A Semicoherent Detection and Doppler Estimation Statistic

Consider a uniform train of M coherent short pulses transmitted by a radar and received with a Doppler shift. When thermal noise is present, let the mth sample of the return at the video be represented by the complex process Zm. A novel detection and Doppler estimation criterion is analyzed which depends on the semicoherent statistic begin{equation*}{Z_{K}}^prime = sum_{m=k+1}^{M} {^{z}m^{z}m-k}^{ *}end{equation*} where the asterisk stands for complex conjugate. Its characteristics are also studied when the real and imaginary parts of Zm are digitized to one bit.     

The Effect of Satellite Spin on Two-Way Doppler Rangerate Measurements

The rotation of a spin-stabilized satellite employing a turnstile antenna for reception and retransmission affects two-way Doppler range-rate measurements. Two different types of tracking systems are considered and, in both systems, the range-rate measurement is changed by the amount begin{equation*} |Delta dot{r}| = frac{|1 pm 1/k|}{2} lambda_{t}f_{s} end{equation*} where k is the turn-around ratio of the satellite transponder, Xt is the wavelength of the ground-based transmitter, and fs is the spin rate of the satellite. The positive sign is used if the turnstile antenna elements are connected to give the same polarization for both reception and transmission. If the antenna connections result in different polarizations, the minus sign is used and the magnitude of the effect is reduced.     

Sensitivity Functions for Linear Discrete Systems with Applications

z-transform techniques are employed to establish general symmetry and simultaneity properties of the first sensitivity functions of the phase-canonical form of single-input, nth-order, linear, constant, discrete-time, controllable systems. It is demonstrated that computation of the first sensitivity function requires one nth-order model in addition to the system model. This simultaneity property is extended to arbitrary single-input, nth-order, linear, constant, discrete systems. In complete analogy with results presented for continuous systems, symmetry and simultaneity properties may be established for the computation of the /th sensitivity function begin{equation*}^{l}beta^{y} triangleq frac{partial^{l}y_{i}}{partialalpha_{Jl}partialalpha_{Jl-1}cdotspartialalpha_{J2}partialalpha_{J1}}|_{alpha=alpha_{0}} {rm for} substack{i = 1,2,ldots,n\ J_{k} = 1,2,ldots,n\ k = 1,2,ldots,l.}end{equation*} Extension of these results to multi-input systems is also mentioned. The usefulness of the simultaneity property is illustrated by applying the results to the design of a low-sensitivity optimal control law.     

Output Probability Density Functions for Cross Correlators Utilizing Sampling Techniques

Sampling techniques provide a practical means of obtaining cross-correlation functions. In this paper, the correlation function is described by sums of the form Z = begin{equation*}Z = Sigma^{N}_{j=1}X_{j}Y_{j}end{equation*}. A general expression is derived for the probability density function of the random variable Z under the condition that Xj and Yj are stationary, jointly Gaussian random processes with nonzero means and unit variances.     

The Least-Square Approximation of Inertial Platform Drift

The drift angle of an inertial platform which is gyro-stabilized with respect to inertial space is equal to the integral of the gyro drift rate. Under controlled laboratory environment the drift angle, denoted by y, may be measured and plotted against time in an interval [0, T]. Without loss in generality, one may take y(0)= 0. A straight line yf can be found, such that the quantity E2 is minimized, where begin{equation*}E^2 = {frac{1}{T}int^{T}_{0}(y-y_f)^{2}}dt.end{equation*} The equation for yf is of the form yf = at + b and, in general, both a and b are nonzero. It is desirable to determine a statistical relationship between the gyro drift rate and the expected value of the minimum E2 for any given interval T. An analysis in this paper determines this relationship and derives a general expression for , where the symbol <*> denotes statistical expectation. It is found that increases linearly with the variance of the gyro drift rate. This general formula is then developed in detail for the case of a first-order Markovian gyro drift. is evaluated numerically and its square root plotted vs. the interval T and the gyro correlation time. The same problem is also solved for the case when yf is constrained to intersect the origin, i.e., when b=0.     

