Observability Requirements for Three-Dimensional Tracking via Angle Measurements

Observability requirements previously established for bearings-only tracking in two dimensions are extended to a class of three-dimensional estimation algorithms capable of processing any pairwise combination of azimuth bearing, conical bearing, and depth/elevation angle measurements. Although these algorithms are intrinsically nonlinear, it is shown that they can be analyzed in a linear framework without sacrificing mathematical rigor. A simplified observability criterion, applicable to both autonomous and nonautonomous linear systems, is presented and utilized to specify conditions on own-ship motion which are both necessary and sufficient for a unique tracking solution. Further analysis reveals that observability dependence on own-ship maneuvers for the three-dimensional algorithms considered here parallels the concomitant two-dimensional requirements. An interesting difference, however, is that under certain conditions, a unique tracking solution can be obtained in three dimensions for unaccelerated own-ship motion.     

Biased Estimation Properties of the Pseudolinear Tracking Filter

Estimation bias in the pseudolinear filter applied to bearings-only target tracking is discussed. Approximate expressions for the pertinent error terms are developed and subsequently used to predict tracking performance under realistic operating conditions. It is shown that once own-ship executes a maneuver, only the estimated range vector remains biased; the corresponding velocity vector becomes asymptotically unbiased. Further investigation reveals that this range bias is highly dependent upon geometry and can be altered by additional own-ship maneuvers. Experimental data are presented to support these findings.     

Observability in passive target motion analysis

The nature of observability of nonlinear systems encountered in passive target motion analysis (TMA) is carefully examined. The approach proposed here is based upon a well-chosen criterion which allows us to answer the major observability questions     

Observability of Relative Navigation Using Range-Only Measurements

A simulation tool is described which is capable of determining the observability of various fleet configurations and maneuvers in a relative navigation environment. The motion of the relative grid established by the navigation controller is explicitly modeled as a function of the errors in his dead-reckoning sensors. The simulation uses centralized, optimal processing of an extended Kalman filter. Results show observability on a good geometry, with some degradation in performance when dead-reckoning sensor errors change rapidly.     

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.     

Bearings-only tracking for maneuvering sources

Classical bearings-only target-motion analysis (TMA) is restricted to sources with constant motion parameters (usually position and velocity). However, most interesting sources have maneuvering abilities, thus degrading the performance of classical TMA. In the passive sonar context a long-time source-observer encounter is realistic, so the source maneuver possibilities may be important in regard to the source and array baseline. This advocates for the consideration and modeling of the whole source trajectory including source maneuver uncertainty. With that aim, a convenient framework is the hidden Markov model (HMM). A basic idea consists of a two-levels discretization of the state-space. The probabilities of position transition are deduced from the probabilities of velocity transitions which, themselves, are directly related to the source maneuvering capability. The source state sequence estimation is achieved by means of classical dynamic programming (DP). This approach does not require any prior information relative to the source maneuvers. However, the probabilistic nature of the source trajectory confers a major role to the optimization of the observer maneuvers. This problem is then solved by using the general framework of the Markov decision process (MDP)     

Data fusion and tracking using HMMs in a distributed sensor network

This work deals with the problem of multiple target tracking, from the measurements made on a field of passive sonars activated by an active sonar (multistatic network). The difficulties encountered then are of two kinds: each sensor alone does not provide full observability of a target, and multiple, possibly maneuvering targets moving in a cluttered environment must be dealt with. The algorithm presented here is based on a discrete Markovian modelization of the targets evolution in time. It starts with a fusion of the detections obtained at each measurement time. Tracking and target motion analysis (TMA) are next achieved thanks to dynamic programming (DP). This approach leads to multiple and maneuvering target tracking, with few assumptions; for instance, the use of deterministic target state models are avoided. Simulation results are presented and discussed.     

Optimal observer maneuver for bearings-only tracking

In bearings-only tracking, observer maneuver is critical to ensure observability and to obtain an accurate target localization. Here, optimal control theory is applied to the determination of the course of a constant speed observer that minimizes an accuracy criterion deduced from the Fisher information matrix (FIM). Necessary conditions for optimal maneuver (Euler equations) are established and resolved, partly by analytical means and partly by an iterative numerical procedure. Examples of optimal observer maneuvers are presented and discussed     

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.     

