现代导航系统详解：惯性导航的核心原理

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"Introduction to Modern Navigation Systems" by Esmat Bekir 现代导航系统介绍现代导航系统是确保从一个地点安全、准确地到达另一个地点的关键技术。导航的本质是设定航行路线，使船只、车辆或飞行器能够从一个期望的位置移动到另一个。这涉及定位和速度的确定。本资源主要关注一种特殊的导航方式——惯性导航。惯性导航系统是一种自包含的导航技术，它不依赖外部环境条件，可以在海洋、水下、陆地、隧道或空中等各种环境中工作。这种系统的优点在于其独立于天气状况，并且只要电源可靠，几乎可以无限期地运行。本书《现代导航系统》由Esmat Bekir撰写，详细阐述了惯性导航系统的原理与应用。作者可能探讨了以下关键知识点： 1. **惯性导航原理**：惯性导航基于牛顿运动定律，通过测量载体的加速度来推算位置和速度。它包括惯性测量单元（IMU），由加速度计和陀螺仪组成，用于实时监测载体的运动状态。 2. **误差分析**：惯性导航系统中的误差来源，如传感器漂移、初始对准误差和集成累积误差，以及如何通过误差校正算法进行补偿。 3. **导航系统组件**：详细介绍了惯性导航系统的核心组成部分，如导航计算机、数据处理算法和传感器集成。 4. **数据融合技术**：可能涉及到与其他导航系统的数据融合，如全球定位系统（GPS）和地磁导航，以提高精度和可靠性。 5. **应用领域**：书中可能会讨论惯性导航在航空、航海、军事、自动驾驶汽车、无人机等领域的应用实例。 6. **最新发展与未来趋势**：介绍现代惯性导航系统的最新技术进步，如微电子机械系统（MEMS）传感器的发展，以及未来可能的技术方向。 7. **法律和版权信息**：书中的版权声明强调未经出版商书面许可，不得复制或以任何形式分发该书内容。此书由世界科学出版社出版，旨在为读者提供一个全面理解现代导航系统，特别是惯性导航的理论基础和实际应用的平台。无论是工程师、研究人员还是对此领域感兴趣的读者，都能从中获得宝贵的见解。

Introduction to Modern Navigation Systems

Navigation is derived of the Latin verb navigare, to sail, which also is

derived of 'navis' a ship. Navigation has been the science, or very much

the art, of determining the position and the velocity of a craft, whether a

car, a ship or an airplane. It is of little wander that navigation become

intertwined with sea and ships because it, by large means, evolved

onboard of ships facing the enormous challenges of charting their

courses. There are certain spots in water that are too shallow, rocky or

turbulent that an experienced sailor would like to avert. Early travelers

identified their locations and charted their routs by landmarks. When

they got into water they, most probably, hugged very closely to the

shoreline.

Navigation rose to higher level of sophistication when ancient Greeks

realized that the Earth is spherical and when Eratosthenes of Alexandria

measured its radius. They drew geographical maps superimposed on

latitude and longitude quadrants.

Early on, people were aware that the sun and the stars can guide them

when traveling long distances in the desert or in the sea. They knew that

the altitude of Polaris, (the north star), indicates the latitude at which they

locate. Near the equator (when Polaris is on the horizon and is difficult to

see) or in daytime they had other means. They realized that at any point

on Earth the sun attains its highest altitude at noon and this is when it

points to the north and with a simple adjustment they can relate this

altitude to the latitude at that point. Therefore, day or night, they could

figure out the latitude. Navigators devised simple means for charting

their routes: determine the initial latitude at the location they embark, sail

north or south to the latitude of the desired destination and finally move

east or west till they encounter their destination.

The latitude approach for navigation came into place because means

for measuring the latitude were possible. Initially they came in the shape

of the astrolabe, a simple apparatus, for measuring the altitude of the

stars. The astrolabe depended on measuring the star altitude with respect

to the horizon, but this meant poor measurements if the boat is rocking

for bad weather or any reason. The astrolabe has evolved into the sextant,

a more accurate tool [1].

Determining the latitude has solved one parameter of the navigation

equation and it remained to determine the longitude. The magnetic

Introduction

needle is discovered, but probably it was not of much help because it

would not point to the true geographic north, nor did it maintain a

constant error. The magnetic compass would be of great use when

magnetic variations, the difference between magnetic north and the true

north, were tabulated.

Crude means for measuring the ship speed became also available that

come in the form of chip log [2]. The means took the shape of a

relatively heavy slug is attached to a long rope of about 700 feet length,

that was knotted every 47 feet and 3 inches. If the sailor wanted to

measure the boat speed, he would toss the slug into the water and let the

rope slip in his hands. He would wait for a 28 seconds during which he is

counting the number of knots that slips between his fingers. The time

was measured by nothing more than the legendary sandglass.

Interestingly, this is why the ship speed is still currently measured in

‘knots’.

