《估计理论与跟踪导航应用》——巴尔沙拉姆经典著作

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"Estimation With Applications to Tracking and Navigation" 是由 Yaakov Bar-Shalom、X.-Rong Li 和 Thiagalingam Kirubarajan 合著的一本专业书籍，该书是 Wiley-Interscience 出版的一个出版物，专注于估计理论在跟踪与导航领域的应用。本书深入探讨了估计理论的基本概念及其在实际跟踪和导航系统中的应用。估计理论是信号处理、控制工程和数据科学中的关键部分，它涉及到从观测数据中提取未知参数或状态的过程。在跟踪领域，这可能涉及对移动目标（如飞机、船只或车辆）的位置、速度和方向的连续估计。在导航中，它则用于确定一个系统（如飞机、卫星或自动驾驶汽车）在地理空间中的精确位置。书中可能涵盖了各种估计方法，包括卡尔曼滤波器，这是一种在噪声环境中进行最优状态估计的常用算法。卡尔曼滤波器在现代导航系统中起着核心作用，因为它能有效地融合来自不同传感器（如GPS、雷达、激光雷达等）的数据。此外，书籍可能会讨论扩展卡尔曼滤波和无迹卡尔曼滤波，这些是针对非线性系统的改进版本。除此之外，作者可能还讨论了其他估计技术，如贝叶斯估计，它基于概率框架来更新对未知参数的信念。在跟踪问题中，这可以用于更新目标状态的概率分布。此外，书里可能也提到了粒子滤波器，这是一种在高维或非线性问题中非常有效的蒙特卡洛方法。书中可能包含了大量的数学公式和实例分析，以帮助读者理解并应用这些估计技术。通过理论讲解和实践应用的结合，读者将能够掌握如何在实际工程问题中解决跟踪和导航中的估计挑战。总而言之，"Estimation With Applications to Tracking and Navigation" 是一本深入研究估计理论及其在现代技术中应用的专业著作，对于在航空、航天、自动控制、机器人学等领域工作的工程师和研究人员来说，是一份宝贵的参考资料。