基于PnP和自适应线性卡尔曼滤波的实时位姿估计

针对实时位姿估计中扩展卡尔曼滤波(EKF)线性化引入非线性误差和依赖已知噪声分布的缺点,提出一种基于PnP的自适应线性卡尔曼滤波位姿估计求解方法。将PnP位姿估计求解策略引入卡尔曼滤波观测方程,通过对动态方程误差统计参数实时估计,自适应调节卡尔曼滤波递推参数。所提算法求解精度高,固定了观测方程的观测向量维度,提高了算法实用性。通过仿真试验,比较了该算法与EKF的位姿估计精度,通过量化误差分析,证明了该方法可以提高三维运动位姿估计精度,也验证了该方法的有效性。     

NONLINEAR FILTERING ALGORITHM FOR INS INITIAL ALIGNMENT

The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonlinear equation can be reduced to a linear one. Extended Kalman filter, iterated filter and second order filter formulas are derived for the nonlinear state equation with linear measurement equation. Simulations results show that the accuracy of azimuth error estimation using extended Kalman filter is better than that of using standard Kalman filter while the iterated filter and second order filter can give even better estimation accuracy.     

捷联惯导系统大失准角下的初始对准研究

针对捷联惯导系统初始对准过程中的大失准角情况,建立了基于欧拉平台误差角概念的捷联惯导系统(SINS)非线性误差模型,对于具有加性噪声的动态方程,当状态方程为非线性而观测方程为线性时,将一种简化的UKF滤波方法运用到捷联惯导系统初始对准中,并在静基座下对捷联惯导系统大失准角初始对准进行了仿真。仿真结果表明,随着失准角的增大,简化的UKF比EKF估计精度更高,是一种在进行捷联惯导系统大失准角条件下的初始对准时实用方法。     

Infrared Systems: I. Accuracy of Angle Measurement

In this paper expressions are derived for the error in position measurement for the problem of estimating the position of an infrared target in a random background and the combined prob lem when white detector noise is also affecting the estimation. Space filters performing linear scanning, nutation, and rotation are considered. A linear scanning infrared system is then considered in greater detail. The noise on the error signal is calculated, taking into account both the estimation error, as discussed in the first part, and "false alarms" occurring in the scan area far from the target.     

Stability of Gyro with Harmonic Nonlinearity in Spinning Vehicle

A stability analysis of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain angular velocity ?z about the spin axis of the gyro is presented. The complete nonlinear equation of motion, which includes the fundamental and second harmonic nonlinear terms, arising due to ?z, is considered. For time-varying ?z(t), using the circle criterion, it is shown that the gimbal motion is globally asymptotically stable if the Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. For the case of uncertain constant ?z, using the Lyapunov approach, conditions for global asymptotic stability (GAS) and asymptotic stability are derived. Stable regions in parameter space of the gyro and state space are obtained. Analytical relations for the selection of gyro parameters are derived.     

用逐步扩阶双递推时域法识别线性振动系统复模态参数

本文给出了从线性振动系统的自由响应识别该系统复模态参数的方法,把自由响应的表达式变为一个自回归方程和一个多项式方程,利用最小二乘递推与逐步扩阶递推的双递推法来进行参数识别。文中讨论了几个应用中的问题,并给出了计算机的模拟计算结果以及越野汽车车架的参数识别试验结果。     

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.     

非线性滤波在捷联惯导系统初始对准中的应用

惯性导航系统(INS)初始对准的误差方程在本质上是非线性的,估计惯性导航初始对准误差普遍采用的做法是把失准角假设为小角度,再将误差模型线性化.但当运载体遭遇恶劣环境姿态变化剧烈时,用于估计小失准角的误差模型将不再满足初始对准的要求.为满足大失准角下惯导系统的初始对准,在建立大失准角下的非线性误差模型基础上,分别应用2种...     

