U.S. patent application number 09/851239 was filed with the patent office on 2001-11-29 for method for determining the position of an object, a positioning system, a receiver and an electronic device.
Invention is credited to Kontola, Ilkka, Syrjarinne, Paula.
Application Number | 20010045905 09/851239 |
Document ID | / |
Family ID | 8558345 |
Filed Date | 2001-11-29 |
United States Patent
Application |
20010045905 |
Kind Code |
A1 |
Syrjarinne, Paula ; et
al. |
November 29, 2001 |
Method for determining the position of an object, a positioning
system, a receiver and an electronic device
Abstract
The invention relates to a method for determining the position
of an object to be searched for. The method applies a receiver
(RX1) for the object to be searched substantially in the vicinity
of the object to be searched, a receiver (RX2) for a searcher, with
respect to which the position of the object to be searched is
determined, and satellites (SV1-SV4) from which a code-modulated
random spectrum signal is transmitted, and positioning data of the
satellites are determined. In the method, a default position (.left
brkt-bot.{circumflex over (x)}.sub.S,.sub.S,{circumflex over
(z)}.sub.S,{circumflex over (t)}.sub.S.right brkt-bot.) is
determined for the receiver (RX2) of the searcher; pseudo ranges
(.rho..sub.i1) to at least three satellites (SV1-SV4) are measured
on the basis of signals received from the satellites in the
receiver (RX1) of the object to be searched; pseudo ranges
(.rho..sub.i2) to at least said three satellites (SV1-SV4) are
measured on the basis of signals received from the satellites in
the receiver (RX2) of the searcher; and at least the direction and
distance (.left brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right
brkt-bot.) of the object to be searched from the receiver (RX2) of
the searcher are determined.
Inventors: |
Syrjarinne, Paula; (Tampere,
FI) ; Kontola, Ilkka; (Julkujarvi, FI) |
Correspondence
Address: |
Clarence A. Green
Perman & Green, LLP
425 Post Road
Fairfield
CT
06430
US
|
Family ID: |
8558345 |
Appl. No.: |
09/851239 |
Filed: |
May 8, 2001 |
Current U.S.
Class: |
342/357.31 |
Current CPC
Class: |
G01S 5/0009 20130101;
G01S 2205/008 20130101; G01S 5/12 20130101; G01S 19/51
20130101 |
Class at
Publication: |
342/357.08 |
International
Class: |
G01S 005/14 |
Foreign Application Data
Date |
Code |
Application Number |
May 8, 2000 |
FI |
20001069 |
Claims
The present invention is not limited solely to the embodiments
presented above, but it can be modified within the scope of the
appended claims.
1. A method for determining the position of an object to be
searched, which method applies a receiver (RX1) for an object to be
searched, substantially in the vicinity of the object to be
searched, a receiver (RX2) for a searcher, with respect to which
the position of the object to be searched is determined, and
satellites (SV1-SV4) from which a code-modulated random spectrum
signal is transmitted; and determining positioning data of the
satellites, characterized in that in the method, at least the
following steps are performed: determining a default position
(.left brkt-bot.{circumflex over (x)}.sub.S,.sub.S,{circumflex over
(z)}.sub.S,{circumflex over (t)}.sub.S.right brkt-bot.) for the
receiver (RX2) of the searcher, measuring pseudo ranges
(.rho..sub.i1) to at least three satellites (SV1-SV4) on the basis
of signals received from the satellites, in the receiver (RX1) of
the object to be searched, measuring pseudo ranges (.rho..sub.i2)
to at least said three satellites (SV1-SV4) on the basis of signals
received from the satellites, in the receiver (RX2) of the
searcher, and determining at least the direction and distance
(.left brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right
brkt-bot.) of the object to be searched from the receiver (RX2) of
the searcher.
2. The method according to claim 1, characterized in that the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched are determined in the receiver (RX2) of
the searcher, wherein information on the measured pseudo ranges is
transmitted from the receiver (RX1) of the object to be searched to
the receiver (RX2) of the searcher.
