Fundamentals and Practices of Sensing Technologies
Keiji Taniguchi, Hon. Professor of
Dr. Masahiro Ueda, Professor of Faculty of Education and Regional Studies
Dr. Ningfeng Zeng, an Engineer of Sysmex Corporation
(A Global Medical
Dr. Kazuhiko Ishikawa, Assistant Professor
Faculty of Education and
[Editor’s Note: This paper is presented as Part III of a series of chapters from the new book “Fundamentals and Practices of Sensing Technologies”; subsequent chapters will be featured in upcoming issues of this Journal.]
1.4 Outlines of GPS
1.4.1 Introduction (1), (21)
The Global Positioning System (GPS) developed by the US Air Force, provides world-widely a three dimensional position, and velocity information for users. The satellite constellation consists of 24 satellites in 20000(Km) orbits. These satellites are usually broadcasting ranging codes and navigation data on three frequency bands of L1, L2 and L5 using a Code Division Multiple Access (CDMA) method. Therefore, the same frequencies with different ranging codes are used for all satellites. The GPS system consists of a dual-use system, and is used for the Standard Positioning Service (SPS) for civil user and the Precise Positioning Service (PPS) for military one. The L1 and L2 frequency bands are used for the legacy system, and the L1(1575.92MHz), L2(1227.5MHz), and L5 (1176.45 MHz) frequency bands are used for the modernized one.
In this section, the legacy system is described.
1.4.2 GPS System Configurations (1)
Figure 1.42 shows the GPS system configuration. This system consists of three
segments : a space segment, a user segment, and a control segment.
The space segment is consists of 24 satellites with 4 satellites in 6 orbit planes,
and these satellites broadcast the radio wave frequencies of 1575.92(MHz) in L1 band,
and 1227.5(MHz) in L2 band as navigation signals.
The control segment consists of a ground based master control station, and five monitor
stations for tracking the satellites.
1.4.3 Determination of User Positions (21)
A Relationship Satellite and User
Figure.1.43 shows the relationship between a satellite and a user on the earth.
In this figure, a satellite- to- user vector is expressed as follows:
The magnitude of vector is also expressed as follows:
where , and are the radius of the earth, a distance between the satellite and the user, and a distance between the center of the earth and the satellite, respectively.
B. Calculation of Equivalent Time
Figure 1.44 shows the relationship between a pseudo range and a geometric range.
The geometric range and pseudo range are expressed as follows:
where we assume that is negligible small because an atomic clock(See Fig.1.46) is used as a main oscillator of all the GPS satellites.
In this figure, is the equivalent time based on a geometric range, is the equivalent time based on a pseudo range, is the starting time that the signal left from the satellite, is the arrival time that the signal reached to a receiver of the user, is the off- set time in the clock of the satellite,
is the off- set time in the clock of the user, and is the propagation speed of radio waves ().
Therefore, Eq. (1.17) can be simplified as follows:
In above equation, can be measured by a satellite-generated ranging code information of a received signal.
C. Calculation of User Position
Only three unknown user position would be required if a clock in the user receiver were synchronized with a clock in the satellite. The clock of a crystal oscillator in the user receiver is usually employed to determine it’s own position, but this clock is not so accurate as the atomic clock. Consequently, four unknown measurements are required (The symbolis shown in Fig.1.44). We need at least the ranging codes information from four satellites by time of arrival (TOA) measurements as shown in Fig.1.45. The following equation can, then, be obtained from Eq.(1.18):
where , and , express the coordination of th satellite positions.
The pseudo range between the satellite and the user’s receiver can be computed by measuring the propagation time of radio waves, which is modulated by a satellite-generated ranging code.
The unknown user position and clock offset of the receiver can be defined as the sum of the approximate components,,, , and the incremental components,,,, as follows:
, , , (1.20)
We also define the pseudo ranges as follows:
The pseudo range can be obtained as a linear approximation as follows by means of the Tailor expansion series:
Substituting Eq.(1.21) and Eq.(1.23) into Eq.(1.22), the pseudo range can be
expressed as follows:
Rearranging the above equation,
For simplicity, we put as follows:
, , ,
then Eq. (1.24) can be described as follows:
Furthermore, a matrix expression of Eq.(1.25) are as follows:
D. Calculation of User Velocity
The user velocities can be obtained by calculating the differentiation of Eq.(1.25 ) as follows:
where, we put as follows :
, , , ,
Eq.(1.25 ) is, then, rewritten as follows:
where can be obtained from the ranging code.
