The Resolution Performance of Range Estimators

The theoretical basis and methods of implementation of a moment algorithm for the range separation estimation of two closely spaced point targets are presented. Moment estimation and noise filtering techniques introduced here result in a considerable improvement over Baum's algorithm. The error bounds are established and it is shown that the spectral moment estimator exhibits optimum (zero bias, minimum variance) performance when the target separation normalized to the standard deviation of the Gaussian pulse is 2?1.5. Monte Carlo simulation is performed to verify the approximations made and to demonstrate the feasibility of the working models.     

一种鲁棒Sigma-point滤波算法及其在相对导航中的应用

研究了一种鲁棒Sigma-point滤波方法在无人机编队相对导航问题上的应用。该方法采用Huber估计方法,将Sigma-point滤波量测更新转化为求解线性回归问题,新的Sigma-point滤波方法是一种混合L1、L2范数最小估计,当量测噪声为受污染的高斯白噪声时,该方法具有一定的鲁棒性。给出了编队无人机相对惯导方程和相对视线矢量测量原理,应用鲁棒Sigma-point滤波方法融合相对惯导信息和相对视线矢量信息,估计出无人机之间的相对姿态、相对速度和相对位置。仿真结果表明,与扩展卡尔曼滤波和常规Sigma-point滤波相比,鲁棒Sigma-point滤波可以获得更高的估计精度。     

一种改进的星图降噪算法研究

在星敏感器的使用过程中,由于外界环境的影响及传感器自身的限制,拍摄出来的星图不可避免地存在一些噪声,因此对星图进行去噪处理是一项非常重要的工作。针对传统高斯模板滤波存在的引入邻域噪声、无法自行根据星图特性修正等造成去噪效果不好的问题,提出了一种改进的星图降噪算法。该方法在滤波前先进行坏点剔除工作,并采用高斯低通滤波与高通滤波结合的方式对图像进行处理,在抑制噪声的同时有效地保留了星点信号。通过阐述星敏感器的工作原理,分析星图的噪声特性,对星图滤波去噪算法进行研究,并进行模拟星图影像提取星点坐标实验。结果表明：使用该算法进行滤波比传统的高斯滤波算法提取的质心坐标精确度更高,较传统方法横坐标提高0.00538个像素点,纵坐标提高0.0077个像素点,证实了图像处理算法的有效性。     

An alternate algorithm for discrete-time filtering

The discrete-time Kalman filter is an optimal estimator for the states of a linear, stochastic system. It assumes that measurements are linear combinations of the states, and all disturbances are Gaussian. The influence diagram, a decision analysis tool that provides an algorithm for discrete-time filtering equivalent to the Kalman filter when the influence diagram represents Gaussian random variables, is discussed. The influence diagram algorithm is a factored form of the Kalman filter, similar to other factored forms such as the U-D filter. Compared with the Kalman filter, it offers improved numerical properties. Compared with other factored forms, it offers a reduced computational load     

Interlaced Kalman filtering of 3D angular motion based on Euler'snonlinear equations

A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study     

混合线性/非线性模型的准高斯Rao-Blackwellized粒子滤波法

 针对混合线性/非线性模型,提出一种新的递推估计滤波算法,称为准高斯Rao-Blackwellized粒子滤波器（Q-GRBPF）。算法采用Rao-Blackwellized思想,将线性状态与非线性状态进行分离,对非线性状态运用准高斯粒子滤波（Q-GPF）算法进行估计,并将其后验分布近似为单个高斯分布,再利用非线性状态的估计值对线性状态进行卡尔曼滤波（KF）估计。将Q-GRBPF应用于目标跟踪的仿真结果表明,与Rao-Blackwellized粒子滤波器（RBPF）相比,Q-GRBPF在保证估计精度的前提下有效降低了计算复杂度,计算时间约为RBPF的58%;与Q-GPF相比,x坐标与y坐标的估计精度分别提升了45％和30％,而计算时间也节省了约30％。     

Performance comparisons of modified SMI and GLR algorithms

Adaptive filtering for signal detection in colored interference of unknown statistics is addressed. The detection performance of a modified version of the well-known sample matrix inversion (SMI) algorithm, called the modified SMI (MSMI), is compared with that of the generalized likelihood ratio (GLR) algorithm in colored Gaussian interference. The performance sensitivity of the MSMI and GLR in colored Weibull and log-normal interference is studied via simulation. It is found that there is almost no need to use the more complicated GLR algorithm in Gaussian interference, while in Weibull or log-normal interference the GLR should be preferable to the MSMI     

Robust H/sub /spl infin// filtering of fuzzy dynamic systems

Robust H/sub /spl infin// filtering of complex nonlinear systems which can be represented by a fuzzy dynamic model is presented. Based on a nominal model, a common positive definite matrix P, and a piecewise continuous Lyapunov function respectively, three kinds of new filtering design methods are proposed using quadratic stability theory and linear matrix inequalities (LMIs). It is shown that the filtering system is quadratically stable with disturbance attenuation if there exists a positive definite matrix solution to a LMI or a set of LMIs. An example is also given to demonstrate the performance of the proposed filtering design methods.     

The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

LQG Guidance Law with Bounded Acceleration Command

A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.     

