Novel quaternion Kalman filter

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.     

Performance Evaluation of Suboptimal Filters

The use of a Kalman filter in an applications problem requires a detailed model of both the system dynamics and the measurement dynamics. The model for many problems may be extremely large in dimensionality. However, in many instances one has a limited computer capability and, thus, must purposely introduce modeling errors into the filter in order to gain a computational advantage. However, as is well known, this may lead to the phenomenon of filter divergence. This paper considers the development of equations which allow one to evaluate a filter of reduced state. The equations are based upon using covariance analysis techniques in order to determine the true root-mean-square estimation error. These equations are computationally more advantageous than others appearing in the literature.     

SINS/ANS integration for augmented performance navigation solution using unscented Kalman filtering

The fundamental concept of the multisensor integrated navigation system is the utilization of a medium precision INS in conjunction with one or more auxiliary sensors which perform as error bounding sources. Strapdown inertial navigation system (SINS) integrated with astronavigation system (ANS) yields reliable mission capability and enhanced navigational accuracy for spacecrafts. The theory and characteristics of integrated system based on unscented Kalman filtering is investigated in this paper. This Kalman filter structure uses unscented transform to approximate the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The filter implementation subsumed here is in a direct feedback mode. Axes misalignment angles of the SINS are observation to the filter. A simple approach for simulation of axes misalignments using stars observation is presented. The SINS error model required for the filtering algorithm is derived in space-stabilized mechanization. Simulation results of the integrated navigation system using a medium accuracy SINS demonstrates the validity of this method on improving the navigation system accuracy with the estimation and compensation for gyros drift, and the position and velocity errors that occur due to the axes misalignments.     

Canonical transform for tracking with kinematic models

A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.     

鲁棒EKF在脉冲星导航系统中的应用

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。     

Balloon gravimetry using GPS and INS

Measurement of the horizontal components of gravity at altitude using balloon-borne instrumentation consisting of a Global Positioning System (GPS) receiver and a strapdown inertial navigation system (INS) is discussed. GPS data are to be used primarily to determine the total inertial acceleration of the balloon, while the INS accelerometers sense all nongravitational accelerations. A covariance analysis based on the Kalman filter shows that conventional gravity estimation from GPS-aided INS data is possible only if external attitude updates are also available. An alternative technique is explored that attempts to estimate at least part of the gravitational spectrum without modeling the gravity disturbance as a state variable or relying on external attitude updates, while, at the same time, admitting uncorrected (long-wavelength) attitude errors. Simulations based on a model for typical balloon motion are used to discuss this possibility     

静电陀螺漂移的补偿和监控方法

简要介绍静电陀螺惯性导航系统的基本原理及其常平架结构。由于静电陀螺具有良好的漂移特性,上述系统位置误差随时间增长速度极低。着重讨论静电陀螺漂移模型及其在系统中补偿和监控方法。利用系统内部冗余轴漂移的实时测量将卡尔曼滤波器应用于上述系统,有效地改善了惯性导航系统的精度;此外还同时估计出绕冗余轴方向陀螺漂移的未知常值偏差,取得满意的仿真结果。     

一种非线性滤波器的误差分析及应用

针对一类具有未建模误差和扰动的非线性系统的状态估计问题,提出一种在线估计并补偿模型误差的非线性滤波算法,该算法利用非线性预测滤波(NPF)基于预测输出残差的方差最小的基本原则估计模型误差,冉利用扩展卡尔曼滤波(EKF)的思想对补偿后的模型进行状态估计;详细推导了状态估计误差及其方差阵的传播模型.以卫星姿态确定系统为例,...     

自适应增量粒子滤波方法

提出自适应增量粒子滤波(AIPF)的概念和定义,建立AIPF模型,给出了分析方法和主要的计算步骤.对于许多实际工程(如深空探测)中存在的由未知系统误差的影响而无法精确建立量测似然函数及滤波过程中的粒子匮乏等问题,通过增量粒子滤波模型对滤波过程中的粒子数进行自适应调整,从而消除这种未知系统和滤波粒子匮乏的影响,自动调整粒子,提高非线性滤波的精度.仿真计算中,滤波误差均值和方差分别降低为原来的3.8%和19.6%.该方法有效地改善了滤波效果,计算简单,便于工程应用.      

