MATLAB实现卡尔曼滤波理论与实践第三版详解

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《卡尔曼滤波理论与实践：MATLAB应用教程（第三版）》是一本由Mohinder Grewal教授和Angus Andrews共同编写的著作，出版于2008年，由John Wiley & Sons, Inc. 出版。本书主要聚焦于卡尔曼滤波这一关键的信号处理技术，该技术在许多领域，如导航、控制系统、信号估计和预测等方面发挥着重要作用。卡尔曼滤波是一种递归最小二乘方法，用于估计动态系统的状态，并考虑到观测数据中的噪声不确定性。本书的核心内容包括以下几个方面： 1. **理论基础**：深入讲解卡尔曼滤波的原理，包括随机过程、线性系统理论、状态空间模型、预测与更新步骤、协方差矩阵和信息增益等概念。读者将理解滤波器如何通过结合系统的动态模型和观测数据来实时估计状态并减小误差。 2. **MATLAB实现**：作者以MATLAB为例，详细介绍了如何在实际项目中使用这个强大的工具进行滤波器设计和仿真。书中提供了大量的代码示例，帮助读者掌握如何编写和调试卡尔曼滤波算法。 3. **应用实例**：书中包含多个实例，涵盖航空导航、自动驾驶、遥感、通信系统等领域，展示了卡尔曼滤波在实际问题中的应用效果和优化策略。 4. **扩展话题**：除了基本的无迹卡尔曼滤波（UKF）和粒子滤波（PF），本书还可能探讨了自适应滤波、非线性滤波和其他高级主题，以满足不同读者的专业需求。版权信息表明，任何未经许可的复制、存储、传输行为均需获得John Wiley & Sons, Inc. 的明确授权。如果你对本书的内容感兴趣，可通过指定的联系方式申请许可。《卡尔曼滤波理论与实践：MATLAB应用教程（第三版）》是一本实用的教材，不仅适合工程学生和研究人员学习卡尔曼滤波理论，也适用于需要在实际项目中应用该技术的专业人士。通过本书，读者将获得深入理解卡尔曼滤波的精髓以及如何利用MATLAB进行高效实现和优化。

that you want to control, and the Kalman ﬁlter provides a means for inferring the

missing information from indirect and noisy measurements. The Kalman ﬁlter is

also used for predicting the likely future courses of dynamic systems that people

are not likely to control, such as the ﬂow of rivers during ﬂoods, the trajectories of

celestial bodies, or the prices of traded commodities.

From a practical standpoint, these are the perspectives that this book will present:

†

It is only a tool. It does not solve any problem all by itself, although it can make

it easier for you to do so. It is not a physical tool but a mathematical one.

Mathematical tools make mental work more efﬁcient, just as mechanical

tools make physical work more efﬁcient. As with any tool, it is important to

understand its use and function before you can apply it effectively. The

purpose of this book is to make you sufﬁciently familiar with and proﬁcient

in the use of the Kalman ﬁlter so that you can apply it correctly and efﬁciently.

†

It is a computer program. It has been called “ideally suited to digital computer

implementation” [95], in part because it uses a ﬁnite representation of the esti-

mation problem—by a ﬁnite number of variables. It does, however, assume that

these variables are real numbers—with inﬁnite precision. Some of the problems

encountered in its use arise from the distinction between ﬁnite dimension and

ﬁnite information and from the distinction between ﬁnite and manageable

problem sizes. These are all issues on the practical side of Kalman ﬁltering

that must be considered along with the theory.

†

It is a consistent statistical characterization of an estimation problem.Itis

much more than an estimator, because it propagates the current state of knowledge

of the dynamic system, including the statistical inﬂuence of random dynamic per-

turbations and the effects of all past measurements. These properties are extremely

useful for statistical analysis and the predictive design of sensor systems.

If these answers provide the level of understanding that you are seeking, then there is

no need for you to read the rest of this book. If you need to understand Kalman ﬁlters

well enough to use them effectively, then please read on!

1.1.2 How It Came to Be Called a Filter

It might seem strange that the term ﬁlter would apply to an estimator. More com-

monly, a ﬁlter is a physical device for removing unwanted fractions of mixtures.

(The word felt comes from the same medieval Latin stem, for the material was

used as a ﬁlter for liquids.) Originally, a ﬁlter solved the problem of separating

unwanted components of gas-liquid-solid mixtures. In the era of crystal radios and

vacuum tubes, the term was applied to analog circuits that ﬁlter electronic signals.

These signals are mixtures of different frequency components, and these physical

devices preferentially attenuate unwanted frequencies.

This concept was extended in the 1930s and 1940s to the separation of signals

from noise, both of which were characterized by their power spectral densities.