3. The method according to claim 1 or 2, characterized in that the
method applies a communication network, wherein a data transmission
link is formed from the receiver (RX1) to be searched and from the
receiver (RX2) of the searcher to said communication network, at
least for the transmission of said information on pseudo
ranges.
4. The method according to claim 1, 2 or 3, characterized in that
the method also comprises at least the following steps: determining
the geometrical distance (r.sub.i) from the receiver (RX2) of the
searcher to said at least three satellites (SV1-SV4) on the basis
of the positioning data and said default position, correcting the
pseudo ranges (.epsilon..sub.i) measured in the receiver (RX1) of
the object to be searched and in the receiver (RX2) of the searcher
on the basis of the determined geometrical distance, and using the
corrected pseudo ranges for determining the direction and distance
(.left brkt-bot..DELTA.x,.DELT- A.y,.DELTA.z,.DELTA.t.right
brkt-bot.) of the object to be searched from the receiver (RX2) of
the searcher.
5. The method according to any of the claims 1 to 4, characterized
in that the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE- LTA.t.right brkt-bot.) of
the object to be searched are determined by determining the
position of the receiver of the object to be searched and by
calculating the difference between the default position of the
receiver (RX2) of the searcher and the position of the receiver
(RX1) of the object to be searched.
6. The method according to any of the claims 1 to 5, characterized
in that the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE- LTA.t.right brkt-bot.) of
the object to be searched are determined by Taylor's method of
linearization.
7. The method according to claim 6, characterized in that the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched are determined by solving the set of
equations: 9 iL = iS - x i - x S S x - y i - y S S y - z i - z S S
z + c t , i = 1 , , n ,in which n=the number of satellites
(SV1-SV4) used for positioning, c=the speed of light, .left
brkt-bot.x.sub.S,y.sub.S,z.sub.S.right brkt-bot.=the position of
the receiver (RX2) of the searcher, .left
brkt-bot.x.sub.i,y.sub.i,z.sub.i=th- e position of the satellites
at the moment of transmission of the signal used in the calculation
of the pseudo ranges, and .DELTA.t=the clock error.
8. The method according to any of the claims 1 to 5, characterized
in that the pseudo ranges are measured by the following formulas:
10 iS = ( x i - x S ) 2 + ( y i - y S ) 2 + ( z i - z S ) 2 iL = (
x i - x L ) 2 + ( y i - y L ) 2 + ( z i - z L ) 2 in which i=1, . .
. , n n=the number of satellites (SV1-SV4) used in the positioning,
.left brkt-bot.x.sub.S,y.sub.S,z.sub.S.right brkt-bot.=the position
of the receiver (RX2) of the searcher, and .left
brkt-bot.x.sub.i,y.sub.i,z.sub.- i.right brkt-bot.=the position of
the satellites at the moment of transmission of the signal used in
the calculation of the pseudo ranges, wherein, for determining the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher,
at least the following steps are performed: a squaring step for
forming the squares of the measured pseudo ranges
.rho..sup.2iS=(x.sub.i-x.sub.S).sup-
.2+(y.sub.i-y.sub.S).sup.2+(z.sub.i-z.sub.S).sup.2,
.rho..sup.2iL=(x.sub.i-x.sub.L).sup.2+(y.sub.i-y.sub.L).sup.2+(z.sub.i-z.-
sub.L).sup.2 and their difference .rho..sup.2iL-.rho..sup.2iS, an
elimination step for eliminating unknown terms from the formulas
formed in the squaring step, and a solution step for solving the
direction and distance from the formulas processed in the
elimination step.
9. A positioning system comprising a receiver (RX1) for an object
to be searched, substantially located in the vicinity of the object
to be searched; a receiver (RX2) for a searcher, in relation to
which the position of the object to be searched is arranged to be
determined; and satellites (SV1-SV4) comprising means for
transmitting a code-modulated random spectrum signal and means for
determining positioning data of the satellites; characterized in
that the positioning system also comprises at least: means (BS) for
determining the default position (.left brkt-bot.{circumflex over
(x)}.sub.S,.sub.S,{circumflex over (z)}.sub.S,{circumflex over
(t)}.sub.S.right brkt-bot.) of the receiver (RX2) of the searcher,
means (CH1-CH4, 2) for measuring pseudo ranges (.rho..sub.i1)
between the receiver (RX1) to be searched and at least three
satellites (SV1-SV4) on the basis of signals received from the
satellites, means (CH1-CH4, 2) for measuring pseudo ranges
(.rho..sub.i2) between the receiver (RX2) of the searcher and said
at least three satellites (SV1-SV4) on the basis of signals
received from the satellites, and means (5) for determining the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the
searcher.