Bearings-only target motion analysis with acoustic propagation models of uncertain fidelity

The augmented bearings-only target motion analysis (TMA) problem arises when the bearing measurements of the classical bearings-only TMA problem are augmented with received signal-to-noise ratio (SNR) measurements. A combined acoustic propagation and sensor (CAPS) performance prediction model specifying the conditional density of the SNR measurements is assumed given; however, mismatch may exist between the CAPS model and the real world. We present a novel "missing data" formulation of the augmented bearings-only TMA problem using an empirical maximum a posteriori (EMAP) method for target parameter estimation, and show that it provides a natural and straightforward technique for mitigating CAPS model mismatch. The EMAP approach leads to an iteratively reweighted, linear least-squares algorithm for solving both the augmented bearings-only TMA problem and the classical (nonaugmented) bearings-only TMA problem. Examples are provided.     

Observability analysis of piece-wise constant systems. II.Application to inertial navigation in-flight alignment [militaryapplications]

For pt.I see ibid., vol.28, no.4, p.1056-67, Oct. 1992. The method of analyzing the observability of time-varying linear systems as piecewise constant systems (PWCS) is applied to the analysis of in-flight alignment (IFA) of inertial navigation systems (INS) whose estimability is known to be enhanced by maneuvers. The validity of this approach to the analysis of IFA is proven. The analysis lays the theoretical background to, and clearly demonstrates the observability enhancement of, IFA. The analytic conclusions are confirmed by covariance simulations. Although INS IFA was handled to various degrees in the past, a comprehensive control theoretic approach to the problem is introduced. The analysis yields practical conclusions and a procedure previously unknown     

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     

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.     

一种常规机动下机载SINS/GPS组合导航系统的可观测性分析

为保证机载捷联惯组的导航精度能够达到要求,需要对惯组定期进行返厂标定,成本高、周期长,也影响载机的使用效率,故而机载惯组在线标校技术的研究一直在不断进行中。对大中型运输机的机载惯组而言,由于其机体较大、机动能力较差,很难完成诸如S机动等复杂的机动动作,故而需要对其常规飞行机动状态下机载SINS/GPS组合导航系统的可观测性进行分析。利用GPS提供的速度和位置信息作为外部观测量来设计Kalman滤波器,采用基于分段线性定常系统(PWCS)的奇异值分解法(SVD),对飞机静止、起降、匀速飞行、匀加减速飞行、转弯等一系列常规机动条件下系统的可观测性和可观测度进行研究。通过Matlab仿真和转台实验,验证了组合导航系统可观测性分析结论的有效性,可为机载惯组的在线标校提供一定参考。     

被动式寻的导弹的运动跟踪变结构制导

应用运动跟踪变结构控制理论设计被动式寻的导弹的制导律。这种运动跟踪变结构制导律（ＭＴＶＳＧ）可以令导弹－目标相对视线角速度按照给定的运动规律变化,从而增强被动跟踪问题（等价于一个非线性系统）的可观性,同时保证导弹有很高的命中精度。仿真研究表明,在ＭＴＶＳＧ下,系统的可观性明显增强,因此系统状态的估计精度较高。进一步的研究表明,ＭＴＶＳＧ对系统状态估计误差有很强的鲁棒性。ＭＴＶＳＧ的上述各种优点使得导弹有很高的命中精度。     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

嵌入式小型智能气流传感器原理及应用研究

高隐身性、高敏捷性和大信息量是未来作战飞机的突出特点,也是基本的战术要求。满足这样条件的大气数据系统,应保证飞机具有光滑的表面,能够精确控制大迎角机动状态下的飞行和作战,同时应具备快速处理大量信息的软件算法和硬件环境。因此大气数据系统的研究集中在取消传统的突出式气动探测器,发展嵌入式的气动探测系统。本文提出了一种嵌入式小型智能气流传感器设计原理和试验方法,对试验结果进行分析和总结。     

对卫星目标的仅测角天基单站无源定位可观测性分析

可观测性分析是无源定位与跟踪系统的前提和基础。由于卫星运动系统方程是状态变量的隐函数形式,以及观测方程的非线性,使得对卫星目标仅测角无源定位的可观测性研究难度较大。鉴于此,从伪线性化角度对非线性系统方程进行改造,推导了关于状态变量的显性系统状态方程,对仅测角条件下的单星对星无源定位系统进行了可观测性分析,为进一步研究仅测角单星对星的无源定轨跟踪提供了理论基础。最后给出了仿真实例,验证了理论分析的正确性。