GENERAL INFORMATION2

constants, there is hardly anything in the universe that is truly constant. The

orbital parameters of the dwarf planet Ceres are not constant, and even the

“ﬁxed” stars and continents are moving. Nearly all physical systems are

dynamic to some degree. If one wants very precise estimates of their character-

istics over time, then one has to take their dynamics into consideration. The

problem is that one does not always know their dynamics very precisely

either. Given this state of partial ignorance, the best one can do is express

our ignorance more precisely—using probabilities. The Kalman ﬁlter allows

us to estimate the state of dynamic systems with certain types of random beha-

vior by using such statistical information. A few examples of such systems are

listed in the second column of Table 1.1.

2. Performance analysis of estimation systems. The third column of Table 1.1

lists some possible sensor types that might be used in estimating the state of the

corresponding dynamic systems. The objective of design analysis is to deter-

mine how best to use these sensor types for a given set of design criteria.

These criteria are typically related to estimation accuracy and system cost.

The Kalman ﬁlter uses a parametric characterization of the probability distribution

of its estimation errors in determining the optimal ﬁltering gains, and this probability

distribution may be used in assessing its performance as a function of the “design

parameters” of an estimation system, such as

†

the types of sensors to be used,

†

the locations and orientations of the various sensor types with respect to the

system to be estimated,

†

the allowable noise characteristics of the sensors,

TABLE 1.1 Examples of Estimation Problems

Application Dynamic System Sensor Types

Process control Chemical plant Pressure

Temperature

Flow rate

Gas analyzer

Flood prediction River system Water level

Rain gauge

Weather radar

Tracking Spacecraft Radar

Imaging system

Navigation Ship Sextant

Log

Gyroscope

Accelerometer

GNSS



receiver



Global navigation satellite system.

GENERAL INFORMATION

1.2.1 Beginnings of Optimal Estimation Theory

The ﬁrst method for forming an optimal estimate from noisy data is the method of

least squares. Its discovery is generally attributed to Carl Friedrich Gauss (1777–

1855) in 1795. The inevitability of measurement errors had been recognized since

the time of Galileo Galilei (1564–1642), but this was the ﬁrst formal method

for dealing with them. Although it is more commonly used for linear estimation

problems, Gauss ﬁrst used it for a nonlinear estimation problem in mathematical

astronomy, which was part of an interesting event in the history of astronomy. The

following account was put together from several sources, including the account by

Makemson in [19].

On January 1, 1801, the ﬁrst day of the nineteenth century, the Italian astronomer

Giuseppe Piazzi was checking an entry in a star catalog. Unbeknown to Piazzi, it

included an error by the printer. While searching for the “missing” star, Piazzi discov-

ered instead something that moved. It was the dwarf planet Ceres—the largest body in

the asteroid belt and the ﬁrst to be discovered—but Piazzi did not know that yet. He

was able to track and measure its apparent motion against the “ﬁxed” star background

during 41 nights before it moved too close to the sun and disappeared.

On January 24, Piazzi had written of his discovery to Johann Bode. Bode is best

known for Bode’s law, which states that the distances of the planets from the sun, in

astronomical units, are given by the sequence

(4 þ3 2

) for n ¼1,0,1,2,?,4,5,...: (1:1)

Actually, it was not Bode but Johann Tietz who ﬁrst proposed this formula, in 1772.

At that time there were only six known planets. In 1781, Friedrich Herschel

discovered Uranus, which ﬁt nicely into this formula for n ¼ 6. No planet had

been discovered for n ¼ 3. Spurred on by Bode, an association of European astron-

omers had been searching for the “missing” eighth planet for nearly 30 years. Piazzi

was not part of this association, but he did inform Bode of his unintended discovery.

Piazzi’s letter did not reach Bode until March 20. (Electronic mail was discovered

much later.) Bode suspected that Piazzi’s discovery might be the missing planet, but

there was insufﬁcient data for determining its orbital elements by the methods then

available. It is a problem in nonlinear equations that Newton himself had declared

as being among the most difﬁcult in mathematical astronomy. Nobody had solved

it and, as a result, Ceres was lost in space again.

Piazzi’s discoveries were not published until the autumn of 1801. The possible

discovery—and subsequent loss—of a new planet, coinciding with the beginning

of a new century, was exciting news. It contradicted a philosophical justiﬁcation

for the existence of only seven planets—the number known before Ceres and a

number defended by the respected philosopher Georg Hegel, among others. Hegel

had recently published a book in which he chastised the astronomers for wasting

their time searching for an eighth planet when there was sound philosophical justiﬁ-

cation for there being only seven. The new celestial object became a subject of

GENERAL INFORMATION6

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MATLAB实现卡尔曼滤波理论与实践第三版详解

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imu_kalman-filter_matlab:使用

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