Optimal Filtering: Detailed Concepts and Applications in Information Science

需积分: 9 179 浏览量更新于2024-07-25 1 收藏 15.06MB PDF 举报

"Optimal Filtering" 是一本由Brian D. O. Anderson和John B. Moore合著的专业书籍，属于Prentice-Hall的信息与系统科学系列，由Thomas Kailath编辑。该书详细介绍了最优滤波的概念和技术，是信号处理和控制工程领域的经典著作。最优滤波是信号处理中的一个重要分支，其主要目标是设计一个滤波器，能够从含有噪声的数据中提取出最准确、最有用的信息。这本书涵盖了滤波理论的基础知识，包括卡尔曼滤波、霍夫曼滤波等经典方法，这些方法在现代通信、导航、控制系统以及航空航天等领域有着广泛的应用。书中可能涉及的知识点包括： 1. **滤波理论基础**：讲解了滤波的基本原理，如线性时不变系统、滤波器设计、滤波器性能分析等。 2. **随机过程和概率论**：作为最优滤波的数学基础，书中可能会深入讨论高斯分布、马尔科夫过程、贝叶斯理论等随机变量和过程。 3. **卡尔曼滤波**：详述了卡尔曼滤波器的设计和实现，它是估计理论中的一个关键工具，特别适用于动态系统的状态估计。 4. **霍夫曼滤波**：霍夫曼滤波是一种非线性滤波方法，用于处理非高斯噪声或非线性系统的问题。 5. **最优决策理论**：探讨如何基于最小化某种误差函数（如均方误差）来制定最优的滤波决策。 6. **应用案例**：书中可能包含实际应用案例，如雷达探测、导航系统、通信系统的信号处理问题，以展示最优滤波技术的实际应用。 7. **噪声处理**：详细讨论了噪声的来源、特性以及测量方法，这对于理解滤波器在实际环境中的性能至关重要。 8. **系统同步与控制**：滤波技术在系统同步和控制中的作用，包括滤波器如何帮助提高系统的稳定性和性能。 9. **滤波器设计**：介绍如何根据具体需求设计和优化滤波器，包括有限 impulse response (FIR) 和无限 impulse response (IIR) 滤波器。通过阅读这本书，读者可以深入理解最优滤波的基本概念，掌握滤波器设计的技术，并学会将这些知识应用于实际工程问题中。这本书不仅适合于学术研究，也适合工程实践中的技术人员参考。

~ INTRODUCTION

Ch. 1

linear systems with associated gaussian random processes; it transpires that

the optimal filter in a minimum mean-square-error sense is then linear. Of

course, man y applications involve nonlinear systems and/or nongaussian

random processes, and for these situations, the optimal filter is nonlinear.

However, the plain fact of the matter is that optimal nonlinear filter design

and implementation are very hard, if not impossible, in many instances. For

this reason, a suboptimal linear filter may often be used as a substitute for an

optimal nonlinear filter, or some form of nonlinear filter maybe derived which

is in some way a modification of a linear filter or, sometimes, a collection of

linear filters. These approaches are developed in this book and follow our

discussion of linear filtering, since one can hardly begin to study nonlinear

filtering with any effectiveness without a knowledge of linear filtering.

Finite u?mensionufity. Itturns out that finite-dimensional filters should

be used when the processes being filtered are associated with finite-dimen-

sional systems. Now most physical systems are not finite dimensional;

however, almost all infinite-dimensional systems can be approximated by

finite-dimensional systems, and this is generally what happens in the modeling

process. The finite-dimensional modeling of the physical system then leads to

an associated finite-dimensional filter. This filter will be suboptimal to the

extent that the model of the physical system is in some measure an inaccurate

reflection of physical reality. Why should one use a suboptimal filter?

Though one can without too much difficulty discuss infinite-dimensional

filtering problems in discrete time, and this we do in places in this book,

finite-dimensional filters are very much to be preferred on two grounds: they

are easier to design, and far easier to implement, than infinite-dimensional

filters.

1.4 OUTLINE OF THE BOOK

The book falls naturally into three parts.

The first part of the book is devoted to the formulation and solution of

the basic Kalman filtering problem. By the end of the first section of Chapter

3, the reader should know the fundamental Kalman filtering result, and by

the end of Chapter 3, have seen it in use.

The second part of the book is concerned with a deeper examination of

the operational and computational properties of the filter. For example, there

is discussion of time-invariant filters, including special techniques for com-

puting these filters, and filter stability; the: Kalman filter is shown to have a

signal-to-noise ratio enhancement property.

In the third part of the book, there area number of developments taking

Ch. 1

REFERENCES 7

off

from the basic theory. For example, the topics of smoothers, nonlinear

and adaptive filters, and spectral factorization are all covered.

There is also a collection of appendices to which the reader will probably

refer on a number of occasions. These deal with probability theory and

random processes, matrix theory, linear systems, and Lyapunov stability

theory. By and large, we expect a reader to know some, but not all, of the

material in these appendices. They are too concentrated in presentation to

allow learning of the ideas from scratch. However, if they are consulted when

a new idea is encountered, they will permit the reader to learn much, simply

by using the ideas.

