Convergence of Relative Efficiencies

This paper considers the detection of a known constant signal in an additive non-Gaussian noise under the assumptions of discrete time and statistically independent noise samples. The objective is to determine how large sample size must be before the easily computed asymptotic relative efficiency becomes a valid measure of performance. The exact small-sample error probabilities are calculated for a Neyman-Pearson optimal nonlinear detector consisting of a zeromemory nonlinearity followed by summation and threshold comparison. "Large-tailed" noise having a double exponential distribution is used as an example. The exact distribution of the test statistics for a linear detector and for the Neyman-Pearson optimal detector are calculated. Then the relative efficiency of the Neyman-Pearson optimal detector, as compared to a linear detector, is computed in order to study the rate of approach of the relative efficiency to its asymptotic value.     

State Estimation and Divergence Analysis

A growing memory discrete dynamic model for performing temporal extrapolations along a predetermined path in a random field is presented. This dynamic model is used to drive a linear system that is itself driven by discrete white noise. The coupled system is used to derive a state estimation scheme that recursively processes noisy measurements of the system. In addition, using the aforementioned dynamic model as a reference (truth) model, the authors develop a covariance analysis to measure the estimation errors that occur when the dynamics along the path through the field are modeled as a Markov linear model and state estimation is performed using discrete Kalman filtering. The performance evaluation of an inertial navigation system influenced by the Earth's gravity field aboard a maneuvering ship is provided as a specific illustrative example.     

广义离散随机线性系统的最优调节器

讨论广义离散随机线性系统在二次型性能指标下的最优控制问题。导出的最优控制律由系统输出和部分状态的线性反馈构成,这不仅降低了滤波的黎卡提方程的阶次,显著地减少了计算量,而且在工程中也是可实现的。     

Optimal Detection of a Signala with Time-Varying Carrier Phase

The problem considered in this paper is the detection of a signal known except for time-varying carrier phase in white Gaussian noise. The method of attacking this problem is to model the time-varying carrier phase as a Markov process. Fourier transform techniques are then applies to yield a simple time-wise adaptive form for the phasetracking detector. Optimal accounting for the time variations in phase is accomplished via a simple algorithm which serves to update the detector memory. Furthermore, it is shown that this memory updating operation is a discrete linear filter whose impulse response is a simple function of the previous memory state and the Markov transitional statistics on the phase. A priori knowledge regarding the phase is summarized in the initial impulse response of the updating filter.     

Optimal Precession Control of Randomly Perturbed Spin-Stabilized Satellite

Dynamics of the satellite angular momenta is modeled by ordinary differential equations with additive white noise. A feedback controller er is desired to maintain tolerable satellite momenta and to economize ze the fuel consumption. The stochastic optimal control problem is transformed into an equivalent deterministic optimization problem involving a parabolic partial differential equation. Necessary optimality y conditions are used to develop a computation algorithm. Results regarding optimal controls, expected costs, and confinement probabilities in different noisy environments are presented.     

Spectral Location of Rayleigh and "m" Fading Signals in White Gaussian Noise

The classical problem is considered of locating a fading sinusoidal signal known to be present in one of several frequency " cells," each of which contains additive white Gaussian noise. The signal fading is assumed to follow the popular Rayleigh distribution, but generalizations tions to non-Rayleigh fading are included in terms of the " in" distribution due to Nakagami. The channel observation time is allowed to be either predetermined or variable (corresponding, respectively, to " fixed sample size" and " sequential" reception), and the practically important situation of intermittent signal transmissions is also examined. Results are in the form of optimal and near-optimal receiver structures, and of measures of performance.     

Cycle slip performance of digitally implemented phase detectors onAWGN channel

Cycle slip performance of digitally implemented phase detectors on additive white Gaussian noise (AWGN) channel is investigated. The performance measure evaluated is the mean cycle slip time of a first-order phase-locked loop. An equivalent phase detector model with state-dependent loop noise is employed. It is shown that this working basis is vital to arrive at correct results. Numerical results for triangular and saw-tooth type phase detectors are reported and compared with those for the multiplier phase detector     

Detection in Laplace Noise

The discrete time detection of a known constant signal in white stationary Laplace noise is considered. Exact expressions describing the performance of both the Neyman-Pearson optimal detector and the suboptimal linear detector are presented. Also, graphs of the receiver operating characteristics are given. The actual performance of the Neyman-Pearson optimal detector is compared to that predicted by a Gaussian approximation to the distribution of the test statistic.     

Optimal measurement scheduling for state estimation

We consider the problem of optimal allocation of measurement resources, when: (1) the total measurement budget and time duration of measurements are fixed, and (2) the cost of an individual measurement varies inversely with the (controllable) measurement accuracy. The objective is to determine the time-distribution of measurement variances that minimizes a measure of error in estimating a discrete-time, vector stochastic process with known auto-correlation matrix using a linear estimator. The metric of estimation error is the trace of weighted sum of estimation error covariance matrices at various time indices. We show that this problem reduces to a nonlinear optimization problem with linear equality and inequality constraints. The solution to this problem is obtained via a variation of the projected Newton method. For the special case when the vector stochastic process is the state of a linear, finite-dimensional stochastic system, the problem reduces to the solution of a nonlinear optimal control problem. In this case, the gradient and Hessian with respect to the measurement costs are obtained via the solution of a two-point boundary value problem and the resulting optimization problem is solved via a variation of the projected Newton method. The proposed method is illustrated using four examples     

Dynamics modeling and pressure control of composites tape winding system based on LQSMC

