Properties and performance of extended target motion analysis

The problem of target motion analysis (TMA) has been the subject of an important literature. However, present methods use data estimated by a short time analysis (azimuths, Dopplers, etc.). For far sources, the nonstationarities of the array processing outputs, induced by the sources motion, may be simply modeled. This model leads one to consider directly a spatio-temporal TMA. Then new (spatio-temporal) data can be estimated. These estimates correspond to a long time analysis. Further, note that they are estimated independently of the (classical) bearings. In this general framework, the concept of source trajectory replaces the classical instantaneous bearings. Corresponding TMA algorithms are then studied. Then the study of statistical performance is carefully studied     

Modified input estimation technique using pseudoresiduals

An adaptive tracking filter for maneuvering targets is proposed using modified input estimation technique. Pseudoresiduals are defined using measurements and the velocity estimate at the hypothesized maneuver onset time. With the pseudoresiduals and a new target model representing transitions of nominal accelerations, a new input estimation method for tracking a maneuvering target is derived. Since the proposed detection technique is more sensitive to maneuvers than previous work, the shorter window length can be employed to detect and compensate target maneuvers. Also shown is that the tracking performance of the proposed filter is similar to that of interacting multiple model method (IMM) with 3 models, while computational loads of our method are drastically reduced     

直升机机动飞行旋翼的气动力模拟

探讨了预测机动飞行旋翼气动力的细节问题。在考察非均匀诱速分布、入流动力学和非定常翼型性能的基础上,建立了一种模拟非定常旋翼气动力的新方法。对某一特定机动科目,首先由逆解技术得到操纵输入和飞行姿态;然后综合应用涡流理论、动力入流理论和非定常翼型气动模型来数值模拟非定常的旋翼气动力。通过样例分析给出了紧急转弯和平飞跃升的计算结果。     

A Decision?Directed Adaptive Tracker

In the design of a tracking filter for air traffic control (ATC) applications, a maneuvering aircraft can be modelled by a linear system with random noise accelerations. A Kalman filter tracker, designed on the basis of a variance chosen according to the distribution of the potential maneuver accelerations, will maintain track during maneuvers and provide some improvement in position accuracy. However, during those portions of the flight path where the aircraft is not maneuvering, the tracking accuracy will not be as good as if no acceleration noise had been allowed in the tracking filter. In this paper, statistical decision theory is used to derive an optimal test for detecting the aircraft maneuver; a more practical suboptimal test is then deduced from the optimal test. As long as no maneuver is declared, a simpler filter, based on a constant-velocity model, is used to track the aircraft. When a maneuver is detected, the tracker is reinitialized using stored data, up-dated to the present time, and then normal tracking is resumed as new data arrives. In essence, the tracker performs on the basis of a piecewise linear model in which the breakpoints are defined on-line using the maneuver detector. Simulation results show that there is a significant improvement in tracking capability using the decision-directed adaptive tracker.     

A tracking algorithm for maneuvering targets

A methodology for the tracking of maneuvering targets is presented. A quickest-detection scheme based on the innovation sequence is developed for a prompt detection of target maneuvers. The optimal length of a sliding window that minimizes the maneuver detection delay for a given false-alarm rate is determined. After maneuver detection, the system model is modified by adding a maneuver term. A recursive algorithm is proposed to estimate the maneuver magnitude. With this estimate, a modified Kalman filter is used for tracking. Simulation results demonstrate the superior performance of the algorithm, especially during target maneuvers     

Discrete-time observability and estimability analysis for bearings-only target motion analysis

Observability in the context of bearings-only tracking (BOT) is still the subject of important literature. Different from previous approaches, where continuous-time analysis was considered, our approach relies on discrete-time analysis. It is then shown that this allows us to use directly and efficiently the simple formalisms of linear algebra. Using the direct approach, observability analysis is essentially reduced to basic considerations about subspace dimensions. Even if this approach is conceptually quite direct, it becomes more and more complex as the source-encounter scenario complexity increases. For complex scenarios, the dual approach may present some advantages essentially due to the direct use of multilinear algebra. New results about BOT observability for maneuvering sources are thus obtained. Observability analysis is then extended to unknown instants of source velocity changes. Even if observability analysis provides thorough insights about the algebraic structure of the BOT problem, the optimization of the observer maneuvers is essentially a control problem. Basic algebraic considerations prove that a relevant cost functional for this control problem is the determinant of the Fisher information matrix (FIM). So, a large part of this work is devoted to the analysis of this cost functional. Using multilinear algebra, general approximations of this functional are given. In order to involve only directly estimable parameters, the source bearing-rates are examined. Using these approximations, a general framework for optimizing the observer trajectory is derived which allow us to approximate the optimal sequence of controls. It is worth stressing that our approach does not require the knowledge of the source trajectory parameters and is still valid for a maneuvering source.     

