Decentralized reduced-order filters

Continuous and discrete methods of designing simple reduced-order local filters within a large-scale network are suggested. The filters are designed to estimate only the local variables of interest and not the entire state vector. The method has the advantage that one need not know the mathematical models of the subsystems generating the interconnection variables. The order of the filter can be small enough so that there is no computational burden associated with the filter. The disadvantage of the method is that performance is lost by using a reduced-order filter instead of a full-order filter. An example that demonstrates one application in the aerospace industry is presented     

Square root parallel Kalman filtering using reduced-order localfilters

The basic parallel Kalman filtering algorithms derived by H.R. Hashemipour et al. (IEEE Trans. Autom. Control. vol.33, p.88-94, 1988) are summarized and generalized to the case of reduced-order local filters. Measurement-update and time-update equations are provided for four implementations: the conventional covariance filter, the conventional information filter, the square-foot covariance filter, and the square-foot information filter. A special feature of the suggested architecture is the ability to accommodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariance or information matrices (or their square roots) from these reduced-order filters are collated at a central filter at each step to generate the full-size, globally optimal estimates and their associated error covariance or information matrices (or their square roots). Aspects of computational complexity and the ensuing tradeoff with communication are discussed     

A relative navigation system for formation flight

A relative navigation system based on both the Inertial Navigation System (INS) and the Global Positioning System (GPS) is developed to support situational awareness during formation flight. The architecture of the system requires an INS/GPS integration across two aircraft via a data link. A fault-tolerant federated filter is used to estimate the relative INS errors based on relative GPS measurements and a range measurement obtained from the data link. The filter is constructed based on a reduced-order model of the relative INS error process. A method for analyzing the filter performance is presented. A case involving two helicopters in formation flight is studied under three different night trajectories to account for the effect of vehicle motion on the INS state transition matrix. The results of the covariance analysis are compared with actual night results over an instrumented test range.     

A reduced-order model for integrated GPS/INS

The dominant factor in determining the computation time of the Kalman filter is the dimension n of the model state vector. The number of computations per iteration is on the order of n³. Any reduction in the number of states will benefit directly in terms of increased computation time. In this paper, a high order model in integrated GPS/INS is described first, then a reduced-order model based on the high-order model, is developed. Finally, a faster tracking approach for Kalman filters is discussed. A typical aircraft trajectory is designed for a complex high-dynamic aircraft flight experiment. A Monte Carlo analysis shows that the reduced order model presented in this paper provides satisfactory accuracy for aircraft navigation     

Control of a large space structure using MMAE/MMAC techniques

The application of moving-bank multiple model adaptive estimation and control (MMAE/MMAC) algorithms to an actual spade structure (Space Integrated Controls Experiment (SPICE)) being examined at Phillips Laboratory at Kirtland AFB, NM, is presented. The structure consists of a large platform and a smaller platform connected by three legs in a tripod fashion. Kalman filtering and LQG (linear system, quadratic cost, Gaussian noise) control techniques are utilized as the primary design tools for the components of the MMAE/MMAC. Implementing a bank of filters or controllers increases the robustness of the algorithms when uncertainties exist in the system model, whereas the moving bank is utilized to reduce the computational load. Several reduced-order models are developed from the truth model using modal analysis and modal cost analysis. The MMAE/MMAC design with a substantially reduced-order filter model provides an excellent method to estimate a wide range of parameter variations and to quell oscillations in the structure.     

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.     

Target tracking in maneuver-centered coordinates

Aircraft targets normally maneuver on circular paths, which has led to tracking filters based on circular turns. A coordinate system to track circular maneuvers with a simple Kalman filter is introduced. This system is a polar coordinate system located at the center of the maneuver. It leads to a tracking filter with range, angle, and angular velocity in the state vector. Simulation results are presented, showing that the algorithm displays improved performance over methods based on constant x-y acceleration when tracking circular turns     

A new adaptive Kalman filter for navigation systems of carrier-based aircraft

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman ...     

Kalman filtering with state equality constraints

Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem     

Convolution Particle Filter for Parameter Estimation in General State-Space Models

The state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter (EKF) and the bootstrap particle filter (PF), fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. We propose a variant of the PF based on convolution kernel approximation techniques. This approach is tested on a simulated case study.     

Multiple target tracking using products of position measurements

The continued development of the symmetric measurement equation (SME) filter for track maintenance in multiple target tracking (MTT) is considered, focusing on the case in which the SMEs are generated by forming sums of products of the original position measurements. The SME filter is developed for the case of N targets whose motions consist of random perturbations about constant-velocity trajectories. It is assumed that measurements of x-coordinate positions are available, and that the number of measurements is equal to the number of targets. Various analytical properties of the SME filter are studied. It is shown that under a very weak condition, the estimation error equation is locally exponentially stable. The performance of the SME filter is investigated by comparing it with an optimal (minimum-variance) estimator and by generating a computer simulation in the six-target case     

On state estimation for an orbiting single tether system

The effects of instrumentation accuracy and configuration on estimation error are studied for the small expandable-tether deployment system (SEDS) using a continuous-discrete extended Kalman filter (CDEKF) state estimator. A twelfth order model that incorporates the rigid body modes of the tether as well as the satellite attitude dynamics is developed. Simulation results using the model and the estimator indicate that the originally planned instrumentation package could not estimate the state vector adequately. Recommendations are made and results presented that reduce the estimation error by adding instruments and increasing selected measurement accuracies     