CONTENTS

10.5.3 Some Error Reduction

Methods

—

Summary

407

10.6

MAXIMUM

POSTERIORI TRAJECTORY ESTIMATION

VIA

DYNAMIC

PROGRAMMING

407

10.6.1

The

Approach

407

10.6.2

The

Dynamic Programming

for

Trajectory Estimation

408

10.7

Nonlinear Continuous-Discrete Filter

409

10.7.1

The

Model

409

10.7.2

The

Fokker-Planck Equation

410

10.7.3 Example

413

10.8

NOTES, PROBLEMS

AND A

PROJECT

414

10.8.1

Bibliographical

Notes

414

10.8.2 Problems

414

10.8.3 Project

—

Nonlinear Filtering with Angle-Only Measurements

419

ADAPTIVE ESTIMATION

AND

MANEUVERING TARGETS

421

11.1

INTRODUCTION

421

11.1.1

Adaptive Estimation

—

Outline

421

11.1.2

Adaptive Estimation

—

Summary

Objectives

423

11.2

ADJUSTABLE LEVEL PROCESS NOISE

424

11.2.1

Continuous Noise Level Adjustment

424

11.2.2

Process Noise with Several Discrete Levels

424

11.2.3 Adjustable Level Process Noise

—

Summary

426

11.3

INPUT ESTIMATION

427

11.3.1

The

Model

427

11.3.2

The

Innovations

as a

Linear Measurement

of the

Unknown Input

428

11.3.3 Estimation

of the

Unknown Input

429

11.3.4 Correction

of the

State Estimate

430

11.3.5

Input Estimation

—

Summary

431

11.4

THE

VARIABLE

STATE

DIMENSION APPROACH

431

11.4.1

The

Approach

431

11.4.2

The

Maneuver Detection

and

Model Switching

432

11.4.3 Initialization

of the

Augmented Model

433

11.4.4

VSD

Approach

—

Summary

434

11.5

COMPARISON

ADAPTIVE ESTIMATION METHODS

FOR

MANEUVERING

TARGETS

435

11.5.1

The

Problem

435

11.5.2

The

White Noise Model

with

Two

Levels

436

11.5.3

The IE and VSD

Methods

436

11.5.4

Statistical Test

for

Comparison

of the IE and VSD

Methods

438

11.5.5

Comparison

Several Algorithms

—

Summary

440

11.6

THE

MULTIPLE MODEL APPROACH

441

11.6.1

Formulation

of the

Approach

441

11.6.2

The

Static Multiple Model Estimator

441

11.6.3

The

Dynamic Multiple Model Estimator

444

11.6.4

The

GPB1 Multiple Model Estimator

for

Switching Models

447

11.6.5

The

GPB2 Multiple Model Estimator

for

Switching Models

449

11.6.6

The

Interacting Multiple Model Estimator

453

11.6.7

Example with

the IMM

Estimator

457

11.6.8

Use of

DynaEst™

Design

an IMM

Estimator

460

11.6.9

The

Multiple Model Approach

—

Summary

465

11.7

DESIGN

OF AN IMM

ESTIMATOR

FOR ATC

TRACKING

466

11.7.1

ATC

Motion

Models

466

11.7.2

The EKF for the

Coordinated Turn Model

468

11.7.3

Selection

Models

and

Parameters

470

11.7.4

The ATC

Scenario

471

11.7.5

Results

and

Discussion

472

11.8

WHEN

IS AN IMM

ESTIMATOR NEEDED?

476

11.8.1

Kalman Filter

vs. IMM

Estimator

477

XVi

CONTENTS

11.9

USE OF EKF FOR

SIMULTANEOUS

STATE

AND

PARAMETER ESTIMATION

481

11.9.1

Augmentation

of the

State

481

11.9.2

Example

of Use of the EKF for

Parameter Estimation

482

11.9.3

EKF for

Parameter Estimation

—

Summary

484

11.10

NOTES, PROBLEMS,

AND

TERM PROJECT

484

11.10.1

Bibliographical Notes

484

11.10.2

Problems

485

11.10.3 Term Project

— IMM

Estimator

for Air

Traffic

Control

488

INTRODUCTION

NAVIGATION APPLICATIONS

491

12.1

INTRODUCTION

491

12.1.1

Navigation Applications

—

Outline

491

12.1.2

Navigation Applications

—

Summary

Objectives

492

12.2 COMPLEMENTARY FILTERING

FOR

NAVIGATION

492

12.2.1

The

Operation

Complementary Filtering

492

12.2.2

The

Implementation

Complementary Filtering

493

12.3 INERTIAL NAVIGATION SYSTEMS

495

12.4

MODELS

FOR

INERTIAL NAVIGATION SYSTEMS

496

12.4.1 State Models

496

12.4.2 Sensor Error

Models

496

12.4.3

Single-Axis Models

497

12.4.4

Three-Axis

Models

499

12.4.5 Coordinate Transformation

500

12.5

THE

GLOBAL POSITIONING SYSTEM (GPS)

501

12.5.1

The GPS

Segments

502

12.5.2

GPS

Satellite Constellation

502

12.6

GPS

POSITIONING

502

12.6.1

The GPS

Principle

502

12.6.2

The GPS

Signals

503

12.6.3

The GPS

Observables

506

12.7

THE

ACCURACY

OF GPS

POSITIONING

507

12.7.1

Dilution

Precision

507

12.7.2

GPS

Positioning Accuracy

509

12.8 STATE-SPACE MODELS

FOR GPS 511

12.8.1 Models

for

Receiver Clock State

511

12.8.2 Dynamic Models

512

12.8.3 Linearized Measurement Model

512

12.8.4

Model

for

Exponentially Autocorrelated Noise

513

12.8.5 Coordinate Transformation

515

12.9

EXAMPLE:

GPS

NAVIGATION WITH

IMM

ESTIMATOR

515

12.9.1 Generation

Satellite Trajectories

516

12.9.2 Generation

Trajectories

and

Pseudorange Measurements

517

12.9.3 State-Space Models

518

12.9.4 Simulation Results

and

Discussion

520

12.9.5

Do We

Need

an IMM

Estimator

for

GPS?

523

12.10

INTEGRATED NAVIGATION

523

12.10.1

Integration

Complementary Filtering

524

12.10.2

Example

525

12.10.3

Integration

Centralized Estimation Fusion

527

12.10.4 Integration

Distributed Estimation Fusion

528

12.11

NOTES

AND

PROBLEMS

530

12.11.1

Bibliographical Notes

530

12.11.2

Problems

530

12.11.3

Term Project

—

Extended Kalman Filter

for GPS 533

BIBLIOGRAPHY

537

INDEX

547

PREFACE

This text, which also doubles

as a set of

lecture notes available

viewgraph version (down-

loadable

detailed below), presents

the

material

from a

graduate-level course

Theory

and

Computational Algorithms

for

Estimation

offered

in the

Department

Electrical

and

Com-

puter Engineering

at the

University

Connecticut. This course

is a

standard requirement

the

department's M.S. program

Information, Communication

and

Decision Systems

and is

meant

for

second-semester graduate students.

