Comparison of Error Propagation in Local-Level and Space-Stable Inertial Systems

A comparison of the error propagation in a local-level reference frame is derived for two inertial navigation systems; one has a local-level configuration, and the other has a space-stable configuration. The error propagation is shown to be equivalent for the two cases considered. This equivalence is demonstrated by starting with the error propagation equations for the space-stable system and transforming them to a local-level reference frame. The transformed equations are then compared with the classical local-level error equations, and the equivalence is noted. The specific implementation used in each case considers velocity damping but not altitude damping.     

Altitude Damping of Space-Stable Inertial Navigation Systems

In order to stabilize the altitude calculation in an inertial navigation system, an altimeter is commonly used. In a conventional local-level mechanization, this is generally accomplished by correcting the vertical channel integrators with the difference between the inertial system and altimeter indication of vertical position. However, in a space-stable system the procedure is not as clear since a vertical channel is not physically present. Three altitude damping mechanizations for a space-stable inertial navigation system are proposed. The equivalent local-level mechanizations are then found by comparing error propagation equations in a common coordinate frame.     

Kalman Filter Design Considerations for Space-Stable Inertial Navigation Systems

Terrestrial inertial navigation is typically performed using an instrumented platform stabilized in a ?local-level? configuration for convenient generation of geographic navigation information. The local-level geographic reference must be maintained by torquing the system gyros, a requirement which may be incompatible with high-precision inertial sensors currently under development. Gyro torquing in a gimballed navigation system can be avoided by employing a ?space-stable? mechanization of the platform where an inertial, rather than geographic, reference is used for navigation calculations. The software design problems associated with this concept, especially those related to the application of Kalman filtering, are the principle focus of this paper. Although the space-stable configuration has been used extensively for spacecraft navigation and guidance, it has not been widely applied to terrestrial navigation, either for air or marine applications. The chief problem in this application is to perform navigation in local-level coordinates, using system outputs generated in an inertial reference frame. It can be demonstrated that, although the navigation system error dynamics are identical for the local-level and space-stable configurations, the dynamics of the sensor errors which drive these systems are quite different. These differences in sensor error propagation characteristics impose new requirements for the design of procedures to accomplish system calibration, alignment, and reset. This paper outlines a Kalman filtering approach which is applicable to all of the above procedures, and presents numerical results to demonstrate its effectiveness.     

Doppler Radar Error Equations for Damped Inertial Navigation System Analysis

The use of Doppler radar measurements to provide velocity damping for an aircraft inertial navigation system is considered. Three different Doppler antenna configurations are examined: two-axis stabilized, azimuth stabilized, and data stabilized antennas. A general reference velocity error equation is presented and appropriately evaluated for each of the Doppler configurations. Specific elements of the error equations are examined and physically interpreted for both local-level and space-stable inertial systems. Detailed examination of the interaction of Doppler radar and inertial navigation velocity error mechanisms is provided.     

A Comparison of Two Approaches to Pure-Inertial and Doppler-Inertial Error Analysis

Error equations for inertial navigation systems are derived using a perturbation (or true frame) approach and a psi angle (or computer frame) approach in a manner which shows the underlying as sumptions and allows direct comparison of the two methods. The comparison is general since the analysis is not associated with any particular mechanization. Different definitions of velocity errors and misalignment angles result from the two methods of error analysis, and, consequently, have significance in testing and analysis of pure-inertial systems, Doppler-inertial systems, and inertially aided weapon delivery systems. Examples and numerical results are presented for a local-level north-pointing mechanization.     

Modeling quaternion errors in SDINS: computer frame approach

We propose new equivalent tilt error models which are applicable to the analysis of the terrestrial strapdown inertial navigation systems (SDINS), based on the quaternions. The currently available equivalent tilt error models, like the conventional Φ model of the gimbaled inertial navigation systems (GINS), are derived only by the true frame approach. The true frame approach has a computational disadvantage that it produces an error model where the attitude error equation is coupled with its position and velocity error equations. The motivation of this work is to solve this problem. As a result, two kinds of error models are derived. Among them, one is derived by the computer frame approach for practical onboard implementations. Thus, like the conventional GINS Ψ model, its attitude error equation is decoupled from the position and velocity error equations. The other is derived in order to show the relationship between the true frame approach and the computer frame approach which are applied to the quaternion-based SDINS. Thus, like the GINS δΘ model, it can be used to transform the error variables into each other which are calculated by the two different approaches     

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.     

视觉辅助惯性定位定姿技术研究

在利用视觉系统辅助捷联惯性导航系统( SINS)进行定位定姿时,由于两者输出的位置表示方法不同,在信息融合时会存在匹配问题。以相对地理坐标系作为定位定姿系统的导航坐标系,重新对SINS进行了力学编排,分析了其误差传递特性,建立了相对地理坐标系下的状态方程模型,并利用Kalman滤波器实现了视觉辅助惯性定位定姿算法。仿真结果表明,方法避免了信息融合时位置匹配问题,同时降低了系统的计算量,满足了定位定姿系统的精度要求。     

Spectral Analysis of Optimal and Suboptimal Gyro Monitoring Filters

Gyro monitoring filters are used to estimate and correct gyro drift rates of local-level inertial navigation systems. Conventional gyro monitoring filters are usually designed based on a simplified model of gyro drift rate. Furthermore, the effectiveness of these filters-and of many filters of the "Kalman" type-is often measured in terms of the root mean square (rms) criterion in contrast to the spectral content criterion typical of classical Wiener filtering theory. This paper has two objectives: to propose a gyro monitoring filter which is based on a more detailed model of gyro drift rate; and to propose a method of filter performance evaluation which uses as criterion a measure of the spectral content of the error process. The proposed gyro monitoring filter is shown to have improved spectral contents resulting in superior navigation performance for the gyro error models used in the calculations (comparable to commercial-grade aircraft gyros).     

