Observability Criteria for Bearings-Only Target Motion Analysis

The observability requirements for bearings-only target motion analysis (TMA) are rigorously established by solving a third-order nonlinear differential equation. Closed form expressions are developed and subsequently used to specify necessary and sufficient conditions on own-ship motion that insure a uniquetracking solution. It is shown that for certain types of maneuvers the estimation process remains unobservable, even when the associated bearing rate is nonzero. Such maneuvers are frequently overlooked in heuristic discussions of TMA observability, which may account for some common misconceptions regarding the characteristics of acceptable own-ship motion.     

单载机相位差无源定位系统可观测性分析(英文)

With a pair of antennas spaced apart, an airborne passive location system measures phase differences of emitting signals. Regarded as cyclic ambiguities, the moduli of the measurements traditionally are resolved by adding more antenna elements. This paper models the cyclic ambiguity as a component of the system state, of which the observability is analyzed and compared to that of the bear- ings-only passive location system. It is shown that the necessary and sufficient observability condition for the bearings-only passive location system is only the necessary observability condition for the passive location system with phase difference measurements, and that when the system state is observable, the cyclic ambiguities can be estimated by accumulating the phase difference measurements, thereby making the observer able to locate the emitter with high-precision.     

多源信息融合卫星组合导航系统的可观度分析

针对基于GNSS卫星、地标矢量和星光矢量的多源信息融合的高轨卫星组合导航系统,分别利用系统可观度分析方法和状态可观度分析方法对其进行分析.仿真结果表明:在GNSS导航卫星不可见时,地标矢量和星光矢量可以有效地提供测量信息,并保证滤波器的稳定.可观度分析结果表明:系统可观度主要受GNSS导航星的可见星数目影响较大,地标矢...     

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.     

Observability of an integrated GPS/INS during maneuvers

An observability analysis of a GPS/INS system during manoeuvers is presented based upon a perturbation model with respect to the Earth-centered-Earth-fixed (ECEF) coordinate system. Analysis is performed on two types of manoeuvers, linear acceleration and steady turn. These manoeuvers could be used for in-flight INS alignment using GPS. During the constant linear acceleration without rotation relative to the Earth, the linear system model is shown to be time-invariant. The observability analysis for the time invariant linear system model shows that linear acceleration does not change the number of observable modes but rather the structure of the observable space. For a nonconstant linear acceleration or a steady turn, the perturbation linear system becomes time varying. For this time-varying system, three types of observability are considered, complete, differential, and instantaneous observability. Instantaneous observability is the strongest properties and means that the state of the system at any time may be determined instantaneously from observation of the output and its derivatives. Instantaneous observability is important for fast in-flight INS alignment. It is shown that the number of instantaneously observable moded is increased by at least 2 during a maneuver. Hence, some linear combinations of the attitude angles become instantaneously observable.     

Dynamic compensator design in nonlinear aerospace systems

Based on differential algebraic results, dynamic controllers are proposed for the feedback regulation of typical aerospace systems. Fliess's generalized observability canonical form (GOCF) is used for specifying a dynamic compensator that smoothly regulates the plant dynamics. The synthesis approach used is also applicable to the design of nonlinear pulsewidth-modulation (PWM) controllers, as well as to sliding-mode control strategies. The three underlying nonlinear control techniques, explored with the aid of illustrative examples, are commonly encountered in aerospace control system design problems. Simulations are also included     

Processing of filtered GPS data

General sufficiency conditions are developed for the stability of a discrete-time cascaded-filter architecture. An application of the result is in the filtering of prefiltered Global Positioning System (GPS) data during times in which the GPS receiver is tracking less than four satellites. Simulation results are presented for the case where the master filter processes the GPS filter estimate after the GPS filter attains uniform complete observability and controllability following its third filter cycle as well as the case where the observability condition is not met     

Simultaneous spacecraft attitude and orbit estimation using magnetic field vector measurements