10. The positioning system according to claim 9, characterized in
that the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.- t.right brkt-bot.) of
the object to be searched is arranged to be determined in the
receiver (RX2) of the searcher, wherein the positioning system also
comprises means (9, NW) for transmitting information on the
measured pseudo ranges from the receiver (RX1) to be searched to
the other receiver (RX2).
11. The positioning system according to claim 9 or 10,
characterized in that the positioning system also comprises a
communication network (9, NW) and means (9, BS) for forming a data
transmission link from the receiver (RX1) to be searched and from
the receiver (RX2) of the searcher to said communication network,
at least for transmitting said information on the pseudo
ranges.
12. The positioning system according to claim 9, 10 or 11,
characterized in that it also comprises: means (5) for determining
the geometrical distance (r.sub.i) between the receiver (RX2) of
the searcher and said at least three satellites (SV1-SV4) on the
basis of the positioning data and said default position, means (5)
for correcting (.epsilon..sub.i) the pseudo ranges measured in the
receiver (RX1) of the object to be searched and in the receiver
(RX2) of the searcher on the basis of the determined geometrical
distance, and means (9, BS) for using the corrected pseudo ranges
in determining the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the
searcher.
13. The positioning system according to any of the claims 9 to 12,
characterized in that the means (5) for determining the direction
and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher
comprise means (9, BS) for determining the position of the receiver
of the object to be searched and means (5) for calculating the
difference between the default position of the receiver (RX2) of
the searcher and the position of the receiver (RX1) of the object
to be searched.
14. The positioning system according to any of the claims 9 to 13,
characterized in that the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher
is arranged to be determined by Taylor's method of
linearization.
15. The positioning system according to claim 14, characterized in
that the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE- LTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher
is arranged to be determined by solving the set of equations: 11 iL
= iS - x i - x S S x - y i - y S S y - z i - z s S z + c t , i = 1
, , n , in which n=the number of satellites (SV1-SV4) used in the
positioning, c=the speed of light, .left
brkt-bot.x.sub.S,y.sub.S,z.sub.S.right brkt-bot.=the position of
the receiver (RX2) of the searcher, .left
brkt-bot.x.sub.i,y.sub.i,z.sub.- i.right brkt-bot.=the position of
the satellites at the moment of transmission of the signal used in
the calculation of the pseudo ranges, and .DELTA.t=the clock
error.
16. The positioning system according to any of the claims 9 to 13,
characterized in that the pseudo ranges are arranged to be measured
by the following formulas: 12 iS = ( x i + x S ) 2 + ( y i + y S )
2 + ( z i - z S ) 2 iL = ( x i + x L ) 2 + ( y i + yL ) 2 + ( z i -
z L ) 2 in which i=1, . . . , n n=the number of satellites
(SV1-SV4) used in the positioning, .left
brkt-bot.x.sub.S,y.sub.S,z.sub.S.right brkt-bot.=the position of
the receiver (RX2) of the searcher, and .left
brkt-bot.x.sub.i,y.sub.i,z.sub.i.right brkt-bot.=the position of
the satellites at the moment of transmission of the signal used in
the calculation of the pseudo ranges, wherein, for determining the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher,
at least the following steps are performed: a squaring step for
forming the squares of the measured pseudo ranges
.rho..sup.2iS=(x.sub.i--
x.sub.S).sup.2+(y.sub.i-y.sub.S).sup.2+(z.sub.i-z.sub.S).sup.2,
.rho..sup.2iL=(x.sub.i-x.sub.L).sup.2+(y.sub.i-y.sub.L).sup.2+(z.sub.i-z.-
sub.L).sup.2 and their difference .rho..sup.2iL-.rho..sup.2iS, an
elimination step for eliminating unknown terms from the formulas
formed in the squaring step, and a solution step for solving the
direction and distance from the formulas processed in the
elimination step.