Accurate solution of proportional navigation for maneuveringtargets

An accurate solution is presented of the nonlinear differential equations describing motion under proportional navigation when the target is laterally maneuvering. A quasilinearization (QL) approach is used, followed by a perturbation technique to obtain closed-form solutions for trajectory parameters. An explicit expression for the pursuer lateral acceleration is derived and shown to contain contributions due to initial heading error and target maneuver, with a coupling between the two effects. The solution is shown to be a substantial and consistent generalization or an earlier accurate solution for nonmaneuvering targets and also of classical linear solutions for maneuvering targets. The generalized QL solution presented provides very accurate estimates of pursuer lateral acceleration over a much broader range of engagement geometries and target maneuvers than presently available closed-form solutions     

Robust extended Kalman filter with input estimation for maneuver tracking

This study investigates the problem of tracking a satellite performing unknown continuous maneuvers. A new method is proposed for estimating both the state and maneuver acceleration of the satellite. The estimation of the maneuver acceleration is obtained by the combination of an unbiased minimum-variance input and state estimation method and a low-pass filter. Then a threshold-based maneuver detection approach is developed to determinate the start and end time of the unknown maneuvers. During the maneuvering period, the estimation error of the maneuver acceleration is modeled as the sum of a fluctuation error and a sudden change error. A robust extended Kalman filter is developed for dealing with the acceleration estimate error and providing state estimation. Simulation results show that, compared with the Unbiased Minimum-variance Input and State Estimation (UMISE) method, the proposed method has the same position estimation accuracy, and the velocity estimation error is reduced by about 5 times during the maneuver period. Besides, the acceleration detection and estimation accuracy of the proposed method is much higher than that of the UMISE method.     

TMA from bearings and multipath time delays

A novel approach for target motion analysis (TMA), which uses conventional passive bearing together with multipath time-delay measurements is examined. This so-called "Multipath TMA" offers two tactical advantages over the classical bearings-only TMA: no requirement for any ownship maneuver, and a good performance in terms of estimation error achieved in a shorter time. Both known and unknown multipath cases are addressed. Finally, Monte-Carlo simulations and at-sea trials demonstrate the practical efficiency of such a multipath TMA.     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

Improved tracking of maneuvering targets: The use of turn-ratedistributions for acceleration modeling

Tactically maneuvering targets are difficult to track since acceleration cannot be observed directly and the accelerations are induced by human control or an autonomous guidance system therefore they are not subject to deterministic models. A common tracking system is the two-state Kalman filter with a Singer maneuver model where the second-order statistics of acceleration is the same as a first-order Markov process. The Singer model assumes a uniform probability distribution on the targets acceleration which is independent of the x and y direction. In practice, it is expected that targets have constant forward speed and an acceleration vector normal to the velocity vector, a condition not present in the Singer model. The work of Singer is extended by presenting a maneuver model which assumes constant forward speed and a probability distribution on the targets turn-rate. Details of the model are presented along with sample simulation results     

机动目标的模型与跟踪算法

 <正> 在机动目标的“当前”统计模型中,目标的加速度被描述为修正的瑞利—马尔科夫过程,对应的自适应跟踪算法呈现出较好的跟踪特性。文献[2]研究了该模型及其自适应算法在实际的机载雷达跟踪系统的应用;文献[3]进一步推广了基于“当前”模型的MPDAF算法。本文提出一个新的机动目标模型,即假定目标加速度为一高斯—马尔     

Continuous-time ECV and ECA track filters with colored measurementnoise

Analytical solutions are presented for two continuous-time track filters with correlation in both the measurement errors and the target maneuvers. The measurement error model is a first-order Markov process, characterized by a correlation time (γ) and a position error variance (r). The target motion is described by one of two dynamic models: the exponentially correlated velocity (ECV) model, and the exponentially correlated acceleration (ECA) model. For both models, the steady-state velocity variance exhibits resonant behavior. The analytical solutions include as special cases several previously published results     

Implementation of tactical maneuvers with maneuver libraries

This study creates and combines the general maneuver libraries for fixed-wing aircraft to implement tactical maneuvers. First, the generalized maneuver libraries are established by analyzing the characteristics of tactical maneuvers required in battlefields. The 7th order polynomial is applied to both the creation of the maneuver libraries and the generation of the trajectories or flight paths for modal inputs. To track the desired trajectory, we design the Attitude Command Attitude Hold (ACAH) system and the Rate Command Rate Hold (RCRH) system using Model Following Controller (MFC). Moreover, the Line-of-Sight (LOS) guidance law is designed. In particular, the CONDUIT® is employed to optimize the gains so that the control systems meet the aircraft Handling Qualities (HQ) criteria. Finally, flight simulations are performed for the longitudinal loop, immelmann-turn, and climb-slalom-descent maneuvers to verify that tactical aggressive maneuvers are realizable via the combination of maneuver libraries. This study can contribute to the development of flight techniques for aircraft tactical maneuvers and to the revision of air force operational manuals.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