Based on magnetometer measurements only, three-axis attitude, rate, and orbit estimation are successfully achieved. A single Augmented Dynamics Extended Kalman Filter (ADEKF) is configured by combining the spacecraft nonlinear attitude dynamics and quaternion kinematics with orbital mechanics. The filter design is adopted for three-axis stabilized spacecraft in low Earth orbits where the aerodynamic drag is the dominant source of disturbances in addition to the spacecraft magnetic residuals. To reduce the computational burden, another Interlaced Extended Kalman Filter (IEKF) is developed to uncouple the attitude/rate from the orbit dynamics. Both filters are implemented using the magnetometer measurements and their corresponding time derivatives. As a part of EgyptSat-1 flight scenario, detumbling and standby modes are used for performance testing of the ADEKF. The concept of local observability is applied to the basic filter and the stability is investigated by incorporating extensive Monte Carlo simulations with uniformly distributed initial conditions. The filter shows the capability of estimating the attitude better than 5 deg and rate of order 0.03 deg/s in each axis. In orbit estimation, the filter is capable of estimating the position with accuracy less than 8 km and velocity upto 5 m/s in each axis.     

Observability, Eigenvalues, and Kalman Filtering

In higher order Kalman filtering applications the analyst often has very little insight into the nature of the observability of the system. For example, there are situations where the filter may be estimating certain linear combinations of state variables quite well, but this is not apparent from a glance at the error covariance matrix. It is shown here that the eigenvalues and eigenvectors of the error covariance matrix, when properly normalized, can provide useful information about the observability of the system.     

Multiposition alignment of strapdown inertial navigation system

The authors demonstrate that the stationary alignment of strapdown inertial navigation system (SDINS) can be improved by employing the multiposition/technique. Using an observability analysis, it is shown that an optimal two-position alignment not only satisfies complete observability conditions but also minimizes alignment errors. This is done by analytic rank testing of the stripped observability matrix and numerical calculation of the error covariance. It is also shown that an optimal three-position alignment accelerates the convergence of the alignment error compared with two-position alignment     

基于“速度+姿态”快速传递对准的可观测性分析

惯导系统初始对准一般采用卡尔曼滤波器对初始姿态误差角进行估计,而在设计卡尔曼滤波器之前通常要对系统进行可观测性分析,确定卡尔曼滤波器的效果。捷联惯导系统的卡尔曼滤波模型在传递对准时,为线性时变系统,而线性时变系统的可观测性分析比较困难。文中采用一种依据系统矩阵的奇异值确定状态可观测度的方法对基于“速度＋姿态”快速传递对准的卡尔曼滤波模型进行可观测性分析,结果表明该方法可直接简单地实现系统状态的可观测度分析。     

空间多机器人协同的多视线仅测角相对导航

研究了空间多机器人对非合作目标的多视线协同仅测角相对导航问题。为利用多视线信息融合提升仅测角相对导航性能,给出了一种可观测度优化的多视线仅测角相对导航方法。首先基于二阶CW方程构建了中心机器人与目标相对动力学模型和状态方程,并构建了仅包含多伴飞机器人视线角的观测方程,结合扩展卡尔曼滤波算法,形成多视线仅测角相对导航系统;然后分析推导得到可观度最优的视线间夹角条件,提出了兼顾可观测度和长期自然维持的多伴飞机器人观测构型优化方法;最后,数学仿真结果表明,提出的多视线仅测角相对导航系统、可观测度最优的视线夹角条件和观测构型优化方法,可以显著提高距离状态可观测度和估计性能,且具有较好的工程可用性。     

Observability analysis of piece-wise constant systems. I. Theory

For pt.II see ibid., vol.28, no.4, p.1068-75, Oct. 1992. A method for analyzing the observability of time-varying linear systems which can be modeled as piece-wise constant systems (PWCS) is presented. An observability matrix for such systems is developed for continuous and discrete time representations. A stripped observability matrix (SOM) is introduced which simplifies the analysis in cases where the use of this matrix is legitimate. The observability analysis is presented as a step-by-step procedure     