17. A receiver (RX2) for a searcher, comprising means (CH1-CH4) for
receiving code-modulated random spectrum signals transmitted by
satellites (SV1-SV4), and means (CH1-CH4, 9) for determining
positioning data of the satellites, characterized in that the
receiver (RX2) also comprises at least: means (BS) for determining
the default position (.left brkt-bot.{circumflex over
(x)}.sub.S,.sub.S,{circumflex over (z)}.sub.S,{circumflex over
(t)}.sub.S.right brkt-bot.) of the receiver (RX2) of the searcher,
means (CH1-CH4, 2) for receiving pseudo ranges (.rho..sub.i1)
transmitted by a receiver (RX1) for an object to be searched,
located substantially in the vicinity of the object to be searched,
measured from the receiver (RX1) to be searched on the basis of
signals received from at least three satellites (SV1-SV4), means
(CH1-CH4, 2) for measuring pseudo ranges (.rho..sub.i2) from the
receiver (RX2) to said at least three satellites (SV1-SV4) on the
basis of signals received from the satellites, and means (5) for
determining at least the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.- t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the
searcher.
18. A receiver (RX2) for a searcher, which is arranged to be used
in a positioning system comprising a receiver (RX1) for an object
to be searched, placed substantially in the vicinity of the object
to be searched for, satellites (SV1-SV4) comprising means for
transmitting a code-modulated random spectrum signal, and means
(CH1-CH4, 9) for determining positioning data of the satellites,
and which receiver (RX2) comprises means for receiving the
code-modulated random spectrum signals transmitted by the
satellites (SV1-SV4), characterized in that the receiver (RX2) of
the searcher also comprises at least: means (CH1-CH4, 2) for
measuring pseudo ranges (.rho..sub.i2) from the receiver (RX2) of
the searcher to said at least three satellites (SV1-SV4) on the
basis of signals received from the satellites, and means (CH1-CH4,
2) for transmitting said measured pseudo ranges (.rho..sub.i2) to
the positioning system, and means (CH1-CH4, 2) for receiving data
on at least the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE- LTA.t.right brkt-bot.) of
the object to be searched from the positioning system, wherein the
positioning system also comprises: means (BS) for determining the
default position (.left brkt-bot.{circumflex over
(x)}.sub.S,.sub.S,{circumflex over (z)}.sub.S,{circumflex over
(t)}.sub.S.right brkt-bot.) of the receiver (RX2) of the searcher,
means (BS) for receiving the pseudo ranges (.rho..sub.i1)
transmitted by the receiver (RX1) of the object to be searched,
placed substantially in the vicinity of the object to be searched,
the pseudo ranges (.rho..sub.i1) being measured between the
receiver (RX1) to be searched and at least three satellites
(SV1-SV4) on the basis of signals received from the satellites,
means (BS) for receiving said pseudo ranges (.rho..sub.i2) measured
in the receiver of the searcher, means (5) for determining at least
the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA- .z,.DELTA.t.right brkt-bot.) of
the object to be searched from the receiver (RX2) of the searcher,
and means (BS) for transmitting data on at least the direction and
distance (.left brkt-bot..DELTA.x,.DELTA.y,.DE-
LTA.z,.DELTA.t.right brkt-bot.) of the object to be searched to the
receiver (RX2) of the searcher.
19. An electronic device comprising a receiver (RX2) for a
searcher, means (CH1-CH4) for receiving code-modulated random
spectrum signals transmitted by satellites (SV1-SV4), and means
(CH1-CH4, 9) for determining positioning data of the satellites,
characterized in that the electronic device also comprises at
least: means (BS) for determining the default position (.left
brkt-bot.{circumflex over (x)}.sub.S,.sub.S,{circ- umflex over
(z)}.sub.S,{circumflex over (t)}.sub.S.right brkt-bot.) of the
receiver (RX2) of the searcher, means (CH1-CH4, 2) for receiving
pseudo ranges (.rho..sub.i1) transmitted by a receiver (RX1) for an
object to be searched, placed substantially in the vicinity of the
object to be searched, the pseudo ranges (.rho..sub.i1) being
measured between the receiver (RX1) to be searched and at least
three satellites (SV1-SV4) on the basis of signals received from
the satellites, means (CH1-CH4, 2) for measuring pseudo ranges
(.rho..sub.i2) between the receiver (RX2) of the searcher and said
at least three satellites (SV1-SV4) on the basis of signals
received from the satellites, and means (5) for determining at
least the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA- .z,.DELTA.t.right brkt-bot.)
between the object to be searched and the receiver (RX2) of the
searcher.