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.     

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     

CFAR detection in clutter with unknown correlation properties

We develop a constant false-alarm rate (CFAR) approach for detecting a random N-dimensional complex vector in the presence of clutter or interference modeled as a zero mean complex Gaussian vector whose correlation properties are not known to the receiver. It is assumed that estimates of the correlation properties of the clutter/interference may be obtained independently by processing the received vectors from a set of reference cells. We characterize the detection performance of this algorithm when the signal to be detected is modeled as a zero-mean complex Gaussian random vector with unknown correlation matrix. Results show that for a prescribed false alarm probability and a given signal-to-clutter ratio (to be defined in the text), the detectability of Gaussian random signals depends on the eigenvalues of the matrix R_c^-1R_s. The nonsingular matrix R_c and the matrix R_s are the correlation matrices of clutter-plus-noise and signal vectors respectively. It is shown that the “effective” fluctuation statistics of the signal to be detected is determined completely by the eigenvalues of the matrix R_c^-1R_s. For example the signal to be detected has an effective Swerling II fluctuation statistics when all eigenvalues of the above matrix are equal. Swerling I fluctuation statistics results effectively when all eigenvalues except one are equal to zero. Eigenvalue distributions between these two limiting cases correspond to fluctuation statistics that lie between Swerling I and II models     

Control of a large space structure using MMAE/MMAC techniques

The application of moving-bank multiple model adaptive estimation and control (MMAE/MMAC) algorithms to an actual spade structure (Space Integrated Controls Experiment (SPICE)) being examined at Phillips Laboratory at Kirtland AFB, NM, is presented. The structure consists of a large platform and a smaller platform connected by three legs in a tripod fashion. Kalman filtering and LQG (linear system, quadratic cost, Gaussian noise) control techniques are utilized as the primary design tools for the components of the MMAE/MMAC. Implementing a bank of filters or controllers increases the robustness of the algorithms when uncertainties exist in the system model, whereas the moving bank is utilized to reduce the computational load. Several reduced-order models are developed from the truth model using modal analysis and modal cost analysis. The MMAE/MMAC design with a substantially reduced-order filter model provides an excellent method to estimate a wide range of parameter variations and to quell oscillations in the structure.     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

High-Order Intermodulation Effects in Digital Satellite Channels

The phenomenon of intermodulation generation due to passive and normally linear components is sometimes called passive intermodulation. A unique characteristic of passive intermodulation interference in communications satellites is that the products causing trouble are of high orders. Due to the immense combinatorial complexity of the problem, both exact analysis and direct simulation are almost impossible. In this paper the problem is simplified by considering a composite interference model consisting of 1) the lowest order intermodulation product (of those high-order ones) at a frequency of interest, 2) a constant-envelope carrier with random phase to account for all other intermodulation interferences by direct overlap or spectrum spreading in the vicinity, and 3) white Gaussian noise (receiver noise). An approximation of the tail statistics of this composite interference is derived, and numerical results (checked by simulation) show that the tail distribution may be very different from Gaussian; careful consideration must be rendered before resorting to the a priori Gaussian assumption.     

利用卡尔曼滤波求取直升机气动导数的应用研究

本文主要介绍利用低通滤波、卡尔曼滤波及最小二乘法求取直升机气动导数的方法。本方法的特点是,通过低通滤波使旋翼高频成份的影响减至最小,同时求取试验数据的测量噪声和过程噪声,然后通过卡尔曼滤波使试验数据包含的随机噪声减至最小,最后用最小二乘法求得直升机的气动导数,为了提高卡尔曼滤波的准确度,用最小二乘法由试验数据求取直升机的气动导数作为卡尔曼滤波时的初始导数。计算结果表明,该方法可使试验数据中包含的噪声大大减小,误差带减少70％以上,而计算工作量又远远小于最大似然法。     

Estimation of 3D angular motion using gyroscopes and linear accelerometers

The authors present a novel, real-time angular motion estimation technique using a linear Gaussian estimator, and the outputs of linear accelerometers and gyroscopes, to assess the actual angular velocity of a rigid body in three-dimensional (3D) space. The method obtains the covariances of the random actual 3D angular velocity, the angular velocity measurement, and the measurement noise from the time averages of the outputs of an array of nine linear accelerometers and the outputs of three orthogonal gyroscopes. These statistics are used by the estimator to calculate the angular velocity of the rigid body in 3D space. The multisensor technique performance is evaluated through a computer simulation. Results indicate that the method leads to more accurate angular velocity values than are obtained conventionally.<>     

一种实时飞行轨迹重构方法

提出一种有效的实时纵向飞行轨迹重构的新方法。为了得到状态估计的快速算法,本文把非线性飞行轨迹重构转化为线性、离散、时变状态和参数估计问题。将数值稳定性好、计算量也小的序列U-D分解滤波算法用于状态方程为线性、观测方程为线性或非线性的滤波问题中。由于测量值中常常含有系统偏差,本文把这些偏差作为增广状态加入增广状态模型中,并利用模型的一些特点,提出偏差分离的U-D分解算法,使计算量大大减少。仿真和实际试飞数据计算表明、本文的方法可得到比平方根协方差滤波更有效的实时飞行轨迹重构结果。     

Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.