Passive target tracking using maximum likelihood estimation

Estimation of target trajectory from passive sonar bearings and frequency measurements in the presence of multivariate normally distributed noise, with unknown inhomogeneous general covariance, is modeled as a nonlinear multiresponse parameter estimation problem. It is shown that maximum likelihood estimation in this case is identical to optimizing a determinant criterion which has a concise form and contains no elements of unknown covariance matrix. A Gauss-Newton type algorithm using only the first-order derivatives of the model function and a new convergence criterion, is presented to implement such estimation. The simulation results demonstrate that performance of the maximum likelihood estimation method with the above noise model is superior to that with the traditional noise assumption     

鲁棒EKF在脉冲星导航系统中的应用

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。     

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.     

Multisensor multitarget bias estimation for general asynchronous sensors

A novel solution is provided for the bias estimation problem in multiple asynchronous sensors using common targets of opportunity. The decoupling between the target state estimation and the sensor bias estimation is achieved without ignoring or approximating the crosscovariance between the state estimate and the bias estimate. The target data reported by the sensors are usually not time-coincident or synchronous due to the different data rates. Since the bias estimation requires time-coincident target data from different sensors, a novel scheme is used to transform the measurements from the different times of the sensors into pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow bias estimation as well as the evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the bias estimate, i.e., the quantification of the available information about the biases in any scenario. Monte Carlo simulation results show that the new method is statistically efficient, i.e., it meets the CRLB. The use of this technique for scale and sensor location biases in addition to the usual additive biases is also presented.     

传感器位置误差条件下仅用到达频率差的无源定位性能分析

传感器自身的位置误差对辐射源的无源定位精度可能有较大影响,详细分析并推导了在存在传感器位置误差条件下,仅使用到达频率差(FDOA)参数对辐射源定位时,定位精度的克拉美罗下限(CRLB)和均方误差(MSE).在传感器位置误差条件下,提出仅用FDOA来同时估计辐射源和传感器位置的泰勒级数方法,并证明该定位方法理论上的MSE...     

Pursuer identification and time-to-go estimation using passive measurements from an evader

We present an algorithm for identifying the parameters of a proportional navigation guidance missile (pursuer) pursuing an airborne target (evader) using angle-only measurements from the latter. This is done for the purpose of classifying the missile so that appropriate counter-measures can be taken. Mathematical models are constructed for a pursuer with a changing velocity, i.e., a direction change and a speed change. Assuming the pursuer is launched from the ground with fixed thrust, its motion can be described by a four-dimensional parameter vector consisting of its proportional navigation constant and three parameters related to thrusting. Consequently, the problem can be solved as a parameter estimation problem, rather than state estimation and we provide an estimator based on maximum likelihood (ML) to solve it. The parameter estimates obtained can be mapped into the time-to-go until intercept estimation results are presented for different scenarios together with the Cramer-Rao lower bound (CRLB), which quantifies the best achievable estimation accuracy. The accuracy of the time-to-go estimate is also obtained. Simulation results demonstrate that the proposed estimator is efficient by meeting the CRLB.     

Moving scanning emitter tracking by a single observer using time of interception: Observability analysis and algorithm

The target motion analysis (TMA) for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception (TOI) measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival (DDOA) model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable (WIV) estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound (CRLB) at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square (PLS) estimator.     

Adaptive Gaussian sum squared-root cubature Kalman filter with split-merge scheme for state estimation

The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.     

一类最佳飞行轨迹的计算

 本文给出了一种简化的直接多重打靶算法,并讨论了该算法在求解一类最佳飞行轨迹上的应用。数值计算结果表明,本文所给的算法收敛性好,对初值无很高要求,因而避免了在计算之前对问题进行冗繁的解析分析。     

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。     

包含乘性噪声自适应修正的非合作目标相对导航算法

无人机（UAV）态势感知的任务是利用机载传感器对未知环境进行目标识别和引导，针对无人机与非合作目标间中远距离的相对导航问题，提出了一种基于角度和距离量测的相对状态估计算法。在现有滤波算法的基础上，为了提高精度和稳定性，本文利用了列文伯格-马夸尔特（LM）优化的思想对迭代卡尔曼滤波（IEKF）算法进行改进，提出了一种LM-IEKF算法，并推导该算法在迭代过程中的状态更新方程及协方差阵的递推公式。在此基础上，考虑到距离传感器由于信号相关特性而引入的乘性噪声，现有的加性噪声模型难以适应，因此，进一步提出了基于量测噪声自适应修正的Modified LM-IEKF方法，通过在线实时更新噪声阵提高滤波的精度，并设置渐消记忆指数平滑估计结果。算法验证结果表明，与现有的EKF、IEKF算法相比，在仅含加性噪声的情况下，LM-IEKF算法具有更好的性能；在包含乘性噪声的情况下，Modified LM-IEKF可以有效地估计量测噪声，与目前广泛使用的EKF算法相比，在综合相对位置和相对速度精度上分别提高了10%和23%。     

Recursive 3-D motion estimation from a monocular image sequence

Consideration is given to the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time. A set of object match points is assumed to be available. The problem is formulated as a parameter estimation and tracking problem which can use an arbitrarily large number of images in a sequence. The recursive estimation is done using an iterated extended Kalman filter (IEKF), initialized with the output of a batch algorithm run on the first few frames. Approximate Cramer-Rao lower bounds on the error covariance of the batch estimate are used as the initial state estimate error covariance of the IEKF. The performance of the recursive estimator is illustrated using both real and synthetic image sequences     