20. The electronic device according to claim 19, characterized in
that it also comprises means (8, 9, 10, 11, 12a, 12b, 12c) for
performing functions of a mobile station.
21. An electronic device which is arranged to be used in a
positioning system comprising a receiver (RX1) for an object to be
searched, placed substantially in the vicinity of the object to be
searched, satellites (SV1-SV4) which comprise means for
transmitting a code-modulated random spectrum signal and means
(CH1-CH4, 9) for determining positioning data of the satellites,
and which electronic device comprises a receiver (RX2) for a
searcher and means (CH1-CH4) for receiving code-modulated random
spectrum signals transmitted by the satellites (SV1-SV4),
characterized in that the electronic device also comprises at
least: means (CH1-CH4, 2) for measuring pseudo ranges (.rho.i2)
between the receiver (RX2) of the searcher and said at least three
satellites (SV1-SV4) on the basis of signals received from the
satellites, and means (CH1-CH4, 2) for transmitting said measured
pseudo ranges (.rho..sub.i2) to the positioning system, and means
(CH1-CH4, 2) for receiving data on at least the direction and
distance (.left brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE-
LTA.t.right brkt-bot.) of the object to be searched from the
positioning system, wherein the positioning system also comprises:
means (BS) for determining the default position (.left
brkt-bot.{circumflex over (x)}.sub.S,.sub.S,{circumflex over
(z)}.sub.S,{circumflex over (t)}.sub.S.right brkt-bot.) of the
receiver (RX2) of the searcher, means (BS) for receiving the pseudo
ranges (.rho..sub.i1) transmitted by the receiver (RX1) of the
object to be searched, placed substantially in the vicinity of the
object to be searched, the pseudo ranges (.rho..sub.i1) being
measured between the receiver (RX1) of the object to be searched
and at least three satellites (SV1-SV4) on the basis of signals
received from the satellites, means (BS) for receiving said pseudo
ranges (.rho..sub.i2) measured in the receiver of the searcher,
means (5) for determining at least the direction and distance
(.left brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right
brkt-bot.) of the object to be searched from the receiver (RX2) of
the searcher, and means (BS) for transmitting data on at least the
direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot.) of
the object to be searched to the receiver (RX2) of the
searcher.
22. The electronic device according to claim 21, characterized in
that it also comprises means (8, 9, 10, 11, 12a, 12b, 12c) for
performing functions of a mobile station.
23. A computing server which is arranged to be used in a
positioning system comprising a receiver (RX1) for an object to be
searched, placed substantially in the vicinity of the object to be
searched, satellites (SV1-SV4) which comprise means for
transmitting a code-modulated random spectrum signal and means
(CH1-CH4, 9) for determining positioning data of the satellites,
and which electronic device comprises a receiver (RX2) for a
searcher and means (CH1-CH4) for receiving code-modulated random
spectrum signals transmitted by the satellites (SV1-SV4),
characterized in that the electronic device also comprises at
least: means (CH1-Ch4, 2) for measuring pseudo ranges
(.rho..sub.i2) between the receiver (RX2) of the searcher and said
at least three satellites (SV1-SV4) on the basis of signals
received from the satellites, and means (CH1-CH4, 2) for
transmitting said measured pseudo ranges (.rho..sub.i2) to the
positioning system, and means (CH1-CH4, 2) for receiving data on at
least the direction and distance (.left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DE- LTA.t.right brkt-bot.) of
the object to be searched from the positioning system, wherein the
positioning system also comprises: means (BS) for determining the
default position (.left brkt-bot.{circumflex over
(x)}.sub.S,.sub.S,{circumflex over (z)}.sub.S,{circumflex over
(t)}.sub.S.right brkt-bot.) of the receiver (RX2) of the searcher.