Strapdown INS error model for multiposition alignment

The relationship between quaternion errors and tilt angles from true navigation frame to analytic platform frame is newly derived for strapdown inertial navigation system (SDINS). Using the relationship it is shown that the quaternion error model for attitude and velocity is equivalent to the conventional perturbation error model. Based upon the equivalency, the quaternion errors during a multiposition alignment are determined and analyzed. Furthermore, it is shown that the heading rotation of 180 deg achieves the minimal quaternion error for 2-position ground alignment     

基于对偶四元数的INS/GPS组合导航算法研究

在基于对偶四元数的捷联惯导解算方法的基础上,推导了以惯性系作为导航系的惯导误差方程,在此基础上设计了卡尔曼滤波组合导航算法。通过激光惯导跑车采集数据,进行了仿真分析,试验结果表明,该组合导航算法能有效的消除惯导累积的速度误差和位置误差,相比于目前广泛应用的INS/GPS组合导航算法,本文描述了INS/GPS组合导航的另一种实现方式,获得了相当的精度,具有一定的工程应用价值。     

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.     

Inertial System Platform Rotation

Differential error equations are derived for the navigation errors of a local level undamped pure inertial platform that continuously rotates in azimuth. From these, the time response equations for the vector position error produced by a constant level gyro drift error, as a function of platform rotation rate, are computed and evaluated. It is shown that platform rotation attenuates the system position error due to level gyro bias and that this attenuation is a nonlinear function of rotation rate.     

平台式惯性测量系统车载试验设计

根据平台式惯性测量系统的实际情况,简化了惯性测量误差模型,推导了平台式惯性测量系统误差观测方程,并进行了车栽试验的试验设计.在输入设计中,通过仿真分析给出了降低系统复共线性的几个条件.在输出设计中,选定了系统的测量量,确定了传感器的类型及安装方式.     

Analysis Strapdown Navigation Using Quaternions

A brief review of the theory of strapdown inertial navigation is presented in which the attitude of the sensor box with respect to inertial space is represented by the four-parameter quaternion vector. . A 4X4 matrix R is defined which aids in relating quaternions to direction cosines and facilitates interpretation of the equations for error propagation, which are also derived. In the interpretation, it is shown that the error in the quaternion vector causes aor-(correctable) scale factor error and an equivalent tilt vector error that propagates the same way as the platform tilt vector in a gimbaled system.     

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     

旋转调制式惯性平台的圆锥运动误差

转调制式空间稳定平台采用陀螺壳体翻滚技术,陀螺壳体翻滚在平台伺服跟踪作用下将形成圆锥运动。圆锥运动误差会引起陀螺漂移,对高精度、长航时惯性导航系统的精度将造成严重影响。首先,介绍了高精度、长航时旋转调制式惯性平台的基本工作原理,推导了平台上的陀螺沿旋转主轴相对地球的角速度。其次,阐述了陀螺壳体翻滚的圆锥运动,推导了壳体翻滚装置和框架伺服系统的跟踪误差及牵连运动角速度引起的圆锥运动附加漂移误差公式。再次,根据数值举例给出了计算机仿真曲线,指出该误差对高精度系统的危害。最后,得出结论：为了实现圆锥运动误差极小化,确保系统长时间运行精度和可靠性,必须实时扣除牵连运动角速度引起的圆锥运动误差分量,并优化设计壳体翻滚装置与平台伺服系统。     

大地测量误差对导弹精度的影响与修正

将导弹发射点的所有测量误差统一为标准发射坐标系与实际坐标系之间的平移和旋转,建立了这两种坐标系之间的变换关系,通过各坐标系内的制导方程,用小偏差法求出了落点偏差与发射点的坐标偏差,高程偏差,方位角偏差及垂线偏差之间的解析关系式,并按该计算模型,对典型远程导弹进行了计算。结果表明,该修正公式计算精度高,能用于导弹射前修正。     

基于视觉的惯性导航误差在线修正

陀螺零偏和加速度计零偏是影响惯性测量单元(IMU)积分精度的重要因素。提供一组精确的实时的零偏估计可以提高IMU的积分精度,为视觉导航提供良好的位姿预测,提高整个系统的动态性能。通过合理地建立IMU的噪声模型以及IMU和视觉的组合方程,利用一种基于李群和李代数知识的IMU预积分方法将零偏进行合理的线性化,运用Kalman滤波进行IMU零偏的在线估计。实验结果表明,通过本文的修正方法,惯性导航的平均积累误差由0.034m/s提高到0.0037m/s,精度明显提高。     

捷联惯性制导系统的圆锥误差及其补偿

圆锥误差是捷联惯导系统,特别是激光陀螺捷联惯导系统重要的误差源,为提高激光捷联惯性系统的导航精度,防止姿态误差的积累,本文研究了圆锥补偿算法和圆锥补偿误差特性,给出了常用的8种圆锥补偿算法,针对激光陀螺惯组的实际应用背景,开展了弹道仿真研究,给出了圆锥误差对激光陀螺捷联惯导系统导航精度的影响和补偿修正的效果。