Last, we make the point that there are many ideas developed in the

problems. Many are not routine.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

REFERENCES

SKILLING,H. H.,

Electrical Engineering Circuits, John Wiley & Sons, Inc.,

New York, 1957.

STORER,J. E.,

Pamive Network Synrhesis, McGraw-Hill Book Company, New

York, 1957.

TERMAN,F. EL,

Electronic and Radio Engineering, McGraw-Hill Book Com-

pany, New York, 1955.

VITERBI,A. J.,

Principles of Coherent Communication, McGraw-Hill Book Com-

pany, New York, 1966.

GOLD, B., and C. M. RADER,

Digital Processing of Signals, McGraw-Hill Book’

Company, New York, 1969.

RABINER,L. R., and B.

GOLD, Theory and Application of Digital Signal Pro-

cessing,

Prentice-Hall, Inc., Englewood Cliffs, N. J., 1975.

OPPENHEIM,A. V., and R. W. SCHAFER,

Digital Signal Processing, Prentice-

Hall, Inc., Englewood Cliffs, N.J., 1975.

WIENER,N.,

Extrapolation, Interpolation & Smoothing of Stationary Time Series,

The M.I.T. Press, Cambridge, Mass., 1949.

KOLMOGOROV,A. N.,

“Interpolation and Extrapolation,”

Bull. de l’acadkmie

des sciences de U.S. S. R.,

Ser. Math. 5, 1941, pp. 3-14.

WAINSTEIN,L. A., and V. D. ZUBAKOV,

Extraction of Signals from Noise,

Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962.

KALMAN,R. E., and R. S. BUCY,“New Results in Linear Filtering and Predic-

tion Theory,”

J. of Basic Eng., Trans. ASME, Series D, Vol. 83, No. 3, 1961,

pp. 95-108.

KALMAN, R. E., “A New Approach to Linear Filtering and Prediction Prob-

lems,”

J. Basic Eng., Trans. ASME, Series D, Vol. 82, No. 1, 1960, pp. 35-45.

FILTERING, LINEAR SYSTEMS, AND ESTIMATION

Ch. 2

Later, we shall pose specific mathematical models for some systems, and

even formally identify the system with the model.

In discussing filtering and related problems, it is implicit that the systems

under consideration are noisy. The noise may arise in a number of ways. For

example, inputs to the system may be unknown and unpredictable except for

their statistical properties, or outputs from the system may be derived with

the aid of a noisy sensor, i.e., one that contributes on a generally random

basis some inaccuracy to the measurement of the system output. Again,

outputs may only be observed via a sensor after transmission over a noisy

channel.

In virtually all the problems we shall discuss here, it will be assumed that

the output measurement process is noisy. On most occasions, the inputs also

will be assumed to be noisy.

Now let us consider exactly what we mean by

jiltering. Suppose there is

some quantity (possibly a vector quantity) associated with the system opera-

tion whose value we would like to know at each instant of time. For the sake

of argument, assume the system in question is a continuous time system, and

the quantity in question is denoted by s(. ).* It may be that this quantity is

not directly measurable, or that it can only be measured with error. In any

case, we shall suppose that noisy measurements Z(.) are available, with Z(. )

not the same as S(.).

The term filtering is used in two senses. First, it is used as a generic term:

filtering is the recovery from Z(.) of s(.), or an approximation to s(.), or

even some information about S(.). In other words, noisy measurements of a

system are used to obtain information about some quantity that is essentially

internal to the system. Second, it is used to distinguish a certain kind of

information processing from two related kinds, smoothing and prediction.

In this

sense, filtering means the recovery at time tof some information about

s(t)using measurements up till time t.The important thing to note is the

triple occurrence of the time argument t.First, we are concerned with obtain-

ing information about S(. ) at time t,i.e., s(t).Second, the information is

available at time t,not at some later time. Third, measurements right up to,

but not after, time t are used. [If information about s(t) is to be available at

time t, then causality rules out the use of measurements taken later than time

t in producing this information.]

An example of the application of filtering in everyday life is in radio

reception. Here the signal of interest is the voice signal. This signal is used to

modulate a high frequency carrier that is transmitted to a radio receiver. The

received signal is inevitably corrupted by noise, and so, when demodulated,

it is filtered to recover as well as possible the original signal.

●Almost without exeeption throughout the book,

x(t) will denote the value taken by

a function at time I, and x(. ) will denote that function. Therefore, x(t) is a number, and

x(. ) an infinite set of pairs, {t, x(t)}, for / ranging over all possible values.

剩余366页未读，继续阅读

zhouhaibing

粉丝: 0
资源: 6

Optimal Filtering: Detailed Concepts and Applications in Informa...

最新资源

Optimal Filtering: Detailed Concepts and Applications in Informa...

Anderson & Moore - Optimal Filtering in Information Science

Anderson & Moore的《Optimal Filtering》电子版分享

Optimal Filtering in Information and System Sciences

optimal filtering(8-11Appendix)

Optimal Filtering with Kalman Filters and Smoothers.pdf

Anderson-1979-Optimal filtering copy.pdf

The joint optimal filtering and fault detection for multi-rate sensor fusion under unknown inputs

Distributed Optimal Kalman Filtering for

Optimal Kalman Filtering for System with Unknown Inputs

Optimal_filtering_with_Kalman_filters_and_smoother

最新资源