Description
[0001] A method for determining the position of an object, a
positioning system, a receiver and an electronic device
[0002] The present invention relates to a method for determining
the position of an object according to the preamble of the appended
claim 1, a positioning system according to the preamble of the
appended claim 9, a searcher receiver according to the preamble of
the appended claim 17, a searcher receiver according to the
preamble of the appended claim 18, an electronic device according
to the preamble of the appended claim 19, an electronic device
according to the preamble of the appended claim 21, and a computing
server according to the preamble of the appended claim 23.
[0003] One known positioning system is the GPS system (Global
Positioning System) which presently comprises more than 20
satellites, of which 4 or more are simultaneously within the sight
of a receiver; for example in Finland, depending on the latitude,
even more than 14 satellites can be detected simultaneously, thanks
to visibility across the North Pole. These satellites transmit e.g.
positioning data of the satellite, as well as data on the time of
the satellite. The receiver to be used in positioning normally
deduces its position by calculating the transmission time of a
signal transmitted simultaneously from several satellites belonging
to the positioning system to the receiver. For the positioning, the
receiver must typically receive the signal of at least four visible
satellites to make it possible to compute the position.
[0004] Each satellite of the GPS system transmits a so-called L1
signal at a carrier frequency of 1575.42 MHz. This frequency is
also indicated with 154f.sub.0, where f.sub.0=10.23 MHz.
Furthermore, the satellites transmit an L2 signal at a carrier
frequency of 1227.6 MHz, i.e. 120f.sub.0. In the satellite, the
modulation of these signals is performed with at least one pseudo
sequence. This pseudo sequence is different for each satellite. As
a result of the modulation, a code-modulated wideband signal is
generated. The modulation technique used makes it possible in the
receiver to separate the signals transmitted from different
satellites, although the carrier frequencies used in the
transmission are substantially the same. This modulation technique
is called code division multiple access (CDMA). In each satellite,
for modulating the L1 signal, the pseudo sequence used is e.g. a
so-called C/A code (Coarse/Acquisition code), which is a Gold code.
Each GPS satellite transmits a signal by using an individual C/A
code. The codes are formed as a modulo-2 sum of two 1023 bit binary
sequences. The first binary sequence G1 is formed with a polynome
X.sup.10+X.sup.3+1, and the second binary sequence G2 is formed by
delaying the polynome X.sup.10+X.sup.9+X.sup.8+X.sup.6+X.sup.3+-
X.sup.2+1 in such a way that the delay is different for each
satellite. This arrangement makes it possible to produce different
C/A codes with an identical code generator. The C/A codes are thus
binary codes whose chipping rate in the GPS system is 1.023 MHz.
The C/A code comprises 1023 chips, wherein the iteration time of
the code (epoch) is 1 ms. The carrier of the L1 signal is further
modulated with navigation information at a bit rate of 50 bit/s.
The navigation information comprises information about the health
of the satellite, its orbit, time data, etc.
[0005] During their operation, the satellites monitor the condition
of their equipment. The satellites may use for example so-called
watch-dog operations to detect and report possible faults in the
equipment. The errors and malfunctions can be instantaneous or
longer lasting. On the basis of the health data, some of the faults
can possibly be compensated for, or the information transmitted by
a malfunctioning satellite can be totally disregarded. Furthermore,
in a situation in which the signal of more than four satellites can
be received, different satellites can be weighted differently on
the basis of the health data. Thus, it is possible to minimize the
effect of errors on measurements, possibly caused by satellites
which seem unreliable.
[0006] To detect the signals of the satellites and to identify the
satellites, the receiver must perform synchronization, whereby the
receiver searches for the signal of each satellite at the time and
attempts to be synchronized and locked to this signal so that the
data transmitted with the signal can be received and
demodulated.
