集成导航系统中的应用数学原理与Kalman滤波

5星 · 超过95%的资源需积分: 9 58 浏览量更新于2024-07-27 4 收藏 8.09MB PDF 举报

身份认证购VIP最低享 7 折!

30元优惠券

"Applied Mathematics in Integrated Navigation Systems" 是一本专注于集成导航系统中应用数学的书籍，主要面向参与导航系统设计、整合以及测试与评估的专业人士。该书假设读者具有包括微积分在内的数学背景。集成导航系统是将机载导航解决方案（位置、速度和姿态）与独立导航数据（导航辅助）相结合，以更新或校正导航解决方案的技术。书中通过卡尔曼滤波算法来实现这种结合。本书分为两大部分。第一部分涵盖了基础数学、运动学、描述导航系统/传感器的方程及其误差模型、导航辅助和卡尔曼滤波的基础知识。书中提供了详尽的推导过程和实例，以帮助理解集成导航系统的这些元素，并包含问题以扩展所呈现材料的应用。第三版增加了更多背景资料、练习和软件。新增内容包括：地球引力势的通用形式及其简化到椭球模型的开发；卫星轨道方程的建立，以及非球形地球重力对卫星轨道参数的影响；无导数卡尔曼滤波器的发展，包括无味卡尔曼滤波和分差滤波的形式。此外，还添加了更多的练习，以补充和扩展文本中的内容，展示卡尔曼滤波的特性。本版还包含了用于模拟随机过程和无导数滤波器实现的附加软件，为处理集成导航系统的不同方面提供了更全面的基础。作者 Robert M. Rogers 在第二版中进一步深化了对集成导航系统各个方面的探讨，使得这本书成为理解和应用这一领域复杂数学原理的重要参考资料。书中涵盖的全球定位系统、卡尔曼滤波等技术在航空航天领域尤其关键，对于理解如何在实际操作中结合数学方法进行导航系统的精确控制和误差修正至关重要。 "Applied Mathematics in Integrated Navigation Systems" 是一个深入学习和实践导航系统集成的宝贵资源，不仅提供理论知识，还包括实践示例和软件工具，有助于读者深化理解并提升在这一领域的专业技能。无论是对于工程师、研究人员还是学生，这本书都提供了丰富的学习材料，以应对现代导航系统设计和实施中的挑战。

资源详情

资源推荐

In Chapter

Kalman filtering equations are developed based on a recursive

weighted least-squares approach. The Kalman filter algorithm is used to estimate

navigation system errors by combining information available from the aids to

navigation with navigation solution system data to obtain an optimal estimate of

the navigation system's errors. Various forms of the Kalman filter algorithm are

presented, including the conventional, Joseph's, and

U-D

factored forms. Kalman

filtering techniques are extended to include modifications to the algorithm for

including summed measurements and combining outputs of several independent

parallel filters to form a single optimal estimate.

Part

Applications

Presented in the second part are case studies illustrating the application of the

elements in Part

to integrated navigation systems.

In Chapter

the first of these case studies addresses the inertial na\ igation sen-

sors' laboratory or factory calibration. In this case study, navigation error dynamic

equations are treated as algebraic equations and a tracking model implemented in

a Kalman filter is used to reconstruct higher derivative errors. With these higher

derivatives available, the fixed sensor errors are estimated from a series of rotations

of an

accelerometerlgyro cluster assembly. Results are presented from simulated

inertial sensor data, allowing a direct evaluation of calibration accuracies.

Trajectory reconstruction is used during flight test and evaluation of inertial

navigation systems to provide an improved source of independent navigation state

data by which to gauge the performance of the navigation system under test. Three

trajectory reconstruction approaches are presented in Chapter

10.

least-squares

technique using ground-based, line-of-sight tracking; a Kalman filter implementa-

tion using an

onboard inertial navigation system aided with TACAN ranging; and

a Kalman filter modeling a sounding rocket's dynamics integrated

with ground-

based radar track data are presented. Data from actual flight tests are used to

illustrate the results obtained from these approaches.

Autonomous inertial navigation system ground alignment is illustrated in Chap-

ter

11.

Initial coarse alignment based on accelerometer and gyro sensor outputs

is presented, with a characterization of the relationship between sensor error and

the resulting alignment accuracy. An illustration of a final fine alignment using

Kalman filtering is also presented. Simulated data are used to illustrate the accu-

racy of alignments achieved.

In Chapter

12,

an operational GPS receiver unit integrated with an inertial nav-

igation unit is the first integrated navigation system case study. In this case study,

the GPS receiver's internal Kalman filter is used to estimate errors associated with

the navigation state data being provided to the unit. The GPS receiver and inertial

navigation unit are loosely coupled. The Kalman filter implementation used by

the GPS receiver is less complete in that it does not incorporate inertial sensor

error states within its state vector. Outputs from the receiver's Kalman filter are

combined with the inertial navigation unit's uncorrected outputs to form an op-

timal estimate of position, velocity, etc. Simulated data are used to illustrate the

accuracy of the receiver's Kalman filter estimates.

In-motion alignment of an inertial measurement unit is presented in Chapter

13.

This case study, which also includes establishing navigation solution algorithms,

is presented for two major subcases. The first is a conventional transfer alignment

with attitude initialization provided by another inertial navigation system. This

application

pennits the use of a small attitude error model implementation in the

alignment Kalman filter. The second

subcase is

alignment without initial atti-

tudes. This application requires a reformulation of the error model to accommodate

large attitude errors. Both approaches are illustrated using results obtained with

actual recorded flight test data.