U-D分解的固定点平滑新算法及其在飞行试验中的应用

 本文根据Rauch固定点平滑公式,提出了一种U-D分解的固定点平滑新算法。这一算法不仅具有良好的数值稳定性和可靠性,而且计算量较少;计算效率是Bryson-Ho Y C固定点平滑计算效率的1.5倍以上。将这种新算法用于飞机运动状态初值的确定,提高了飞机气动参数辨识精度。     

受地效影响飞机起飞着陆运动模型的参数辨识

利用基于最小模型误差法和线性不连续跳跃多重打靶法建立的非线性辨识法，辨识了飞机起飞着陆过程的非线性动态模型。对于包含复杂非线性项的动态系统，本方法可以从实际试验测量的系统非线性数据，确定飞机处于地面效应影响运动过程的系统模型，而不需要预先详细描述系统的非线性形式。算例表明该方法对于原始近似动态系统的状态估计是足够精确的。     

Particle filters for tracking with out-of-sequence measurements

An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.     

Attitude Determination from Vector Observations: Quaternion Estimation

Two recursive estimation algorithms, which use pairs of measured vectors to yield minimum variance estimates of the quaternion of rotation, are presented. The nonlinear relations between the direction cosine matrix and the quaternion are linearized, and a variant of the extended Kalman filter is used to estimate the difference between the quaternion and its estimate. With each measurement this estimate is updated and added to the whole quaternion estimate. This operation constitutes a full state reset in the estimation process. Filter tuning is needed to obtain a converging filter. The second algorithm presented uses the normality property of the quaternion of rotation to obtain, in a straightforward design, a filter which converges, with a smaller error, to a normal quaternion. This algorithm changes the state but not the covariance computation of the original algorithm and implies only a partial reset. Results of Monte-Carlo simulation runs are presented which demonstrate the superiority of the normalized quaternion.     

多渐消因子Kalman滤波器在SINS初始对准中的应用(英文)

针对系统模型和统计信息不能精确已知的条件下Kalman滤波无法给出最优解这一问题,单一渐消因子Kalman滤波算法对于简单的系统是有效的,但是对于复杂的多变量系统,仅仅利用单个的渐消因子是不够的。本文提出了一种多渐消因子滤波算法,通过利用开窗法计算新息序列协方差的无偏估计获得渐消因子矩阵。利用渐消因子矩阵调节一步预测均方误差矩阵k|k1P,对不同的滤波通道提供不同的渐消速率。将该方法应用于SINS的初始对准中,仿真和试验结果表明:当真实系统噪声统计特性同设定参数不一致时,对准精度明显高于其他滤波算法。其对不确定性噪声具有较低的敏感度,对系统参数具有较好的滤波效果。因而,在实际应用中具有重要的参考价值。     

Resolution of signal sources via spectral moment estimation

In different practical situations it is desired to estimate the number of signal sources and their positions in space or in frequency domain. The first problem is known as the detection or the order estimation and the second one as the resolution. For the resolution problem techniques such as nonlinear least squares (NLSM), high-order Yule-Walker method (HOYW), multiple signal classification (MUSIC), Pisarenko harmonic retrieval method, min-norm method, estimation of signal parameters by rotational invariance technique (ESPRIT), were proposed (Marple, 1987 and Stoica and Moses, 1997). All these high-resolution methods are based on the analysis of the signal covariance matrix. But the covariance matrix is not the only choice to represent the signal spectrum. In different applications (weather radars, synthetic aperture radar (SAR) signal processing, ultrasound imaging in medicine, atmospheric turbulence measurements) the signal spectrum can be modeled through its algebraic moments. Recently a number of efficient nonparametric methods have been proposed to estimate the algebraic spectral moments (Monakov, 1999). The presented paper is an attempt to solve the direction of arrival (DOA) problem via estimation of the algebraic spectral moments. A method proposed in the article is comparable in its accuracy with the MUSIC method. At the same time its computational burden is much lower. The method permits to estimate the signal power of sources easily to complete the full spectral line analysis. Additionally the method shows good robustness in situations when signal sources have noticeable spatial extend     

基于最大似然估计的TDOA/FDOA无源定位偏差补偿算法

在到达时差/到达频差(TDOA/FDOA)无源定位系统中,定位问题的非线性使得定位的结果存在偏差,特别是在噪声较大或者接收站布站不合理的情况下,定位的偏差尤其显著。针对这一问题,提出了一种基于最大似然估计的偏差补偿算法。该方法分为3步:首先,利用最大似然估计器对目标的位置和速度进行求解;其次,通过利用目标定位的估计值和含噪的测量值,对目标的位置和速度偏差值进行理论分析和推导;最后,将最大似然估计解减去理论偏差值,得到经过偏差补偿的新的目标定位解。理论分析和实验仿真证明,在一定噪声的情况下,所推导的目标位置和速度的理论偏差值与实际偏差值相符,并且经过偏差补偿后的定位算法,在保持目标定位的均方根误差(RMSE)与原最大似然算法一致的情况下,目标的位置和速度偏差值远远小于原最大似然算法的偏差值,目标定位精度得到了有效的提高。