Posterior Cramer-Rao bounds for multi-target tracking

This study is concerned with multi-target tracking (MTT). The Cramer-Rao lower bound (CRB) is the basic tool for investigating estimation performance. Though basically defined for estimation of deterministic parameters, it has been extended to stochastic ones in a Bayesian setting. In the target tracking area, we have thus to deal with the estimation of the whole trajectory, itself described by a Markovian model. This leads up to the recursive formulation of the posterior CRB (PCRB). The aim of the work presented here is to extend this calculation of the PCRB to MTT under various assumptions.     

Maneuvering Target Tracking Using Adaptive State Estimation

Two approaches to a nonlinear state estimation problem are presented. The particular problem addressed is that of tracking a maneuvering target in three-dimensional space using spherical observations (radar data). Both approaches rely on semi-Markov modeling of target maneuvers and result in effective algorithms that prevent the loss of track that often occurs when a target makes a sudden, radical change in its trajectory. Both techniques are compared using real and simulated radar measurements with emphasis on performance and computational burden.     

一种关于目标与安全管道相对位置估算方法

针对靶场试验安全控制中目标与安全管道位置估算的实际需求,结合靶场实时数据处理要求,提出了利用滑动窗口技术,动态载人理论弹道数据,并采用折半查找和KNN查询相结合的思想实现了目标与理论弹道最近邻点查询,完成了飞行目标与理论规划航迹间的位置等参数偏差查询。利用区间估计原理,给出了目标与安全管道相对位置估算方法,解决了传统试验中无法对目标与管道边界的接近程度进行量化的问题。     

Direct dynamic-simulation approach to trajectory optimization

This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest. To effectively implement this concept, the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior. As a result, the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables. In addition, the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints. Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit, including the detailed analyses for the de-orbiting phase. The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.     

Generalized input-estimation technique for tracking maneuveringtargets

A new input estimation technique for target tracking problem is proposed. Conventional input estimation techniques assume that the target maneuver level is constant within the detection window, which has been the major drawback of the techniques. The proposed technique is developed to overcome this drawback by modeling the target maneuver as a linear combination of some basic time functions. The resulting algorithm has a generalized formulation including earlier works on input estimation. A detection performance of the proposed algorithm is analyzed by investigating the detection sensitivity according to the selection of maneuver models and other design parameters such as the detection window size, measurement noise level, and sampling step size. A computer simulation study shows that the estimation performance of the proposed algorithm is comparable to Bogler's input estimation method while the computation time is greatly reduced     

Three-dimensional trajectory estimation from image position and velocity

A recursive algorithm for estimating the three-dimensional trajectory and structure of a moving rigid object in an image sequence has been previously developed by Broida, Chandrashekhar, and Chellappa [1990]. Since then, steady advances have occurred in the calculation of optical flow. This work improves 3D motion trajectory and structure estimation by incorporating optical flow into the estimation framework. The new solution combines optical flow and feature point measurements and determines their statistical relationship. The feasibility of a hybrid feature point/optical flow algorithm, demonstrated through detailed simulation on synthetic and real image sequences, significantly lowers bias and mean squared error in trajectory estimation over the feature-based approach.     

基于超短基线声传感器阵的高速目标轨迹估计

针对低空高速飞行目标跟踪问题,首先研究了某典型目标噪声信号的时频特性,发现其信号呈现宽带低频特征,难以从频域对目标轨迹进行估计。在此基础上,从各路接收信号的到达时延量入手,考虑到声基阵只能布设于有限空间内的制约,提出了一种基于超短基线阵时延估计的目标跟踪方法。该方法利用各个超短基线阵接收声强极值点分别估计目标运动轨迹垂线方向,计算多个垂线的叉乘向量实现对目标运动方向的估计,再利用多面交汇的方式获估计得到目标运动轨迹。分别对目标俯仰角、方位角及运动轨迹估计的理论误差进行了推导,根据理论估计误差,为能够实现对目标运动轨迹的估计,各个超短基线阵应尽量保证与目标运动轨迹不在同一平面上。根据仿真结果,在采用4个传感器基阵时,角度估计平均误差在4°以内,位置估计相对误差在5%左右。仿真结果验证了该方法的有效性。     