The next case study is for a differential GPS- (DGPS) aided dead-reckoning

(DR) land navigation system and is presented in Chapter 14. In this case study,

higher rate navigation data, as required by an autonomous vehicle for real-time

steering and control, are provided at a comparable level of accuracy as available

from the lower-rate DGPS position outputs. The DR navigation solution is formed

using outputs from a single-axis gyro

and a Doppler radar ground speed sensor.

In this case study, test data from an actual real-time implementation are used to

illustrate the benefits and performance available from this integration.

In Chapter 15, attitude determination and estimation case studies are presented.

These case studies address navigation problems, like those of the previous chapter,

that use less than a complete suite of accelerometer and gyro sensors. The prob-

lem of attitude determination involves determining a transformation matrix that

transforms known information from one reference frame to another. This problem

has applications in both terrestrial and spacecraft navigation. Attitude estimation

continues with the integration of a navigation solution, in this case only attitude,

with other sensor data via a Kalman filter. Examples of these two applications are

presented.

Summarized in Chapter

are several design options available for an integrated

navigation system based on one of many possible navigation frame implementa-

tions. These options illustrate various navigation system error models discussed

and developed in this book that are candidates for implementation in a Kalman

filter algorithm. Mathematical methods presented provide the reader, whether in-

volved in design, integration, or test and evaluation, the tools to establish a new

integrated navigation system or evaluate an existing one.

While treating specific subjects, notation is used that is consistent with publica-

tions relating to those subjects. However, because a variety of subjects are covered,

the same notational variables assume different meanings in various parts of the

book. The reader is cautioned not to assume that the symbology

one subject

area has the same meaning in another. Finally,

practical aspect of presenting

the variety of material limits the depth to which each area can be developed. The

reader is encouraged to investigate those areas that are only summarized to the

level necessary to understand their application in an integrated navigation system.

Robert

Rogers

August

2003

Introduction

Navigation systems are used for land, sea, airborne, and space vehicles. These

systems provide an operator

and/or control system with the necessary information

to effect some action in response to data provided by these systems. For example,

this action can be a course correction indication for an aircraft pilot or a feedback

control signal to guide an autonomous vehicle. These systems incorporate

onboard

sensors coupled with a computer, permitting self-contained operations with little

or no assistance required from sources external to the vehicle.

The core of the navigation system is a set of sensors combined with a computer

that can provide a relatively stable and accurate source of navigation. These sys-

tems output navigation state data, which usually include position, velocity, and

attitude. As a result of imperfections in navigation sensors and computational

errors, errors develop in the navigation state data and grow in time. Tht: host vehi-

cle's operating environment also influences the error growth rate. Long-term error

growth is minimized by including other sensors that provide independent redun-

dant navigation data,

i.e., position, in an integrated system that optimally combines

this independent data source with the core navigation system. These independent

sensors, referred to as navigation aids, are characterized by long-term

error stabil-

ity, which can compliment the short-term error stability of the navigation system's

sensors. When combined within a computer algorithm, such as a Kalman filter,

errors from both the core sensors and navigation aids can be estimated to reduce the

integrated navigation system's errors. The resulting navigation system will exhibit

improved performance, even if independent data are used intermittently or are not

available for a short timespan.

The majority of this book addresses navigation systems that are

mechanized

with accelerometer and gyro inertial sensors. These inertial sensors provide sensed

accelerations (velocity changes over a time interval) and rates (attitude changes

over a time interval). Accelerometers and gyros are mounted in orthogonal triad

clusters and enclosed within an inertial measurement unit (IMU) to provide three

components of acceleration and rate outputs. These outputs are provided to a

computer-implemented numerical integration process that computes a navigation

solution yielding a complete set of navigation state data,

i.e., position, velocity,

and attitude. These mechanizations are generally referred to as an inertial naviga-

tion unit when enclosed within a case that can be easily removed and replaced.

Implementations that include the inertial sensors, computer, and navigation aids

are referred to as an inertial navigation system (INS).

Other navigation systems that use fewer than the full three-axis accelerometer

and gyro sensors are presented. These systems include a Dead-Reckoning system

and attitude reference systems. The Dead-Reckoning system uses speed (distance

traveled) and heading sensors to compute a dead-reckoning navigation solution.

This solution is less complete and generally provides only position and heading

剩余350页未读，继续阅读

opp77

粉丝: 4
资源: 19

集成导航系统中的应用数学原理与Kalman滤波

applied mathematics in integrated navigation systems

the princeton companion to applied mathematics pdf

基于merton跳扩散模型的实证研究最新文献

the beauty of mathematics in computer science pdf

ct重建算法的文献推荐

圈养湖羊的空间利用率数学建模

写一遍关于数学的英文学术期刊

annals of mathematics怎么样？

The Mathematics of Computerized Tomography

影响力大的数学建模网站有哪些？常见的赛题类型有哪些

{ }_{t_{0}}^{C} D_{t}^{\alpha} V(x(t)) \leq-\mu V^{\gamma}(x(t)) \quad \forall \alpha \in(0,1)，帮我找10篇用到上述式子分析分数阶系统有限时间稳定的文献

Assets\MegaFiers\Scripts\MegaFiers\Modifiers\MegaConformMod.cs(5,13): error CS0234: The type or namespace name 'Mathematics' does not exist in the namespace 'Unity' (are you missing an assembly reference?)

能推荐几篇遗传算法优化的文献吗

mathematics 下载 csdn

properties MATLAB

驾校管理系统今年英文文献

what if Multivariate Polynomial Ring has been created

Fractal structure

OpenGL Mathematics

【CSS Tricks】像素风字体、图片

最新资源