A modified Gaussian sum approach to estimation of non-Gaussiansignals

A Gaussian sum estimation algorithm has previously been developed to deal with noise processes that are non-Gaussian. Inherent in this algorithm is a serious growing memory problem that causes the number of terms in the Gaussian sum to increase exponentially at each iteration. A modified Gaussian sum estimation algorithm using an adaptive filter is developed that avoids the growing memory problem of the previous algorithm while providing effective state estimation. The adaptive filter is comprised of a fixed set of estimators operating in parallel with each individual estimate possessing its own corresponding weighting term. A simulation example illustrates the new non-Gaussian estimation technique     

多传感器组合导航系统的多尺度异步信息融合算法

首先,将状态方程采用数据块变换的方式得到新的状态块方程,并将量测方程表达为数据块的形式;然后,将量测向量进行多层小波变换以得到新的量测向量,结合状态块方程进行卡尔曼滤波;最后,利用异步贯序滤波的方法,建立了基于全局的最优估计值。将上述算法应用于GPS/SST/高度表/SINS多组合导航系统,仿真结果表明:相对于单一尺度的异步滤波算法,该算法可明显地提高系统的滤波精度。     

基于I、Q信号的北斗接收机跟踪环路设计

传统的北斗接收机一般采用标量跟踪环,每个通道的卫星相互独立,在此 基础上,又发展起来了基于矢量跟踪的接收机,使每个通道的卫星跟踪不再相互独立。 提出的基于I、Q 信号观测的接收机跟踪环路,保留矢量跟踪的特点,并且采用EKF 作 为跟踪环路预处理滤波器,代替传统跟踪环路的鉴别器,可以在高动态的环境下对卫星 信号进行跟踪,提高环路的稳定性,从而可以有效地提高BDS/INS 深组合导航滤波器观 测量的估计精度。主要对高动态信号跟踪进行仿真,并与传统的标量跟踪方法和矢量跟 踪方法的跟踪能力进行比较。实验表明, 改进的矢量跟踪环能够在高动态的环境下运 行,比起传统环路有更小的跟踪误差。     

面向再入目标跟踪的估计与辨识联合优化算法

准确的弹道系数辨识和精确的目标状态估计是再入目标高精度跟踪与高可靠识别的关键。一方面,状态估计的误差会造成模型参数(弹道系数)的辨识风险;另一方面,模型参数的辨识偏差又会导致模型失配从而降低目标状态的估计精度。因此,需要实现再入目标的状态估计和参数辨识的联合优化。针对再入目标弹道系数未知情形,提出了一种基于期望最大化(EM)框架并采用粒子滤波(PF)平滑器实现的PF-EM联合优化算法。在E步基于粒子平滑器得到目标状态的后验平滑估计,M步采用数值优化算法更新上一次迭代的弹道系数,通过E步和M步的不断迭代,以保证状态估计和弹道系数辨识的一致性。算法仿真对比表明:所提算法的状态估计和参数辨识精度均优于传统的状态增广算法。     

自适应飞机驾驶员最优控制模型研究及应用

针对驾驶员最优控制模型(OCM)无法反映飞行员在未知环境下渐进适应过程这一缺点,采用自适应状态估计理论对OCM进行改进,建立了基于自适应状态估计的驾驶员最优控制模型(MOCM-AE),给出了算法流程。通过对比飞行试验数据和未知扰动下的着舰应用,对模型进行了评估。通过人机闭环仿真进行了飞行试验再现,得到了人机闭环频域曲线。对比结果表明,与OCM相比MOCM-AE的频域特性曲线与试验更为吻合。在着舰应用中,引入低空紊流作为未知扰动进行着舰仿真,结果表明OCM强烈依赖于先验经验,而MOCM-AE无论是否具有先验经验,无论是否存在未知扰动,均能取得良好着舰效果。在未知扰动和舰尾流影响下,MOCM-AE比传统OCM着舰精度提高59%,着舰点分布范围缩小29%,这体现了飞行员对未知环境的适应能力。     

A divide and conquer approach to least-squares estimation

The problem of estimating parameters &thetas; which determine the mean μ(&thetas;) of a Gaussian-distributed observation X is considered. It is noted that the maximum-likelihood (ML) estimate, in this case the least-squares estimate, has desirable statistical properties but can be difficult to compute when μ(&thetas;) is a nonlinear function of &thetas;. An estimate formed by combining ML estimates based on subsections of the data vector X is proposed as a computationally inexpensive alternative. The main result is that this alternative estimate, termed here the divide-and-conquer (DAC) estimate, has ML performance in the small-error region when X is appropriately subdivided. As an example application, an inexpensive range-difference-based position estimator is derived and shown by means of Monte-Carlo simulation to have small-error-region mean-square error equal to the Cramer-Rao lower bound     

基于磁强计测量的微小卫星轨道姿态 耦合确定方法

针对基于磁强计测量的微小卫星, 提出了基于串并联混合策略的轨道姿态 耦合确定方法。滤波初期,考虑到估计误差较大,采用先地磁场大小测量的轨道确定、 后地磁场矢量测量的姿态确定的串联策略;稳定后,采用基于矢量测量的轨道、姿态同 步确定的并联策略。为降低轨道、姿态确定的相互影响,设计了基于信息的鲁棒Kalman 滤波,通过自动调节增益矩阵处理两个滤波系统间的影响。仿真表明,该方法在提高鲁 棒性的同时,还能适当提高状态估计的精度。     

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.