[0007] The positioning receiver must perform the synchronization
e.g. when the receiver is turned on and also in a situation in
which the receiver has not been capable of receiving the signal of
any satellite for a long time. Such a situation can easily occur
e.g. in portable devices, because the device is moving and the
antenna of the device is not always in an optimal position in
relation to the satellites, which impairs the strength of the
signal coming to the receiver. Also, in urban areas, buildings
affect the signal to be received, and furthermore, so-called
multipath propagation can occur, wherein the transmitted signal
comes to the receiver along different paths, e.g. directly from the
satellite (line-of-sight) and also reflected from buildings. This
multipath propagation causes that the same signal is received as
several signals with different phases.
[0008] The positioning arrangement has two primary functions:
[0009] 1. to calculate the pseudo range between the receiver and
the different GPS satellites, and
[0010] 2. to determine the position of the receiver by utilizing
the calculated pseudo ranges and the position data of the
satellites. The position data of the satellites at each time can be
calculated on the basis of the Ephemeris and time correction data
received from the satellites.
[0011] The distances to the satellites are called pseudo ranges,
because the time is not accurately known in the receiver. The
pseudo range can be computed by measuring the pseudo range lags
between the signals from different satellites. Because time is not
known with absolute precision, the position and the time must be
found out preferably by iteration of the measured data with a
linearized set of equations. Thus, the determinations of the
position and of the time are iterated until a sufficient precision
has been found with respect to the time and position.
[0012] After the receiver has been synchronized with the received
signal, the information transmitted in the signal is demodulated to
find out e.g. the Ephemeris and time data transmitted from the
satellites.
[0013] Positioning systems and positioning receivers of prior art
are intended for finding out the position of one object only, i.e.
the positioning receiver. However, in practice, situations may
occur in which it should be possible to determine the direction and
distance between one positioning point and an object. For example,
when a mother loses eye contact to her child, the mother should be
able to find out in which direction and how far the child has gone.
In general, when a searcher is searching for an object, it is
primarily these direction and distance data and not the absolute
coordinates that are significant for the searcher. If such a
problem could be solved by using equipment of prior art, a
positioning receiver on the object to be found should transmit
positioning data to the positioning receiver of the searcher. Thus,
the positioning receiver of the searcher could compute the
direction vector on the basis of the positioning data of the object
and on the searcher. In practice, the accuracy of such a
determination is not always the best possible. In both
positionings, errors may occur which in the worst case are
accumulated upon calculating the direction vector between the
positions. Furthermore, this method has the drawback that two
different receivers may use signals transmitted from different
satellites for their positioning, wherein the significance of
non-compatible interference may increase.
[0014] The most significant sources of error affecting the
calculation of the pseudo ranges include the atmosphere,
intentional inaccuracy, multi-path propagation, and the receiver.
Some of the atmospheric effects are dependent on the frequency to
at least some extent. However, atmospheric effects cannot be
significantly compensated for in receivers intended for civil use,
because for civil use there is only one carrier frequency (L1)
available to be received in the positioning receiver. The
organization maintaining the GPS satellite positioning system (U.S.
Department of Defence) intentionally provides selective
availability (SA) of the signals of the satellites, which impairs
the accuracy of the positioning. This inaccuracy is induced either
by changing the positioning data transmitted by the satellites or
by inducing inaccuracy in the clock of the satellite. As a result
of multipath propagation, the receiver may be erroneously
synchronized with a multipath propagated signal instead of a
directly propagated signal. The path propagated by such a signal is
longer than that of a directly propagated signal, wherein the
positioning is distorted to some extent. Furthermore, errors can be
caused by unideal properties of the positioning receiver. For
example, errors can be caused by a deviation of the reference clock
of the receiver from the GPS time. The measurement results are also
distorted by asymmetries on the different receiving channels of the
positioning receiver.
[0015] Said primary sources of error can further be divided into
common-mode errors and non-common-mode errors. Errors caused by
atmospheric effects and said selective availability are common-mode
errors. These errors can be assumed to be substantially the same in
the vicinity of the receiver. Thus, common-mode errors have
substantially the same effect on all the positioning receivers in
the same area, provided that they receive the signals of the same
satellites. Multipath propagation and unideal properties of the
receiver are non-common-mode sources of error, wherein these
sources of error can also cause different errors in positioning
devices in the same area.