自主机动条件下的实时定轨方法

中继卫星在跟踪自主机动用户目标时,由于机动轨道未知,需要利用中继卫星下传的星载GNSS(Global Navigations Satellite System,全球导航卫星系统)数据进行实时轨道确定与预报,为中继卫星跟踪提供实时的引导信息,以方便中继卫星快速捕获目标和连续稳定跟踪。针对该类用户目标的任务需求,讨论了基于星载GNSS数据自主机动条件下的实时定轨方法,建立了连续推力机动力学模型。以某一型号卫星的实测数据进行分析验证,并对轨道机动进行辨识,计算的机动加速度和机动时间与试验单位提供的结果一致。针对卫星不同机动情况,5min的观测数据定轨预报10min的弧段,最大位置误差小于8km,可以为中继卫星快速捕获提供高精度的引导信息。     

基于Backstepping和扰动观测器的导引律

考虑目标机动和自动驾驶仪动态特性等情况,基于扰动观测器(DOB)技术及Backstepping的设计思想,提出了一种新型的三维导引律。运用Backstepping的设计思想,将包含驾驶仪动态特性的制导环路分为外环和内环两个环路。将目标机动及俯仰和偏航平面间的交叉耦合项当成外环扰动,将驾驶仪参数不确定当成内环扰动,分别设计内外扰动观测器将它们估计出来,利用估计值做前馈补偿得到的外环控制器可抑制目标机动对制导精度的影响及实现两个平面的解耦控制,内环控制器补偿驾驶仪动态特性对制导精度的影响。导引律的设计在于使得导弹的实际加速度跟踪上外环的虚拟控制。仿真结果表明:在目标做大机动、考虑驾驶仪动态特性的情况下,这种导引律仍然具有良好的制导精度。     

Interacting acceleration compensation algorithm for trackingmaneuvering targets

The two-stage Kalman estimator has been studied for state estimation in the presence of random bias and applied to the tracking of maneuvering targets by treating the target acceleration as a bias vector. Since the target acceleration is considered a bias, the first stage contains a constant velocity motion model and estimates the target position and velocity, while the second stage estimates the target acceleration when a maneuver is detected, the acceleration estimate is used to correct the estimates of the first stage. The interacting acceleration compensation (IAC) algorithm is proposed to overcome the requirement of explicit maneuver detection of the two-stage estimator. The IAC algorithm is viewed as a two-stage estimator having two acceleration models: the zero acceleration of the constant velocity model and a constant acceleration model. The interacting multiple model (IMM) algorithm is used to compute the acceleration estimates that compensate the estimate of the constant velocity filter. Simulation results indicate the tracking performance of the IAC algorithm approaches that of a comparative IMM algorithm while requiring approximately 50% of the computations     

A non-Bayesian segmenting tracker for highly maneuvering targets

The segmenting track identifier (STI) is introduced as a new methodology for tracking highly maneuvering targets. This nonBayesian approach dynamically partitions a target track into a sequence of track segments, making hard estimates of when the target's maneuvering mode transitions occur, and then estimates the parameters of the target model for each segment. STI is compared with two variable structures interacting multiple model (VS-IMM) algorithms through simulations, where it is shown to have a three fold performance advantage in median absolute turn rate estimation errors, as well as better position estimation for very highly maneuvering targets. STI is also shown to outperform a Rauch-Tung-Striebel (RTS) fixed-interval smoother when estimates are retrospectively derived, and STI accurately characterize the temporal pattern of maneuvers.     

Tracking a 3D maneuvering target with passive sensors

A novel application of the interacting multiple models (IMM) algorithm in which passive infrared sensors are fused for tracking a target maneuvering in three dimensions is discussed. More accurate models of target motion are proposed to improve performance. When the general models are used to describe the maneuvering periods, it is shown that the IMM behaviour is not satisfactory, in that the innovations associated with the different models do not discriminate between the corresponding target maneuvering regimes. The turning of the Markov chain transition matrix, i.e., a priori information, is then crucial to obtaining the correct ordering of the a posteriori regime probabilities. On the contrary, a more satisfactory behavior of the IMM algorithm is obtained by carefully selecting the target motion models in the different regimes