The

prerequisites

are a

solid knowledge

linear

systems

and

probability theory

at the

first-semester graduate level. These,

well

some

additional

useful

material

from

Statistics,

are

summarized

for

ready reference

Chapter

1 to

enable readers

acquire

the

necessary background

review

it.

This makes

the

text completely

self-contained

and

accessible

for a

person with

typical B.S.E.E.

degree

equivalent. This text

major

revision

and

expansion

of Y.

Bar-Shalom

and X. R. Li,

Estimation

and

Tracking:

Principles, Techniques,

and

Software, originally published

Artech House, 1993

(©YBS

Publishing, 1997).

The

main goal

is to

convey

the

knowledge necessary

for the

design

and

evaluation

state estimation algorithms that operate

in a

stochastic environment. These algorithms

form

the

backbone

information extraction systems

for

remote sensing

moving objects

well

other similar applications. Since information fusion

—

combination

information

from

several

sources

— is an

area with significant recent activity,

should

kept

mind

that

information extraction

is a

crucial step before

fusion.

Furthermore, since

fusion

should

done accounting

for the

existing uncertainties,

it is

important

quantify

the

accuracies

of the

information

to be

fused.

This book also provides

opportunity

for

sharpening

the

students' analytical skills

addition

using

software.

While

the

greatest

recent

advances

have

been

computation,

the

quality

software

is (in a

simplistic manner)

the

product

of the

software

skills

and

algorithmic skills

that went into

its

development.

The

algorithm development requires analytical skills, which,

unfortunately,

have become

too

scarce lately.

While

the

Kalman

filter

(KF)

is the

best-known state estimator,

it is

neither

the

only

one

nor

the

most versatile.

The

material, which covers

number

practical estimation algorithms

(as

many

as it is

felt

practical

for a

semester-long course), leads

to a

major

design project that

unique

this text

— it

combines

the

basics

standard estimation with

the

latest adaptive

multiple

model techniques, which

use KFs as

modules.

The

emphasis

is on

mapping

the

phys-

ical properties

of the

object

interest (typically called

"target,"

whether

friendly

not)

and

the

sensors

—

e.g.,

aircraft

in a

radar-based

air

traffic

control tracking system

—

into

the

parameters

of the

mathematical model, namely,

the

statistical characterization

of the

random

processes describing

the

uncertainties

this problem.

As a

prelude

state estimation, para-

meter estimation

discussed

sufficient

detail

convey

the

concept

"limit

extractable

information"

in a

system.

xvii

XV111

PREFACE

The

approach

is a

balanced combination

mathematics

—

linear systems

and

probability

theory

— in

order

understand

how a

state estimator should

designed, with

the

necessary

tools

from

statistics

order

interpret

the

results.

The use of

statistical techniques

has

been

somewhat neglected

in the

engineering literature pertaining

state estimation,

but it is

necessary

for

(the nontrivial task

of)

interpreting stochastic data

and

answering

the

question whether

design

can be

accepted

"good."

This

particularly important

for

practicing engineers

and is

presented

sufficient

detail based

on our

belief (and extensive experience with real systems)

that

should

be an

integral part

advanced engineering education.

The

material covers

the

topics usually taught

control-oriented EE/systems

and

aeronauti-

cal

engineering programs.

The

relevance extends

other areas dealing with control

mechan-

ical

chemical engineering. Recently,

the

state estimation techniques have been gaining wider

attention

due to

their applicability

such

fields

robotics, computer vision

for

autonomous

navigation,

and

image

feature

extraction with application

medical diagnosis. While

the

course

mainly directed toward

the

M.S. students,

it is

also part

of the

Ph.D. program

at the

University

Connecticut, with

the

intent

providing

the

students with

the

knowledge

tackle real-world

problems, whether

using existing algorithms

or by

developing

new

ones.

The

presentation

of the

material stresses

the

algorithms, their properties

and the

under-

standing

of the

assumptions behind them.

We do not

to the

philosophy

"Give

the

facts

and

don't bother

with

details."

Consequently,

proofs

are

given

to the

extent that

they

are

relevant

understanding

the

results. This

intended

to be a

modest step

bridging

the

much talked about "gap between theory

and

practice"

— it

will illustrate

students

the

usefulness

state estimation

for the

real world

and

provide

engineers

and

scientists working

industry

laboratories

broader

understanding

of the

algorithms used

practice.

might

also avoid

the

situation summarized

by a

participant

at one of the

continuing education courses

taught

by the

first

author

follows:

"Although

studied Kalman

filters

when

worked

to-

ward

Ph.D.

(at one of the

major

U.S. universities),

I did not

expect that they worked with

real

data."

This happens when, because

of the

theorems,

the

students cannot

see the

forest

applications.