低成本的多普勒-捷联惯性组合导航系统

本文研究了一种采用低精度的惯性器件,应用卡尔曼滤波技术的多普勒捷联惯性组合导航系统。讨论了组合方案,推导了系统的动态方程,设计了一种最优和四种次优卡尔曼滤波器。对系统进行了协方差分析。分析结果表明,采用随机漂移为0.1°/h的陀螺仪,零位误差为10^-4g的加速度计,应用卡尔曼滤波技术可以实现1nmile/h的导航精度,成为一种低成本、中等精度的导航系统。     

Attitude determination with UD implementation of decoupled bias estimation

The application of the UD implementation decoupled bias estimation to attitude determination is analyzed here. The advantage of decoupled bias estimation in general is the reduction in the dimensions of the filter and the subsequent reduction in the amount of processing. The purpose of the UD implementation is to mitigate the effects of round-off errors. A unique advantage of the application of decoupled bias estimation to attitude determination is that the bias processing can easily be turned off whenever a reconfiguration to a bias-free estimator mode is necessary. A comparison of the attitude error of the UD decoupled Kalman filter attitude uncertainty is given with respect to the coupled Kalman filter attitude uncertainty during the time periods when the bias processing is turned off. A detailed discussion of the UD implementation is given.     

基于多参量模型的光纤陀螺温度误差补偿

温度漂移误差是制约光纤陀螺精度的重要因素之一。针对传统光纤陀螺温度补偿方法仅对温度项建模导致补偿精度差的问题,提出了一种新型多参量模型来补偿光纤陀螺温度误差的方法。通过对陀螺零漂误差和温度各相关项进行相关性分析,将温度和温度速率的乘积项及温度梯度滞后项引入到温度漂移误差模型中,建立了多参量分段补偿模型对零偏进行补偿,显著改善了光纤陀螺的零偏稳定性。使用实测光纤陀螺数据对提出的补偿方法进行实验验证,结果表明采用该方法补偿后,零偏误差平方和降低2个数量级,陀螺漂移均值、方差稳定在零点附近,补偿效果优于温度项分段拟合方法,与非线性模型预测效果相当。     

Analysis of Modeling and Bias Errors in Discrete-Time State Estimation

This paper concerns the effects of modeling and bias errors in discrete-time state estimation. The newly derived algorithms include the effect of correlation between plant and measurement noise in the system. The effects of nonzero mean noise terms and bias errors are considered. With plant or measurement matrix errors, divergence can occur. The local or linear sensitivity approach to error analysis, where the sensitivity is defined as a partial derivative with respect to a variable parameter taken about the modeled value, will not show this divergence due to neglect of higher order terms. Approximate algorithms are presented which circumvent the problem inherent in the local sensitivity approach. These make use of a "conditional bias" concept which views system error as a bias, conditioned on knowledge of the state estimates. It is shown that the actual error in optimum estimation is orthogonal to the residue error for suboptimum estimation where the residue error is defined as the difference between the actual estimation error and the optimum estimation error. Two examples, one concerning an integrated navigation system, demonstrate the theoretical results.     

一种实时飞行轨迹重构方法

提出一种有效的实时纵向飞行轨迹重构的新方法。为了得到状态估计的快速算法,本文把非线性飞行轨迹重构转化为线性、离散、时变状态和参数估计问题。将数值稳定性好、计算量也小的序列U-D分解滤波算法用于状态方程为线性、观测方程为线性或非线性的滤波问题中。由于测量值中常常含有系统偏差,本文把这些偏差作为增广状态加入增广状态模型中,并利用模型的一些特点,提出偏差分离的U-D分解算法,使计算量大大减少。仿真和实际试飞数据计算表明、本文的方法可得到比平方根协方差滤波更有效的实时飞行轨迹重构结果。     

基于改进联邦Kalman滤波的组合校准方法研究

联邦滤波器广泛应用于多传感器信息融合领域,联邦滤波中的信息分配原则影响滤波精度.针对联邦Kalman滤波器进行改进,采用基于估计协方差阵奇异值动态确定信息分配系数.对子滤波器进行重置时,采用新的重置方法,保证了子滤波器误差协方差阵的对称性,确保Kalman滤波器的一致收敛稳定性.新的联邦滤波算法允许每个状态分量拥有不同的动态信息分配因子,从而改进了联邦滤波信息融合的精度.设计了SINS/GPS/电子罗盘组合导航系统,仿真结果说明,与传统联邦滤波算法相比,改进的联邦滤波器估计精度得到了提高,可以更好地对SINS误差进行校准,提高系统的精度.     