However, practically, this method is not so accurate for noise problems.
(b) Carrier Doppler Phase Shift Method
A carrier Doppler phase shift arises by the relative motion between the satellite and the user, and is expressed as follows:
In the above equation,
where is the transmitting frequency, is the receiving frequency, is the satellite-to- user relative velocity, is the velocity of the satellite(), is the unit vector pointing along the line of sight from the user to the satellite() , is the propagation speed of radio waves, is the measured estimate of the receiving frequency, and is the drift rate of the user clock. The following equation is, then, obtained from Eqs.(1.30) and (1.31),.
The user velocity can, thus be obtained by processing carrier phase measurements due to the Doppler frequency shift.
1.4.4 Configurations of GPS Transmitter and Receiver (21)
A. Configurations of GPS Transmitter
Figure 1.46 shows a block diagram of the GPS transmitter. The satellite frequency , which is generated by means of the highly accurate free running atomic clock, expresses the main oscillator. Two elements, BPSK and QPSK, express a binary phase shift keying modulator and a quardrature phase shift keying modulator (See comment 1.2).
A symbol expresses an exclusive OR operation (modulo two addition), and its operation is defined as follows: .
Prior to the QPSK modulation, the 50 bps navigation message data is combined with both the coarse/acquisition code (C/A code) and the precision code (P(Y) code).
Figures 1.48 (a),(b),(c) and (d) show the basic configuration of the BPSK Modulator, a carrier waveform, a data signal waveform, and a modulated waveform, respectively.
Transmitting signal L1, and L2 of the GPS transmitter are , and , respectively.
Fig.1.46 Simplified block diagram of the GPS
Fig.1.46 Simplified block diagram of the GPS Transmitter
【Example 1.15】Figures1.47 (a) and1.47 (b) show an example of signal waveforms of a code(shown in Fig.1.46) , and data(shown in Fig.1.46), respectively.
Find the waveform of .
【Solution】: The waveform of shown in Fig.1.46 is expressed as Fig.1.47( c ).
The following modulators are used in the GPS system.
(1) Binary Phase Shift Keying (BPSK) Modulator
Figure 1.48 shows the configuration of a BPSK modulator and its signal waveforms.
(2) Quadrature Phase Shift Keying（QPSK）Modulator
Figure 1.49 shows the configuration of a QPSK modulator. This modulator consists of two BPSK modulators, and has the following two data signal inputs: and. The output signal of this modulator is expressed as: .
B. Configurations of GPS Receiver
Figure 1.50 shows a block diagram of the GPS receiver. The GPS receiver consists of five principal components: an antenna, a receiver, an integration processor, a control and display units, and a power supply.
The user receiver determines at least pseudo ranges, and also determines pseudo range rates by the Doppler measurements of its own- clock frequency.
Figure 1.51 shows a block diagram of a vehicle navigation receiver.
The vehicle navigation receiver has auxiliary sensors for an integrated processor as shown in Fig.1.51, and then can calculate the optimized user position.
The digital road map is also used for looking-up the nearest street address.
1.4.5 Differential GPS Systems (21)
The Differential GPS (DGPS) is used for improving the positioning and timing performance of GPS user by means of one or more reference stations whose positions are precisely known. Figure 1.52 shows a differential GPS system configuration.
These systems can eliminate some of errors containing commonly in the user and the reference station. These errors are satellite clock errors, satellite position errors, tropospheric errors, and ionospheric errors.
1.4.6 Other navigation systems (21)
There exist other navigation systems except the GPS:
A. European Union Gallileo Satellite System
The Gallileo Satellite System (GSS) is developing by the European Union (EU). This system consists of 30 satellites in 23222 (Km) orbits. These satellites are usually broadcasting ranging codes and navigation data on L5-E5 (1164-1214MHz), E6 (1260-1300MHz), and E2-L1-E1 (1559-1591MHz) bands, and are fully compatible with the GPS system.