Trajectory prediction in pipeline form for intercepting hypersonic gliding vehicles based on LSTM

The interception problem of Hypersonic Gliding Vehicles (HGVs) has been an important aspect of missile defense systems. In order to provide interceptors with accurate information of target trajectory, a model based on an improved Long Short-Time Memory (LSTM) network for trajectory prediction pipeline is proposed for the interception of a skip gliding hypersonic target. Firstly, for trajectory prediction required by intercepting guidance laws, the altitude, velocity and velocity direction of the target are formulated in the form of analytic functions, consisting of linear decay terms and amplitude decay sinusoidal terms. Then, the dynamic characteristics of the model parameters are analyzed, and the target trajectory prediction pipeline is proposed with the prediction error considered. Finally, an improved LSTM network is designed to estimate parameters in a dynamically-updated manner, and estimation results are used for the calculation of the final trajectory prediction pipeline. The proposed prediction algorithm provides information on the velocity vector for midcourse guidance with the effect of prediction errors on interception taken into account. Simulation is conducted and the results show the high accuracy of the algorithm in HGVs’ trajectory prediction which is conducive to increasing the interception success rate.     

New approach for target locations in the presence of wall ambiguities

A technique for target location estimation in through-the-wall radar imaging applications is presented. The algorithm corrects for the shifts in target positions due to ambiguities in the wall thickness and dielectric constant. We consider uniform walls and perform imaging using wideband beamforming, with the antennas placed against the wall. Behind-the-wall images are obtained using different structures of transmit and receive arrays. For each array structure, a trajectory of the shifts in the target locations is generated assuming different wall parameters. The target position is estimated as the intersection of the corresponding trajectories. The paper shows that for unknown wall thickness or dielectric constant, the point of intersection is the true target position. In the case when both parameters are unknown, the estimated target location is in close proximity to the target true position. It is demonstrated that the performance of the proposed technique is rather insensitive to the target location behind the wall and to various array structures.     

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     

A maximum likelihood approach to data association

An approach is presented to data association (DA) problems for which measurements are independent from scan to scan. It is demonstrated that maximum likelihood (ML) estimation of target parameters may be efficiently implemented by an EM iterative scheme. The algorithm is applied to multitarget trajectory estimation of constant-velocity targets from passive (bearing-only) sensors     

Estimation of singularities for intercept point forecasting

In this paper, a recursive approach (an algorithm for estimation of singularity (AES)) is proposed to forecast the intercept point of a target and the pursuing interceptor recognized as the estimated singularity of a nodal cubic curve fitted to the data. The data comprises direction of arrival (DOA) estimates of both target and interceptor obtained at regular intervals of time using the maximum likelihood (ML) DOA estimation method. The estimates of coefficients of the cubic polynomial are given by a recursive least squares solution. From these coefficients, closed-form solutions for angle of interception and intercept time are obtained which are the forecasted coordinates of the intercept point. Experimental results demonstrate performance of the proposed algorithm     

ARMAX模型参数估计的新两步法

 本文提出了一种ARMAX模型参数估计的新两步法。这种方法与其它递推估计方法（如增广矩阵法,极大似然法,Durbin两步法、三步法等）比较,具有较好的收敛特性,对参数的估计,特别是对C参数的估计比较精确,这是利用其它方法,一直未能很好解决的一个难题。     

High-resolution multiple target angle tracking

An approach to high-resolution multiple-target-angle tracking that uses the output of an array of sensors is presented. The results of direction-of-arrival estimation by eigenstructure analysis are extended to derive a recursive procedure for tracking moving sources. This procedure involves recursive eigenvalue decomposition and a zero-tracking algorithm, using the coefficient derived from the minimum-norm criterion. The algorithm has superresolution capability in that a pair of closely spaced target angles can be resolved and tracked even though the angular separation between them is less than the reciprocal of the aperture size. Simulation results verify that the algorithm works well in tracking multiple-target sources     

Constant gain tracker with variable frame time

A three-parameter constant-gain recursive filter is augmented by a residual-dependent frame time algorithm that automatically increases sampling rates when a target maneuvers. Computer simulations show that tracking performance is essentially independent of the particular target trajectory. It is found that radial distance errors remain effectively constant over different trajectories. It is the number of observations dictated by the adaptive frame time algorithm that is trajectory-dependent. The filter equations along with the frame time adjustment algorithm are first described, and a comparison made with a similar procedure. Examples given use the nonlinear observations generated by a passive sensor system     