基于奇异值分解的组合导航可观测度计算

以捷联惯组为主惯导的组合导航系统具有短时定位精度高、可靠性强等优点,但其依然存在长时间导航精度不高、运算量大、组合效率不高等问题。为更好地完善组合导航系统的误差补偿和抑制技术,对SINS/DVL组合导航系统的可观测性能进行了研究。在分段定常系统(Piece-wise Constant System,PWCS)的可观测性分析方法及基于奇异值分解的系统状态可观测度分析方法基础上,结合可观测性矩阵的遗传特性,提出了一种简化的状态量可观测性分析方法,并对该方法进行了理论仿真。为方便比较状态量的可观测程度,对各状态的可观测度进行了归一化处理。最后,通过湖面跑船实验设计了不同的航迹机动方式,计算了关键导航参数的可观测性能。实验证明,该方法可以实时计算组合导航参数的可观测度,根据可观测度设计的航迹可以有效提高导航精度,定位精度可提高1个量级,收敛速度也获得了明显提高。     

一种基于可观测度分析的SINS/GPS自适应-反馈校正滤波新方法

 针对机载捷联惯导系统(SINS)/全球定位系统（GPS）组合导航系统不完全可观测导致滤波器精度下降甚至发散的问题,提出了一种基于系统状态可观测度分析的自适应反馈校正滤波新方法。该滤波方法改进了系统可观测度的归一化处理方法,将归一化处理后的系统状态可观测度作为反馈因子,对SINS系统进行自适应反馈校正。最后,将该方法应用于机载合成孔径雷达(SAR)运动补偿用SINS/GPS组合导航系统中,飞行试验结果表明该方法在系统不完全可观测的情况下有效地提高了导航精度。     

Coordinated target localization base on pseudo measurement for clustered space robot

This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for target localization with respect to slavery space robots is proposed;then the basic mathematical models,including coordinated relative measurement model and cluster centralized dynamics,are established respectively.By employing the linear Kalman flter theorem,the centralized estimator based on truth measurements is developed and analyzed frstly,and with an intention to inhabit the initial uncertainties related to target localization,the globally stabilized estimator is designed through introduction of pseudo measurements.Furthermore,the observability and controllability of stochastic system are also analyzed to qualitatively evaluate the convergence performance of pseudo measurement estimator.Finally,on-orbit target approaching scenario is simulated by using semi-physical simulation system,which is used to verify the convergence performance of proposed estimator.During the simulation,both the known and unknown maneuvering acceleration cases are considered to demonstrate the robustness of coordinated localization strategy.     

航天器多约束交会的仅测角导航最优多目标闭环制导

研究了航天器多约束交会的仅测角导航最优多目标闭环制导问题,优化目标包括交会时间、燃耗和仅测角导航可观性指标,并考虑了视觉传感器视场角、推力器推力幅度和最小安全距离等各种约束条件,建立了多约束、多目标优化下的仅测角导航和闭环制导问题的数学模型,分析了仅测角导航和闭环制导之间的耦合关系。最后,通过Matlab遗传算法工具箱中的多目标优化函数,求解得到了该多目标优化模型的Pareto最优解集,结果显示交会时间、燃耗和仅测角导航可观性指标不能同时达到最优,存在相互制约关系,即提高其中一种优化目标的性能会降低其他优化目标的性能。     

基于可观测度分析的稳定姿态滤波器

提出一种适用于惯性/天文组合航天飞行器的稳定姿态滤波器,可以在不降低系统可观测度的前提下解决滤波计算中的奇异问题。对于奇异问题的传统解决方案是删除观测方程的一行,通过对比删除前后系统可观测度的变化,证明此解决方案会导致系统可观测度下降,并指出如何选择最优删除方案以使系统可观测度下降最小。根据对传统解决方案的分析结果,提出了不降低系统可观测度的投影算法。理论分析和仿真试验证明,应用了投影算法的姿态滤波器更为稳定,估计效率更高。     

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.     

高空长航时无人机SINS/CNS组合导航系统仿真研究

根据高空长航时无人机的特点研究了SINS/CNS组合导航系统并进行了仿真。研究了分段定常系统(PWCS)的可观测性分析方法和基于奇异值分解的系统状态可观测度分析问题,并提出了一种改进的状态可观测度分析方法,在求状态变量的可观测度时,抛开了观测量,只利用可观测矩阵进行分析,然后将该理论应用到SINS/CNS组合导航系统中,证明了其合理性与可行性,进一步根据可观测度分析的结果对系统进行反馈校正,通过仿真结果证明导航精度得到了提高。