Tuning

of a KF — the

choice

of its

design parameters

— is an

art.

One of the

contributions

this text

is to

make

less

of a

black magic technique

and

of a

systematic approach

connecting

the

filter

parameters

physical system parameters, namely,

the

object motion

uncertainty

— its

predictability

— and the

sensor measurement uncertainty

— the

sensor errors.

This

particularly important when

KFs are

used

modules

in an

adaptive estimator, like

the

Interacting Multiple Model (IMM) estimator. Another contribution

providing guidelines

as to

what estimator should

used

specific

problems, namely, when

(adaptive)

IMM

estimator

preferable

over

a KF.

The

Text

and

Hyperlinked

Viewgraph

Format

The

format

this text

also unique

—

textgraph

— in

that

dares

attempt

accomplish

two

goals

in one

format:

serve

as a

self-contained concise text, without excess verbosity, and,

the

same time,

enable

the

lecturer

to use the

pages

this text

viewgraphs

for

lectures.

this purpose,

double-spaced version

of all the

pages

this text (with appropriate page breaks)

The

authors

disclaim

any

responsibility

for

severe

damage

readers

might

suffer

when

falling

asleep

face

forward

while

reading

this

book.

As Ben

Franklin

said,

the

goal

in his

life

was "to

rise

to an

(sic)

happy

mediocrity

and

secure

competency."

Our

objective

is to

provide

the

tools

for

future

successful

applications.

PREFACE

XIX

available

for

instructors

in the

form

of a pdf

file

http://esplabl.ee.uconn.edu/estvu.zip

with

the

password

for

downloading obtainable (upon

the

adoption

this book

as a

course

text)

from

ybs@ee.uconn.edu. Instructors

can

prepare transparencies

for

conventional projector

viewgraphs,

or the pdf

file

can be

used

for

direct electronic projection.

For

projection

from a

computer,

additional feature

available: hyperlinks

in the pdf

file

for all

cross-references

(equations, figures,

tables,

sections, bibliographical items). Starred sections

(or

subsections)

can

skipped

lecturing

at the

discretion

of the

lecturer

— by

clicking

on the

star

the

hypertext

display will automatically

go to the end of the

corresponding section, marked

by a

box.

Experience over

number

years shows that students with

copy

these notes

front

them

can

concentrate

on the

ideas, rather than having

copy

copious amount

equations

from

the

board. Some

of the

graduate students

who

took

the

Estimation course taught using

this

textgraph™ even complained that other graduate courses

had not

adopted this instruction

method.

This

format

also

a way of

making lectures more

efficient

since

makes

possible

convey more material than through

the

standard lecturing technique where

one has to

write

everything

on the

board.

Last,

but not

least,

the

need

spend time

preparing lecture notes,

well

as the

main hazard

of the

teaching profession (the inhalation

chalk

marker dust),

can

avoided.

The

ready availability

such class notes also makes

much easier

hold

in-house courses

in an

industrial

government laboratory environment where senior

staff

—

with

knowledge

of the

material

but

limited

time

— can

serve

lecturers.

is our

hope that this text will contribute

to the

education

future

practitioners,

well

of use to

those already involved

in the

application

state estimation

real-world problems.

This

textgraph™

was

written with

the

philosophy that engineers should

able

to do

than

run-of-the-mill work

—

they should

prepared

work

at the

frontiers

knowledge.

Note

on the

Printing

Style

For the

convenience

of the

reader,

all

major

concepts/terms, when they

are

introduced

used

particular application,

are in

italic

boldface

and

indexed. Also,

all the

index terms appear

the

text

slanted boldface.

Italics

are

used

for

emphasized ideas/properties.

The

main equations

important algorithms

are

highlighted with boxes,

and the

algorithms

are

summarized

flowcharts.

The

Companion

Software

DynaEst™

is a

completely self-explanatory menu-driven

interactive

design

and

evaluation

tool

for

Kalman

filters

and an

adaptive Interacting Multiple Model (IMM) estimator.

The

package

provides

the

following important

flexibilities

as a

design tool:

Estimator

design.

The

user

may

specify

any

linear Gaussian true plant (dynamic)

and

measurement models,

well

as the

plant

and

measurement models

for the

estimator.

The

true

and the filter-assumed

models

can be

different.

Models

are

valid

for all

dimensions.

Reduced-order

filters can be

implemented.

Selection

model parameters.

The

user

may

specify

any

parameter

of the

true model

and/or

the filter-assumed

model(s), such

as the

noise means

and

covariances.

As the

ancient Romans would have said: "Orchides

forum

trahite, cordes

mentes veniant."

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