B. Russian Global Navigation Satellite System
The Russian Global Navigation Satellite System (GLONASS) is consists of 24 satellites in 19100(Km) orbits. These satellites are usually broadcasting same ranging code and navigation data in different frequencies on two frequency bands: 1246-1257 (MHz), and 1602-1616 (MHz), using a frequency division multiple access (FDMA) method.
C. Chinese Bei Dou Navigation System
This is the Chinese multistage satellite navigation program designed to Chinese military and civil users.
D. Japanese QZSS Program
This program is to intend the navigation services to address shortfalls in GPS satellite visibility in urban canyons and mountainous terrain.
1.5 Outlines of RFID Tags
1.5.1 Introduction (22)
A RFID (Radio Frequency IDetification) system consists of readers (interrogators)
and tags(transponders). A reader communicates with a tag by means of a wireless system and collects information attached in a tag.
There are three types of tags from their operating principles: a passive tag, a semi-passive tag, and an active tag.
1.5.2 Coupling of RFID Tags ( 22)
In the passive tags, there are coupling techniques of two different types:
a near field tag, and a far field tag.
1.5.3 Types of Passive Tags (22)
A. Near Field Tag
Figure 1.53 shows a block diagram of the near field tag system. The frequencies commonly used in this system are 128(KHz), and 13.56(MHz). A disadvantage of this system is that a large antenna coil is required.
The distance between the reader and the tags is expressed as follows:
where is the wavelength of radio waves (See 1.5.4 B).
B. Far Field Tag
Figure 1.54 shows a block diagram of the far field tag system. The operation frequencies used in this system are 860-960(MHz), or 2.45(GHz) in the UHF band.
The antenna of this reader (interrogator) is usually designed to the length of ( is the wavelength of radio waves).
The distance between the reader and the tags is expressed as follows:
where is the wavelength of radio waves (See 1.5.4B).
1.5.4 Near and Far Fields of radio waves (23 ),(24), (25)
For designing smaller sizes of tags, some knowledge of antenna pattern is the most important key points. So we will show here these outlines.
A. Electric and Magnetic Fields Intensities
(a) Electric Source Case
An infinitesimal electric dipole antenna (, is the wavelength of radio waves) is shown in Fig.1.55. Practically, this antenna can be constructed by a capacitor-plate in order to maintain the current uniformly on the antenna.
In Fig.1.55, the field components, , , and , and the field components,, , and radiated from this antenna, are expressed as follows:
where () is the length of this antenna, is the radial distance in the propagation of radio waves, is the intrinsic impedance of free space, is the antenna current, symbol means the definition, , and .
Furthermore, the field components, and express the intensities of the induction electric field, and static electric field, respectively.
The field components,, and express the intensities of the radiation electric field, the induction electric field and static electric field, respectively.
The field components, and express the intensities of the radiation magnetic field and the induction magnetic field, respectively.
(b) Magnetic Source Case
Figure 1.56 shows an infinitesimal magnetic dipole antenna. The field
components,, , and radiated from this antenna, are also expressed as follows:
, , ,
where is the surface area of the antenna, is the radial distance in the propagation of radio waves, is the intrinsic impedance of free space, is the antenna current, ,and . Furthermore, the field components, and express the intensities of the induction magnetic field, and static magnetic field, respectively.
The field components,, and express the intensities of the radiation magnetic field, the induction magnetic field and static magnetic field, respectively.
The field components, and express the intensities of the radiation electric field and the induction electric field, respectively.
【Example 1. 16】
In Fig.1.56, find the angle for which the coupling between the two loop
From this figure, and Eq. (1.36), we get the following equations:
(1), (2), (3).
From these equations,
B. Boundary between Near Field and Far Field
InFigs.1.53 and 1.54, when the angle between the transponder antenna and the tag antenna equals to the ninety degree, we get the following equations:
, ,, ,
From these equations, the distance where the induction field equals to the radiation field, is expressed as follows:
C. Numerical Examples of Boundary between Near Field and Far Field
Table1.2 shows several numerical examples of the boundary between the near field
and the far field intensities calculated by using Eq.(1.37).