Between the sextant, the magnetic compass and the ship speed,

navigators were able to chart their ship courses to move to different

places. It should be remembered that these computations were not

accurate and possibly crude. A rolling ship would certainly prevent

collecting accurate sextant measurements as the sextant must be steady

and resting on a perfectly horizontal surface. Crude, may be, but good

enough to go to places. With these tools Christopher Columbus set sail to

the Americas and charted his way back home.

Columbus trip in the final years of the 15

century was a monumental

epoch in navigation; it opened a new era for longer trips that lasted

longer periods in uncharted waters to uncharted lands. Ships tended to

become larger to carry more people and larger cargos to sail between the

new lands and Europe. Older methods and navigation tools resulted in

larger tragedies and needed to be improved.

It was not until the 18

century that navigation got a great boost when

John Harrison invented and developed the 'chronometer' and perfected it

to measure time with an error of less than .1 seconds per day. Recall

earlier that sun at noon points to the north and that, in a way, points to

local longitude. Suppose a navigator set sail from a point on the

Greenwich line (i.e. 0 longitude) and purposely sets the clock at noon to

12:00PM. Few days later, the clock is found to read 11:00 at noontime,

Introduction to Modern Navigation Systems

the navigator would immediately know that the local longitude is 15

degrees east. This is because the Earth is girded with 360 longitude lines

and since the Earth makes a complete circle every 24 hours, noon will

differ by one hour every (360/24) 15 degrees of longitude. With

Harrison's chronometer, British naval officer and explorer James Cooks

was able in 1772-1775 to circumnavigate the Earth [3]. From

information he gathered on his voyage, Cook completed many detailed

charts of the world that completely changed the nature of navigation.

More accurate and much lighter sextants continued to evolve.

However rough waters, which causes the ship to roll unsteadily, and fog,

which causes the true horizon to be obscured, rendered the sextants very

difficult to use under these conditions. Tools were needed to steady the

sextant. Nothing but gyroscopic action that could do the job. Indeed it

was a very fortunate moment when the roads of navigation and

gyroscopes crossed and opened a new page in the history of navigation.

A gyroscope, basically, is a top that when rotates at very large rates,

its upper surface would be horizontal and its axis of rotation and the

Earth's axis make a plane that point to the north. What's more is that if

the surface, on which the top spins, is disturbed the top will restore its

phenomenon unless it is disturbed once more [4]. Amazing isn't it! It

worth noting to mention that it was Foucault that named it 'gyroscope' in

1852. Not much time later when Admiral Fleuriais developed the

gyroscopic sextant in 1885. But this is when the sextant reached its great

year and started to give way to the gyro. Few factors has hastened the

development of the new gyro: Larger ships made with iron alloys

rendered the use of magnetic compassed very difficult, and temporal

navigation and orientation tools – magnetic compasses and sextants – in

submersibles were of little use.

The early days of the 20

century witnessed the dawn of the airborne

aviation, and with it came the need for navigation tools on board of these

flying machines. The legacy compass was still used to point direction.

The new gyros, at the same time were being developed into the vertical

and directional instruments to indicate the vertical and azimuth directions

respectively. It turned out that the human sensing for the vertical

direction while flying is very poor and hence the need for the vertical

gyro to fly straight and level.

Introduction

It all started by inventing and developing the 'Gyrocompass' – the

practical instrument that indicates the direction to the north [5]. It

performs well up to 80 degrees latitude. The gyrocompass was invented

and developed by Dr. Hermann Anschuetz-Kaempfe in Kiel, Germany in

1908 [6]. “Compared with the conventional marine-type magnetic

compass, the gyrocompass was far more accurate, being capable of

indicating the north within a small fraction of one degree. It has no

variation error” [7]. The gyrocompass was also developed in the USA by

Elmer Sperry whose company has produced many versions. These

gyrocompasses were installed on board commercial and navy ships.

The era of inertial navigation has started when gyros and

accelerometers were used as a guidance tools in the German V2 rockets.

With the end of the Second World War came a speedy activity for

developing an inertial navigation system. This system comprises one

triad of accelerometers and another triad of gyros, both are mounted on

top of a platform called the stable element. The stable element is

mounted on two or more orthogonal gimbals that allow it to have a

complete three degrees of freedom orientation. With the gyros aid, the

system is so designed that, the stable element will maintain its attitude

with respect to the surface of the Earth. This attitude, as an example, is

parallel to the local surface of the Earth and pointing to the north. With

this arrangement, the accelerometer outputs are integrated once to give

the craft velocity and integrated once more to give its location. Indeed it

is a remarkable tool for navigation. Short of a reliable source of power, it

can work almost indefinitely. With one of these systems the US Navy

Nautilus navigated under ice to reach the North Pole in 1958.

This inertial navigation system is self-contained: it is independent of

weather conditions and is operable anywhere – in seas, underwater,

lands, tunnels, or in air. On the other hand it is very costly (in the order

of $100,000 in the 1970s), bulky and comprises many delicate

components, sensitive to temperature variations and hence is very

expensive to maintain.

In 1956, W. Newell patented the idea of the Strapdown Inertial

Navigation System (INS). The patent described the implementation of an

INS strapped down of its gimbals and literally fixing the inertial platform

to the body of the craft. The thought is to trade the mechanical

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