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.     

Inertial navigation system synthesis approach and gravity-inducederror sensitivity

A design criterion for improving the performance of the speed-damped inertial navigation system is presented. The single-axis speed-damped system is approached by optimizing the response of the system to a step-function disturbing signal. Butterworth, integral of time-multiplied absolute-value of error (ITAE), and solution-time standard forms are assumed to be the figures of merit for optimizing the system performance. The steady-state RMS (root-mean-square) gravity-induced navigation errors that are excited in the speed-damped system are determined for two gravity uncertainty models. The proposed figures of merit are compared. These comparisons reveal the sensitivity of predicted navigation errors to uncertainties in the gravity statistics, and simplify the choice of a suitable figure of merit for use in the design and error analysis of inertial navigation systems     

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.     

Ground Testing of Inertial Navigators to Improve Dynamic Performance

A ground testing method has been devised to evaluate the dynamic errors of an inertial navigation system. A trimmed stationary inertial system in the navigation mode can be subjected to programmed platform orm drift rates, and generate position outputs which are compared with those of a perfect navigator. The linearized error equations for this testing mode are derived and the resulting position error propagation is analyzed using Kalman filtering in order to identify the error sources. A simulated platform with a fixed set of error sources is analyzed to evaluate this testing concept. An example is presented to show that the gyro and accelerometer scale factor and misalignment error coefficients can be estimated.     

Effects of Geodetic Uncertainties on a Damped Inertial Navigation System

Gravity uncertainties are an inexorable source of error in all inertial navigation systems and are particularly important in high-quality inertial navigation systems. In this paper the steady-state rms errors that are excited in a damped inertial navigation system are analytically determined for four gravity uncertainty models and two vehicle maneuver models. The statistical approach used in this paper is compared with an alternate scheme (?direct simulation?) that does not require statistical models for gravity uncertainties.     

双轴旋转式激光捷联惯导系统的转位方案研究

惯性导航系统的误差随时间累积,旋转调制技术可以有效地提高惯导系统的长航时精度,旋转调制方案是决定旋转式捷联惯导系统导航精度的一个重要因素.针对双轴旋转惯导系统,相较于16次序转位方案,提出了一种新的32次序双轴旋转调制方案.根据捷联惯导系统的误差方程,推导出旋转捷联惯导的误差方程,分析了误差补偿的机理,研究了惯性器件常值偏置误差、标度因数误差和安装角误差的传播特性.仿真结果表明,32次序双轴旋转调制方案相对于16次序转位方案有明显的优势,可以有效地降低姿态角误差和经纬度误差.     

纬度未知条件下捷联惯导系统晃动基座的初始对准

针对纬度未知条件下捷联惯导系统(SINS)晃动基座的初始对准问题,提出晃动基座下的纬度估计算法和初始对准方法。前者通过惯性坐标系下两个不同时刻的重力加速度向量的夹角来求取纬度;后者利用惯性坐标系下的姿态更新来实时地反映载体在晃动干扰下的姿态变化,结合初始姿态的最优估计实现初始对准。理论分析表明,本文提出的纬度估计算法的误差主要由加速度计误差决定,陀螺误差和晃动干扰对其影响很小。仿真结果表明,本文提出的纬度估计算法和初始对准方法适用于纬度未知条件下晃动基座的初始对准。     

弹道导弹天文/惯性导航误差修正方法研究

通过分析导弹天文导航和惯性导航的导航原理和误差模型,在基于充分利用高精度天文导航参数的思想上,提出了组合导航的误差修正方法。首先对两种导航参数进行了归算,而后提出了利用多次的天文测量参数对惯性测量误差进行修正的方法。该方法能较为准确地分离出引起射程误差较大的关机点速度、位置等的误差值,从而为实现利用天文导航进行射程误差修正提供前提条件。仿真计算表明,该方法是行之有效的。     