Pressure fluctuations during the composite fiber winding process seriously affect the product's compactness strength, fatigue resistance, stress uniformity, and resin content. The accuracy of pressure control systems is affected by nonlinear disturbances, such as friction, parameter perturbation, and measurement noise. A robust control algorithm based on linear quadratic optimal control and sliding mode control (LQSMC) is proposed to overcome these problems. The method is based on the system state space expression and linear quadratic optimal control. The state space model of the system is improved by using a Kalman filter and control input for state estimation, and a new sliding surface equation is defined. The ameliorated control algorithm exhibits good performance and can effectively suppress sliding mode control (SMC) chattering. Simulation and experimental results show that LQSMC offers high control precision, much stronger anti-interference, and robustness, which can effectively improve the positioning and tracking accuracy of a pressure control system compared with linear quadratic optimal control (LQC). The winding pressure control precision is improved by 45% to 50%. The results show that the porosity of composite fiber tape winding products decreased thanks to our method.     

飞机的随机变结构最优控制方法

 <正> 一、引言 系统的变结构控制(VSC——Variable Structure Control)方法,最初是由苏联学者Utkin等人提出来的,近二十年来发展非常迅速,并越来越多地应用于各个工业领域,其中包括航空部门。变结构系统(VSS——Variable Structure System)的主要特征是存在滑动模态。处于滑动模态时,系统的运动等价于一个低阶系统。研究表明,VSS比传统的控制系统有更好的优点:快速性,对参数变化及外加扰动有强鲁棒性以及实现简单等。然而,VSC的不足之处在于需要获得全部状态变量,这是很难保证的。     

An LMI-based decoupling control for electromagnetic formation flight

Electromagnetic formation flight(EMFF) leverages electromagnetic force to control the relative position of satellites. EMFF offers a promising alternative to traditional propellant-based spacecraft flight formation. This novel strategy is very attractive since it does not consume fuel. Due to the highly coupled nonlinearity of electromagnetic force, it is difficult to individually design a controller for one satellite without considering others, which poses challenges to communications.This paper is devoted to decoupling control of EMFF, including regulations, constraints and controller design. A learning-based adaptive sliding mode decoupling controller is analyzed to illustrate the problem of existing results, and input rate saturation is introduced to guarantee the validity of frequency division technique. Through transformation, the imposed input rate saturation is converted to state and input constraints. A linear matrix inequalities(LMI)-based robust optimal control method can then be used and improved to solve the transformed problem. Simulation results are presented to demonstrate the effectiveness of the proposed decoupling control.     

Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

宏观机敏机构的振动主动控制

研究了具有压电作动器与应变传感器的柔性连杆机构的振动主动控制问题。应用复模态理论对宏观机敏机构的动力学方程进行解耦,建立了包含系统噪声与观测噪声的受控系统状态空间表达式,并分别设计了离散LQG状态反馈控制器与离散Kalma。滤波器。宏观机敏机构的在线振动控制实验表明,柔性连杆的应变峰值降低了80％,机构的动力学性能得到了显著改善。     

基于冗余伪观测的自适应滤波算法

现有的二阶互差分(SOMD)算法能够给出与状态估计误差解耦的观测噪声协方差估计，但是需要满足冗余测量的条件，但这一条件往往难以满足。 针对这一问题，提出了一种利用状态预测值构造相邻2个时刻伪观测的方法，将原SOMD算法扩展到具有单测量的系统中。使用目标跟踪问题对该算法的有效性进行验证。仿真结果表明，当采样周期较小时，该算法能够忽略状态估计误差的影响并给出较准确的观测噪声方差，在精度和鲁棒性方面优于其他参考算法。     

Novel quaternion Kalman filter

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.     

Calculation of Output Noise Variances for Discrete Time-Invariant Filters

Certain calculations to minimize output noise variance are introduced. Many applied problems in sampled data systems require that data be smoothed in the presence of noise for the prediction of future positions, velocities, or accelerations. Smoothing coefficients in discrete time-invariant filters are computed to minimize the output noise variance, but under the constraints that the function and derivatives be predicted ahead. The output noise variance is seen to be a function of the input noise, the number of input signals (N+1) that the filter has to smooth, and the prediction time ?T. Four examples are given in the derivation of smoothing coefficients for step and ramp inputs subjected to either almost white noise or Gaussian-Markoff noise. The examples illustrate the number of constraint relations that the filter smoothing coefficients must satisfy for function and/or derivative convergence under noise-free conditions. The smoothing coefficients are also a function of the type of noise input into the system or the discrete filter. From the examples, it can be observed that as N becomes larger, the output noise variance becomes smaller, but the computation time is increased.     

On the Mean Frequency Measurement System Using Correlation Detection

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.     

Satellite formation reconfiguration and station-keeping using state-dependent Riccati equation technique

The current paper presents optimal reconfigurations and formation-keeping for formation flying satellites. The state-dependent Riccati equation (SDRE) technique is utilized as a non-linear controller for both the reconfiguration problem and formation-keeping problem. For the SDRE controller, a state-dependent coefficient (SDC) form is formulated to include non-linearities in the relative dynamics and J₂ orbital perturbation. The Taylor series and a transformation matrix are used to establish the SDC form. Optimal reconfiguration trajectories that minimize energy in satellite formation flying are obtained by the SDRE controller and compared with those obtained from a linear quadratic regulator (LQR) and a linear parameter varying (LPV) control method. It is illustrated that the SDRE non-linear controller of the current study obtains relocation accuracy of less than 0.1% of formation base-line length, while the LQR controller and LPV controller yield relatively large relocation errors. The formation-keeping controller developed using the SDRE technique in the current study also provides robustness under severe orbital perturbations.