Communications: directive radio wave systems and devices (e.g. – Directive – Including a satellite
Reexamination Certificate
2003-01-13
2004-04-27
Issing, Gregory C. (Department: 3662)
Communications: directive radio wave systems and devices (e.g.,
Directive
Including a satellite
Reexamination Certificate
active
06727850
ABSTRACT:
This application claims priority to an application entitled “Apparatus and Method for Selecting Optimal Satellites in Global Positioning System” filed in the Korean Industrial Property Office on Jun. 12, 2002 and assigned Serial No. 2002-32955, the contents of which are hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to GPS (Global Positioning System), and in particular, to an apparatus and method for selecting optimal GPS satellites to locate an object.
2. Description of the Related Art
Along with today's dramatic development in personal, portable communication devices, a variety of additional services are supported. In particular, some countries have mandated the use of positioning devices such as GPS in mobile terminals to provide location-based services to users.
Many GPS satellites broadcast their ephemeredes and system time, circling the earth in predetermined orbits, so that GPS receivers can determine their positions. The orbits of GPS satellites are carefully chosen so that at least four of them can be observed around the earth to allow the locations, velocities, and clock errors of the GPS receivers to be calculated. The GPS receivers can trace their positions with an error of 20 or less meters in urban areas.
Navigation data broadcasted from each satellite contains the PRN (Pseudo-Random Noise) code of the satellite corresponding to its satellite ID. Since the GPS navigation message is transmitted in CDMA (Code Division Multiple Access) format, a GPS receiver can receive the navigation data from each satellite accurately. The GPS receiver calculates its position using the navigation data. With the use of its internal algorithm, the GPS receiver tracks GPS satellite signals. Once it tracks one satellite signal, the GPS receiver can achieve information about the relative positions of other satellites using the received satellite orbit infomation. Thus the GPS receiver can track signals from all available satellites within a short period of time. Recently, the A-GPS (Assisted-GPS) is widely used which enables a GPS receiver to receive the ephemeris and timing information from a base station. Therefore, information of all available satellites is immediately available to the GPS receiver.
In general, a GPS receiver on the ground can observe 6 to 12 satellites simultaneously. To initially acquire CDMA signals from the satellites, a typical GPS receiver is required to search a wide range of frequency and code for each satellite signal. This search process is a major time-consuming factor that determines time to first fix (TTFF).
The GPS receiver can acquire at least 4 satellite signals more rapidly by assigning a plurality of independent channels to track the satellite signals. However, a system such as a small-sized portable terminal having a limited size uses a relatively small number of hardware channels and, in some cases, assigns multiple hardware channels to one satellite to reduce the TTFF.
In this case, it is difficult to track all the satellites that are visible to the GPS receiver because of the limited number of hardware channels. Thus, the GPS receiver selectively tracks a subset of visible satellites. The accuracy of a navigational solution, when a fixed number of satellites is to be selected, depends mainly on the quality of the subset (GDOP) that is being selected. Accordingly, a number of methods of selecting satellites that minimizes the positioning error of the GPS receiver (hereinafter, referred to as optimal satellites) have been proposed.
The primary requirements for optimal satellites are that they must minimize GDOP (Geometric Dilution Of Precision) and that their signals can actually be acquired through tracking. If GDOP is not minimized, position error could increase by a factor of five or more in some cases.
A unit vector pointing from a GPS receiver to a satellite i is defined as an LOS (Line-Of-Sight) vector los
i
. If there are N visible satellites in the three-dimensional space, their coordinates can be expressed as an N×3 (x, y, z coordinates)-LOS matrix of
H
=
[
x
1
y
1
z
1
x
2
y
2
z
2
…
x
N
y
N
z
N
]
=
[
los
1
los
2
…
los
N
]
(
1
)
where H represents line of sight matrix for N visible satellites.