Advanced Development of ESG Strapdown Navigation Systems

The fundamental problem of inertial navigation, double integration of acceleration to obtain position, is defined and discussed. Mechanizations of both space-stable and local-vertical platform systems are exhibited. The synthesis problem for an electrically suspended gyro (ESG) strapdown system is defined and discussed: readout, readout errors due to vehicle motion, synchronization of readout with system computer, alignment, correction and calibration for mass unbalance drift, and digital mechanization. Alignment, calibration, and acceleration measurement are also discussed. Sources of error involved in the electronic gimbaling including those peculiar to strapdown configuration are discussed and compared to mechanically gimbaled systems. Advanced developments required in the component and systems areas are listed, and it is shown that such development will lead to reduced complexity, higher accuracy, and increased reliability and utility for inertial systems.     

高分影像辅助下的航空高光谱严密几何检校方法

 惯性测量单元(IMU)与传感器视准轴的偏心角和偏心矢量是造成航空线阵列高光谱数据几何校正误差的主要原因之一。在分析偏心角与偏心矢量误差来源之后提出该误差由IMU主轴与传感器主轴的角度偏差、测区固定偏差、GPS中心与传感器投影中心相对偏差组成,在此基础上建立了较为严密的检校模型。针对模型解算时需要大量高精度控制点的问题,提出了一种高分影像辅助下的亚像元精度控制点自动提取方法。通过多地区、多传感器高光谱航测实验表明,亚像元精度控制点能有效提高模型解算精度。新检校模型可获得亚像元校正精度,推扫式传感器——应用型机载成像光谱仪(AISA)建模中误差约为0.39个像元,摆扫式传感器——实用型模块化成像光谱仪(OMIS)建模中误差约为0.23个像元,校正后的影像可直接进行拼接。     

Feedback Realization of a Continuous-Time Optimal Filter

Another derivation of a continuous-time optimal linear filter is presented. Using this result as a point of departure, a feedback version of this continuous filter is postulated and shown to be optimal in the limit as the ``feedback gain' becomes infinite. It is then demonstrated that the need for this infinite feedback gain can frequently be eliminated. This feedback realization of the continuous optimal filter has application to the problem of optimally mixing two or more redundant signals, each contaminated by random noise. The feedback configuration has the advantages of simplicity and the bounding of otherwise troublesome very large errors. A simple example is given of the mixing of two (velocity) references each having exponentially correlated error.     

基于改进容积卡尔曼滤波的惯性/光流组合自主测速方法

针对容积卡尔曼滤波算法在惯性/光流组合测速数据融合时出现由于各系统输出数据频率不一致导致融合精度有限的问题,提出了一种基于多速率残差校正的改进容积卡尔曼滤波算法.通过当前时刻误差估算组合导航系统残差,再使用估算后的残差对速度估计值进行补偿,最终实现惯性/光流组合系统速度测量值的数据融合.实验结果表明,通过提出的改进容积...     

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     

Error estimation of INS ground alignment through observabilityanalysis

A systematic analysis of the observability of an inertial navigation system (INS) in ground alignment with Bar-Itzhack and Berman's error model is presented. It is shown that the unobservable states are separately contained in two decoupled subspaces. The constraints on the selection of unobservable states are discussed. An estimation algorithm which is derived fully from the horizontal velocity outputs for computing the misalignment angles is provided. It reveals that the azimuth error can be entirely estimated from the estimates of leveling error and leveling error rate, without using gyro output signals explicitly     

基于相对导航的多平台INS误差联合修正方法

在机群协同编队飞行中,编队成员仅装载惯性导航系统(INS)的方式具有隐蔽、抗干扰等明显的优势,但随着航时的增加,INS误差将不断累积.使导航系统失效,为此,提出基于相对导航的多平台INS误差联合修正方法.首先,建立了编队成员相对导航运动模型及非线性观测模型,采用量测重构技术构造了伪线性观测模型并推导了观测噪声协方差矩阵...     

