轻松掌握卡尔曼滤波追踪：《Tracking and Kalman Filtering Made Easy》简介

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"《追踪与卡尔曼滤波轻松入门》（Tracking and Kalman Filtering Made Easy）是一本由Eli Brookner编著的专业书籍，专注于介绍卡尔曼滤波这一核心的信号处理和估计技术。卡尔曼滤波是信息技术领域中的重要工具，尤其在导航、控制系统、机器学习和传感器数据分析中发挥着关键作用。该书旨在以易于理解的方式阐述复杂的技术概念，使得非专业人士也能掌握其基本原理。书中详细探讨了卡尔曼滤波器的设计、理论基础以及实际应用，包括线性系统建模、状态更新、观测更新、预测和估计等核心步骤。作者以其丰富的咨询科学家经验，通过实例和案例研究，帮助读者深入理解滤波器如何处理噪声、动态环境下的数据融合以及如何在不断变化的信息中做出最优估计。《追踪与卡尔曼滤波轻松入门》特别适合对跟踪技术感兴趣的工程师、研究人员和学生阅读，无论是希望提升现有技术能力，还是初次接触这个领域的人员，都能从中获益匪浅。同时，由于版权保护，未经许可，读者必须遵守1976年美国版权法的规定，不可进行任何形式的复制或传播，除非符合法规的合理使用条款。这本书作为一项宝贵的资源，不仅提供了理论知识，还为实践者提供了实用的指导，使其能够更有效地应用卡尔曼滤波技术解决实际问题，推动科技发展。对于从事IT行业的专业人士来说，理解和掌握卡尔曼滤波是提升竞争力和创新力的重要一步。"

processing orthonormal transformation methods to the DOLP approach used in

Section 5.3 for obtaining a polynomial ﬁt to data. The two methods are shown

to be essentially identical. The square-root Kalman ﬁlter, which is less sensitive

to round-off errors, is discussed in Section 14.5.

Up until now the deterministic part of the target model was assumed to be

time invariant. For example, if a polynomial ﬁt of degree m was used for the

target dynamics, the coefﬁcients of this polynomial ﬁt are constant with time.

Chapter 15 treats the case of time-varying target dynamics.

The Kalman and Bayes ﬁlters developed up until now depend on the

observation scheme being linear. This is not always the situation. For example,

if we are measuring the target range R and azimuth angle  but keep track of the

target using the east-north x, y coordinates of the target with a Kalman ﬁlter,

then errors in the measurement of R and  are not linearly related to the

resulting error in x and y because

x ¼ R cos  ð1Þ

and

y ¼ R sin  ð2Þ

where  is the target angle measured relative to the x axis. Section 16.2 shows

how to simply handle this situation. Basically what is done is to linearize

Eqs. (1) and (2) by using the ﬁrst terms of a Taylor expansion of the inverse

equations to (1) and (2) which are

R ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ y

ð3Þ

 ¼ tan

ð4Þ

Similarly the equations of motion have to be linear to apply the Kalman–

Bayes ﬁlters. Section 16.3 describes how a nonlinear equation of motion can be

linearized, again by using the ﬁrst term of a Taylor expansion of the nonlinear

equations of motion. The important example of linearization of the nonlinear

observation equations obtained when observing a target in spherical coordinates

(R, , ) while tracking it in rectangular (x, y, z) coordinates is given. The

example of the linearization of the nonlinear target dynamics equations

obtained when tracking a projectile in the atmosphere is detailed. Atmospheric

drag on the projectile is factored in.

In Chapter 17 the technique for linearizing the nonlinear observation

equations and dynamics target equations in order to apply the recursive Kalman

and Bayes ﬁlters is detailed. The application of these linearizations to a

nonlinear problem in order to handle the Kalman ﬁlter is called the extended

Kalman ﬁlter. It is also the ﬁlter Swerling originally developed (without the

xviii PREFACE

ACKNOWLEDGMENT

I would like to thank Fred Daum (Raytheon Company), who ﬁrst educated me

on the Kalman ﬁlter and encouraged me throughout this endeavor. I also would

like to thank Erwin Taenzer (formally of the Raytheon Company), from whose

many memos on the g–k and g–h–k ﬁlters I ﬁrst learned about these ﬁlters. I am

indebted to Barbara Rolinski (formerly of the Raytheon Company), who helped

give birth to this book by typing a good part of its ﬁrst draft, including its many

complicated equations. This she did with great enthusiasm and professionalism.

She would have ﬁnished it were it not that she had to leave to give birth to her

second child. I would also like to thank Barbara Rolinski for educating her

replacement on the typing of the text with its complicated equations using the

VAX Mass-11 Word Processor. I would like to thank Lisa Cirillo (formerly of

the Raytheon Company), Barbara Rolinski’s ﬁrst replacement, for typing the

remainder of the ﬁrst draft of the book. I am most appreciative of the help of

Richard P. Arcand, Jr. (Raytheon Company), who helped Barbara Rolinski and

Lisa Cirillo on difﬁcult points relative to the use of the VAX Mass-11 for typing

the manuscript and for educating Ann Marie Quinn (Raytheon Company) on the

use of the Mass-11 Word Processor. Richard Arcand, Jr. also meticulously made

the second-draft corrections for the ﬁrst part of the book. I am most grateful to

Ann Marie Quinn for retyping some of the sections of the book and making the

legion of corrections for the many successive drafts of the book. Thanks are also

due the Ofﬁce Automation Services (Raytheon Company) for helping to type

the second draft of the second part of the book. Sheryl Evans (Raytheon

Company) prepared many of the ﬁgures and tables for the book and for that I

am grateful. I am grateful to Richard Arcand, Jr. for converting the text to

Microsoft Word on the MAC. I am extremely grateful to Joanne Roche, who

completed the horrendous task of retyping the equations into Microsoft Word

xxi

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