When n satellites are to be selected from N number of the total visible satellites,
N
C
n
number of satellite combinations can be produced where
N
C
n
represents the number of combinations of the n selected satellites among the N visible satellites. Then, T (T=
N
C
n
) number of n×3 LOS matrices h
1
, h
2
, . . . , h
T
are formed. The selected line of sight (LOS) matrices are represented by h. Using the j
th
combination h
j
, the position of the GPS receiver is calculated by using the following linearized equation
&dgr;{overscore (&PHgr;)}=
h
j
&dgr;{overscore (x)}+{overscore (&ngr;)}
(2)
where &dgr;{overscore (&PHgr;)} is an (n×1) vector containing measurements received from satellites, &dgr;{overscore (x)} is a three-dimensional vector with which an intended navigational solution is updated, and {overscore (&ngr;)} is an (n×1) vector indicating the measurement noise of the satellite signals (Ev=0 and Evv
T
=&sgr;
2
I. Here, &sgr; is the noise standard deviation and I is an identity matrix).
The estimation procedure of the &dgr;{overscore (x)} is
&dgr;{overscore (x)}=(
h
j
T
h
j
)
−1
h
j
T
&dgr;{overscore (&PHgr;)}−(
h
j
T
h
j
)
−1
h
j
T
{overscore (&ngr;)}
&dgr;{overscore (x)}=(
h
j
T
h
j
)
−1
h
j
T
&dgr;{overscore (&PHgr;)} (3)
The influence of the measurement error {overscore (&ngr;)} on the navigational solution is calculated by
&ngr;
e
=(
h
j
T
h
j
)
−1
h
j
T
{overscore (&ngr;)} (4)
The statistics of the effective noise &ngr;
e
is
E&ngr;
e
=E
[(
h
j
T
h
j
)
−1
h
j
T
{overscore (&ngr;)}]=0
E&ngr;
e
&ngr;
e
T
=E
[(
h
j
T
h
j
)
−1
h
j
T
{overscore (&ngr;)}&ngr;
T
h
j
(
h
j
T
h
j
)
−1
]=(
h
j
T
h
j
)
−1
&sgr;
2
(5)
From Eq. (5) GDOP is defined as
GDOP={square root over (TRACE [(
h
j
T
h
j
)
−1
])} (6)
Where TRACE is an operator that indicates the sum of the diagonal elements of the matrix, which is equal to the sum of all Eigen-values. It is noted from Eq. (6) that the measurement error of the GPS receiver is influenced by the geometrical positions h
j
of satellites. If GDOP is less than 1, the effective noise standard deviation is less than the measurement noise standard deviation. If GDOP is larger than 1, the former is higher than the latter by a multiple of GDOP. Therefore, it is desired to select the combination h that minimizes GDOP in order to achieve an optimal navigational solution.
FIG. 1
is a flowchart illustrating a conventional satellite selection method for optimal satellite selection. In the optimal satellite selection, GDOP is calculated for all possible subsets of the available satellites and the subset that minimizes the GDOP is selected by comparing the GDOPs of all possible subsets. It is assumed in this process that a GPS receiver has already received information about the relative positions of all the other satellites from an initially observed satellite.
Referring to
FIG. 1
, the GPS receiver calculates N unit vectors (LOS vectors) representing the three-dimensional coordinates of N available/visible satellites with respect to the GPS receiver, using the relative positions of the satellites in step S
10
and generates T (=
N
C
n
) LOS combinations h
1
, h
2
, . . . , h
T
from the N LOS vectors in step S
20
. The GPS receiver sets a variable k to 1 in step S
30
. The variable k is used to identify a LOS combination. The GPS receiver calculates the GDOP for a kth combination, GDOP(k) by TRACE(h
k
T
h
k
)
−1
in step S
40
and stores it in step S
50
. After calculating the GDOPs for all T number of combinations, increasing the variable
How Jonathan P.
Park Chan-Woo
Dilworth & Barrese LLP
Issing Gregory C.
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