1.5.5 Far Field Tags (25 ) , (26), (27)
A. Examples of UHF Tags
B. Approved Frequency ranges
Table 1. 3 shows the approved frequency ranges where the printers (transponders) are certified(See www.paxar.com).
1.5.6 Application Examples of Tags (22) ,(27)
Applications of tags are as follows: supply chain, access control, transport payment, E-pass ports, automotive security, livestock ID, automated libraries, health care,
detecting and locating buried unexploded ordnance (25) , etc,.
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1.1 Find the inverse Fourier transform of .
Let, then , and . As a result,
1.2 An actual analog to digital conversion can not be executed instantaneously, For this reason, an actual high precision analog to digital (A/D) converter includes a sample and hold (S/H) circuit as shown in Fig. 1.58. In this figure, the relationship between and is shown in Fig. 1.59.
Fig. 1.58 Configuration of an A/D converter including a
Fig. 1.58 Configuration of an A/D converter including a S/H circuit
In these two figures, determine and .
(1) , for , , for otherwise.
where , ＊denotes the operation of convolution.
1.3 Derive Eq.(1.8).
(i) If transmitting power with omni-directional were uniformly radiated in all direction of a free space, then the power density at a distance from the antenna would be expressed as follows:
(ii) The power is actually radiated from a beam antenna with gain . The power density at the center of beam is therefore expressed as follows:
(iii) The object with the radar cross section reflects some of the power toward the transmitting antenna, since the object operate as a reflector. The reflecting power is then expressed as follows:
(iv) A power density at the location of the transmitting antenna is expressed as follows:
(v) The receiving power is expressed as follows:
where is the effective area of the antenna.
(vi) The relationship between and of the antenna is expressed as follows:
whereis the wavelength of the transmitting signal and is the factor which expresses the efficiency of the antenna.
(vii) Using the results described above, the receiving power is expressed as follows:
1.4 Find the Fourier transform of :
(1) The inverse Fourier transform of .
Therefore 2, and 2
(2)Using the Euler’s formula, .
(3)From the result described above, we obtain
As described above, the spectrum of consists of two impulse components.
1.5 Find the Fourier transform of given by:
, , for , , for .
. Therefore .
1.６ Derive Eq.(1.35).
(A) Cartesian Coordinate System:
The vector potential A using the Cartesian coordinate system, is expressed as follows:
where ,and are the unit vectors aligned in the,and axes, and
, and are the components of aligned in the,andaxes, respectively.
In the case of Fig.1.55, the vector potential is expressed as:
where is the current flowing the length of the ideal infinitesimal dipole, is the permeability, is the radial distance from the origin of the coordinate system, respectively. The wave number is given as: .
(B) Spherical Coordinate System:
The vector potential A using the spherical coordinate system, is expressed as follows:
where ,andare the unit vectors aligned in the, and axes, and , and are the components of aligned in the, and axes,, respectively.
The relationships between the Cartesian coordinate system and the spherical coordinate system are given as follows:
(C) Vector Product:
In the spherical coordinate system, the vector product ∇×Ais expressed as follows:
(D) Calculation of Magnetic Fields:
The relationship between the magnetic field and the vector potential
is expressed as follows:
From the above equations, we can obtain the following equation:
From the above equation, the field components, ,and are expressed as follows:
where , , .
(G) Calculation of Electric Fields:
The relationship between the electric field and the vector potential is expressed as follows:
From the above equations, we can obtain the following relations:
From the above equations, the field components, , , and are expressed as follows:
where , .
(H) Components of Electric Fields:
From Eq. (14), the three electric field components are expressed as follows:.
(1) Static electric field :
(2) Induction electric field : ( 16 )
(3) Radiation electric field :
1.７ Derive Eq.(1.36).
(A) Transforming Current Source into Magnetic Source:
Table 1 shows the relationship between the current source and the magnetic source.
There are the duality between them.
Table 1 Transforming current source into magnetic
Table 1 Transforming current source into magnetic source
(B) Component of Magnetic Fields:
(1) By transforming Eq.(1.35 ),we get the following relations:
where , , .
(2) By transforming Eq.(1.35 ),we get the following relations:
(C) Component of Electric Fields:
By transforming Eq.(1.35 ),we get the following relations:
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