Model-based robust estimation and fault detection for MEMS-INS/GPS integrated navigation systems

In micro-electro-mechanical system based inertial navigation system（MEMS-INS）/global position system（GPS） integrated navigation systems, there exist unknown disturbances and abnormal measurements. In order to obtain high estimation accuracy and enhance detection sensitivity to faults in measurements, this paper deals with the problem of model-based robust estimation（RE） and fault detection（FD）. A filter gain matrix and a post-filter are designed to obtain a RE and FD algorithm with current measurements, which is different from most of the existing priori filters using measurements in one-step delay. With the designed filter gain matrix, the H-infinity norm of the transfer function from noise inputs to estimation error outputs is limited within a certain range; with the designed post-filter, the residual signal is robust to disturbances but sensitive to faults. Therefore, the algorithm can guarantee small estimation errors in the presence of disturbances and have high sensitivity to faults. The proposed method is evaluated in an integrated navigation system, and the simulation results show that it is more effective in position estimation and fault signal detection than priori RE and FD algorithms.     

Kalman filter mechanization for INS airstart

A strapdown mechanization and associated Kalman filter are developed to provide both ground align and airstart capabilities for inertial navigation systems (INSs) using Doppler velocity and position fixes, while not requiring an initial heading estimate. Position update during coarse mode is possible by defining sine and cosine of wander angle as filter states and modeling the position error in geographic frame while integrating velocity in the wander frame. INS Global Positioning System (GPS) differential position due to GPS antenna moment arm can aid heading convergence during hover turns in helicopter applications. Azimuth error state in the fine mode of the filter is defined as wander angle error to provide continuous estimation of navigational states, as well as inertial/aiding sensor errors, across the coarse-to-fine mode transition. Though motivated by a tactical helicopter application, the design can be applied to other vehicles. Advantages over conventional systems in addition to the airstart capability include robustness and versatility in handling many different operational conditions     

Strapdown inertial measurement units for motion compensation forsynthetic aperture radars

It is shown that synthetic-aperture radar (SAR) motion can be compensated by using an antenna-mounted strapdown inertial measurement unit (IMU) as the motion sensing system, but sensor and system errors affect SAR image quality. A strapdown IMU consists of three accelerator channels and three gyro channels. Strapdown IMU errors include gyro-scale and accelerometer-scale factor and bias errors, velocity error, platform tilt, and errors induced by limited inertial sensor bandwidth. The effects of these errors on the SAR image quality are presented in terms of the SAR impulse response. IMU errors that cause low-frequency phase errors (less than one cycle per array time) are categorized in terms of quadratic and cubic phase errors. IMU errors that cause high-frequency phase errors (greater than one cycle per array time) are categorized in terms of the integrated sidelobe ratio and peak sidelobe ratio. A motion compensation system conceptualization is described wherein a strapdown IMU is attached to an antenna and transfer-aligns to the aircraft's master navigator     

Statistically Linearized Estimation of Reentry Trajectories

Several filters are applied to the problem of state estimation from inertial measurements of reentry drag. This is a highly nonlinear problem of practical significance. It is found that a filter based on the technique of statistical linearization performs better than the extended Kalman in this application. This is believed to be the first application of the statistically linearized filter to a practical dynamics problem. A sensitivity analysis is performed to demonstrate the relative insensitivity of this filter to modeling errors and approximations.     

一种基于逆向导航的双轴旋转惯导系统自标定方法

针对惯导系统高精度自标定的需求,提出了一种基于逆向导航的双轴旋转惯导系统自标定方法。通过转位运动对系统误差进行激励,利用Kalman滤波器进行误差估计,同时存储标定数据,待正向导航滤波结束后,利用逆向导航算法对存储数据二次利用,继续进行误差估计,直到所有状态量收敛到一定精度,实现了对数据的充分挖掘。仿真和试验结果表明,该方法可以实现对双轴旋转惯导系统的全参数自标定,提高了标定精度。