基于可观测性分析的旋转式惯导系统在线自标定方法的设计

本文建立了速度误差外观测量的静基座双轴旋转式惯导系统在线标定卡尔曼滤波模型,其状态向量包括地速误差、姿态失准角和惯性器件零偏、标度因数误差、安装误差,可估计旋转式惯导系统失准角与惯性器件误差参数。通过分段线性定常系统(PWCS)可观测性分析方法分析不同旋转方式下系统可观测性变化情况,得出双轴连续旋转的角运动方案可以改善卡尔曼滤波滤波的可观测性。根据基于奇异值分解的可观测度分析结果进行模型降阶,同时结合旋转式惯导系统的工程应用特性,得到12阶卡尔曼滤波参数模型。降阶系统阶数降低约55%,可以显著降低运算量,有效提高了导航计算机运算效率和实时性。仿真实验表明：降阶模型的估计精度不低于原模型,而且部分状态量的滤波收敛速度有提高。     

Detecting Instrument Malfunctions in Control Systems

A scheme for automatically detecting incipient failures in the feedback sensors (or instruments) of control systems is described. The feasibility of the scheme is investigated by applying it to a simplified version (fourth order) of the flight control system for a hydrofoil boat. A single set of inertial instruments is used to provide the feedback signals; the redundancy which is normally obtained by multiple instrument sets is obtained here, artificially, by a subsystem of multiple Luenberger observers and logic circuits. Tests indicate that scale factor errors, errors due to threshold effects, and bias errors in the instruments are detected as they occur. The tests also indicate further analytical work which should be done to explore the limitations of the basic scheme.     

Characterization of Kalman filter residuals in the presence ofmismodeling

The mean and covariance of a Kalman filter residual are computed for specific cases in which the Kalman filter model differs from a linear model that accurately represents the true system (the truth model). Multiple model adaptive estimation (MMAE) uses a bank of Kalman filters, each with a different internal model, and a hypothesis testing algorithm that uses the residuals from this bank of Kalman filters to estimate the true system model. At most, only one Kalman filter model will exactly match the truth model and will produce a residual whose mean and standard deviation have already been analyzed. All of the other filters use internal models that mismodel the true system. We compute the effects of a mismodeled input matrix, output matrix, and state transition matrix on these residuals. The computed mean and covariance are compared with simulation results of flight control failures that correspond to mismodeled input matrices and output matrices     

Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors

We are concerned with obtaining bounds on the performance of Kalman-type, linear, continuous-time filters susceptible to modeling errors. Limiting the discussion to stationary performance, we obtain bounds on the performance index, the mean square error of estimates for suboptimal and optimal (Kalman) filters. The bounds are expressed in terms of the model matrices and the range of errors of the matrices. The results are useful to a designer in comparing the performance of a suboptimal filter with that of the optimal filter when he has information on the range of modeling errors. The tightness of the bounds is shown by an application of the results in the estimation of the motion of an aircraft carrier at sea.     

临近空间高超声速跳跃滑翔式目标自适应跟踪模型

针对临近空间高超声速跳跃式滑翔目标跟踪问题,在将加速度建模为具有正弦波（SW）自相关随机过程的基础上,提出一种自适应非零均值正弦波相关（ANM-SW）模型。其核心是对正弦波相关模型进行均值补偿构建ANM-SW模型,并推导了模型状态方程;为深入分析均值补偿的作用,分别从时域和频域的角度探讨了自适应非零均值模型的物理本质;此外,为进一步说明模型的适应性问题,结合Kalman滤波推导了SW及ANM-SW模型状态更新的系统动态误差,验证了ANM-SW模型在机动适应方面的优越性;最终仿真表明与SW模型相比,ANM-SW模型在跟踪精度及机动适应能力方面具有一定的优势性。