Optimal pure proportional navigation for maneuvering targets

The optimal pure proportional navigation (PPN) guidance law with time-varying navigation gains is considered. Unlike the conventional optimal PPN approach where linearized model was assumed in the optimization process, this work exploits the exact nonlinear formulation of PPN to derive analytically the optimal time trajectory of the navigation gain to minimize a performance index which is a weighted sum of the final time and the integral of the squared acceleration. It is verified that the PPN scheme with constant navigation gain is not only optimal in the vicinity of the interception point, but also optimal for the whole trajectory, if the navigation constant is designed by the methodology proposed here. Based on the optimization results for nonmaneuvering targets, a recursive optimal PPN scheme is proposed for maneuvering targets, wherein the optimal navigation gain and time-to-go are predicted recursively during the interception, and trajectory and performance of the interceptor guided by optimal recursive PPN scheme are evaluated analytically.     

Moving target imaging and trajectory computation using ISAR

Novel algorithms for moving target imaging and trajectory computation using a two-receiver radar are presented. The range-bin alignment is implemented with an adaptive method using the envelope correlation feature of different returns and the angular trajectory equation is solved using a linear least squares method combined with a unique phase-unwrapping technique. The angular positions of the synthetic array elements are determined from the trajectory computation. Three target models moving along a perturbed straight line are used to verify the proposed algorithms     

Constant-False-Alarm-Rate Signal Processors for Several Types of Interference

Distribution-free methods and maximum-likelihood estimation technique have been previously suggested for constant-false-alarm-rate (CFAR) processors. The first technique assumes no a priori environmental knowledge and the second assumes almost complete environmental knowledge. Several intermediate environmental assumptions are considered. The performance of single-pulse transmission signal processors that produce CFAR for the different environments is analyzed. Probability of target detection is evaluated for Rayleigh interference and Swerling I target. It is shown that adaptive threshold techniques implemented by logarithmic amplifiers, instead of linear amplifiers, can attain better false-alarm-rate control with only small loss in target detectability.     

无人机群体视角下的轨迹预测CSCD

利用无人机对观测目标的运动轨迹进行预测是当前无人系统领域的关键任务之一。目前的目标轨迹预测研究通常基于单一无人机所采集的轨迹数据,但由于场景中障碍物以及视角倾斜等因素的影响,单无人机不易稳定监测目标具体位置,容易导致目标丢失。而且,现有利用无人机的目标轨迹预测一般基于鸟瞰视角,没有发挥出无人机的灵活性。随着无人机集群协同技术的发展,无人机群体视角为目标全方位监测提供了新的思路,在解决目标丢失和目标遮挡问题中具有明显的优势。同时,基于多无人机的位姿估计可以估计出目标的准确三维坐标,为无人机的灵活视角观测提供基础。因此,从轨迹预测的相关工作出发,探讨无人机群体视角下轨迹预测中面临的挑战和解决思路,以期对未来的轨迹预测研究以及集群协同技术发展提供一定帮助。     

Robust altitude estimation for over-the-horizon radar using a state-space multipath fading model

In previous work, a matched-field estimate of aircraft altitude from multiple over-the-horizon (OTH) radar dwells was presented. This approach exploits the altitude dependence of direct and surface reflected returns off the aircraft and the relative phase changes of these micro-multipath arrivals across radar dwells. Since this previous approach assumed high dwell-to-dwell predictability, it has been found to be sensitive to mismatch between modeled versus observed micro-multipath phase and amplitude changes from dwell-to-dwell. A generalized matched-field altitude estimate is presented here based on a state-space model that accounts for random ionospheric and target-motion effects that degrade the dwell-to-dwell predictability of target returns. The new formulation results in an efficient, robust recursive maximum likelihood (ML) estimation of aircraft altitude. Simulations suggest that the proposed technique can achieve accuracy within 5,000 ft of the true aircraft altitude, even with relatively high levels of uncertainty in modeling of dwell-to-dwell changes in the target return. A real data result is also presented to illustrate the technique.