存在观测站位置误差的转发式时差无源定位

无源定位中,由于观测站安放在运动平台等原因造成的观测站位置误差会影响无源定位精度性能。另外到达时间差(简称时差)(TDOA)的转发式测量需要将不同观测站截获到的辐射源信号都转发到同一位置,如主观测站。针对这两个问题,提出了基于约束总体最小二乘(CTLS)的无源定位算法。首先将转发式时差的非线性定位方程转化为不需要中间变量的直接线性方程,再基于CTLS算法依次转化为约束优化问题和无约束优化问题,最后推导给出定位近似闭式解。仿真实验表明在观测站误差较大时,该算法与其他算法相比定位精度性能较好。     

DR/GPS组合导航系统滤波技术研究

陆用航位推算系统（DR）的精度主要受到里程系数和航向误差的制约,其误差模型本质具有非线性,因此采用非线性滤波算法能显著提高里程系数和航向误差的估计精度。本文将粒子滤波应用到航位推算（DR）/GPS组合导航系统数据融合过程中,对航位推算 (DR) 与GPS组合导航系统中的里程系数误差和航向误差进行辨识估计,并对里程系数和航向进行修正。粒子滤波存在的主要问题是粒子的退化现象严重,本文将量子粒子群优化 (PSO) 算法与粒子滤波相结合,提出了量子PSO粒子滤波算法,该算法采用量子位对粒子进行编码,引入量子旋转门与变异操作保持了粒子集的多样性,通过量子PSO搜索寻优重新分配粒子,使粒子集有效地逼近真实的后验概率分布,从而有效地减轻了退化现象,提高了粒子滤波的精度。跑车实验结果表明,该算法有效地抑制了DR导航系统误差的增长,提高了组合导航系统的定位精度。     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

压电陶瓷叠层作动器迟滞蠕变非线性自适应混合补偿控制方法

压电陶瓷叠层作动器的迟滞蠕变非线性特性严重影响了控制系统的稳定性及动态跟踪精度。针对其迟滞蠕变非线性补偿控制问题,提出了一种高精度动态补偿压电陶瓷叠层作动器非线性特性的自适应混合补偿控制方法,即迟滞蠕变前馈补偿与自适应滤波反馈补偿结合的前馈-反馈混合控制方法。采用改进的Prandtl-Ishlinskii（Modified Prandtl-Ishlinskii,MPI）模型对压电陶瓷叠层作动器迟滞蠕变非线性特性进行精细化建模,并得到其逆补偿模型进行前馈补偿。根据前馈补偿误差,采用自适应滤波反馈控制对输入信号进行实时调控,实现对压电陶瓷叠层作动器的迟滞非线性及lg（t）型蠕变特性的实时精确补偿控制。数值仿真与实验结果表明,相比于常规前馈迟滞蠕变补偿,所提出的自适应混合补偿控制方法可以有效降低压电陶瓷叠层作动器的迟滞补偿误差,极大提高了迟滞蠕变非线性动态跟踪精度以及自适应性。     

Raster Scan Track of a Radar Scatterer Ensemble

A method is discussed for tracking the radar cross-section centroid of an ensemble of scatterers, using a raster scan observation technique. Estimation of the mean-squared dimensions of the ensemble is also considered. A maximum permissible beam separation is defined for the scan. Expressions for the bias and variance of the centroid estimates are given. Advantages of the approach are that individual scatterers need not be resolvable, and that the number of beams is independent of the number of scatterers.     

连续最小阶奇异滤波器

 本文讨论了当动态噪声统计特性未知时,奇异线性定常连续随机系统最小阶滤波器的设计问题。在系统部分观测量能精确测量的情况下,利用广义逆阵方法选择L矩阵,以消除动态噪声对降阶系统的影响,从而推导出缺动态噪声统计特性时的降阶奇异最优滤波器,其阶数为n-m+r。当量测方程奇异假设条件成立及引理有解时,本文证明了最小阶奇异滤波器必定存在。文中举例说明了这一降阶滤波方法的可行性。     

Unscented Kalman滤波在空间飞行器被动测距中的应用

介绍了Unscented Kalman滤波及其空间飞行器被动测距中的应用。Unscented Kalman滤波通过设计少量的sigma(抽样)点,计算这些点经过非线性函数的传播,获得滤波值基于非线性方程的更新。Unscented Kalman滤波避免了广义Kalman滤波等线性化方法的缺点,并提高了滤波精度。