[0016] It is an aim of the present invention to provide a method
for positioning another GPS receiver to be found in an electronic
device performing the searching and comprising at least a
positioning receiver. The invention is based on the idea that the
searching device finds the direction and distance of the object to
be searched with respect to the searcher by utilizing the fact that
the common-mode errors can be eliminated. Thus, to start the
computing, the position of the searcher is used as the initial
position of the object to be found. More precisely, the method
according to the present invention is characterized in what will be
presented in the characterizing part of the appended claim 1. The
positioning system according to the present invention is
characterized in what will be presented in the characterizing part
of the appended claim 9. The receiver according to an advantageous
embodiment of the present invention is characterized in what will
be presented in the characterizing part of the appended claim 17.
The receiver according to another advantageous embodiment of the
present invention is characterized in what will be presented in the
characterizing part of the appended claim 18. The electronic device
according to an advantageous embodiment of the present invention is
characterized in what will be presented in the characterizing part
of the appended claim 19. The electronic device according to
another advantageous embodiment of the present invention is
characterized in what will be presented in the characterizing part
of the appended claim 21. The computing server according to the
present invention is characterized in what will be presented in the
characterizing part of the appended claim 23.
[0017] Considerable advantages are achieved with the present
invention when compared with methods and receivers of prior art.
Using the method of the invention, the direction and distance of an
object to be searched from the searcher can be determined in a
significantly more accurate way than is possible to achieve with
methods and systems of prior art.
[0018] The present invention will be described in more detail with
reference to the appended drawings, in which
[0019] FIG. 1 shows, in a reduced block chart, a receiver to be
searched and in which the method of the invention can be
applied,
[0020] FIG. 2 shows, in a principle view, the effect of various
sources of error on the determination of the position to be
searched by a preferred embodiment of the method of the invention,
and
[0021] FIG. 3 shows, in a reduced principle view, the positioning
system according to a preferred embodiment of the invention.
[0022] FIG. 1 shows a positioning receiver RX1, RX2 of an
electronic device ED according to a preferred embodiment of the
invention, in which a signal to be received via a first antenna 1
is converted preferably to an intermediate frequency or directly to
a carrier frequency on receiving channels CH1-CH4. The receiver
RX1, RX2 of FIG. 1 comprises four receiving channels CH1-CH4, but
it is obvious that the number of channels can be different from
that presented here. The signal converted to the intermediate
frequency or carrier frequency in the receiving channels CH1-CH4
comprises two components, known as such: I and Q components, with a
phase difference of approximately 900 therebetween. These analog
signal components, converted to the intermediate frequency, are
digitized. During the digitizing of the signal components,
preferably at least one sample is taken of each chip, i.e. in the
GPS system, at least 1,023,000 samples are thus taken in a second.
Furthermore, the I and Q components of the digitized signal are
multiplied by a signal formed with a first numerically controlled
oscillator 4 (NCO). This signal of the first numerically controlled
oscillator 4 is intended to correct a frequency deviation due to
the Doppler shift and the frequency error of the local oscillator
13 of the receiver 1. The signals formed in the receiving channels
CH1-CH4 and indicated with the references Q(a),I(a)-Q(d),I(d) in
FIG. 1, are preferably led to a digital signal processor 2. In
block 14, also reference codes ref(k) are generated, corresponding
to the codes used in code modulation of the satellites to be
received. Using e.g. this reference code ref(k), the receiver RX1,
RX2 attempts to find the code phase and frequency deviation of the
signal of the satellite to be received on each receiving channel,
to be used in operations after the synchronization.
[0023] A control block 5 is used to control e.g. a code phase
detector 7 which is used to adjust the frequency of the numerically
controlled oscillator 4, if necessary. The synchronization will not
be described in more detail in this specification, but it is prior
art known per se. After the receiving channel has been synchronized
with the signal of a satellite SV1, SV2, SV3, SV4, it is possible
to start demodulation and storage of the navigation information
transmitted in the signal. The digital signal processor 2 stores
navigation information preferably in first memory means 3.
[0024] Furthermore, the control block 5 preferably controls e.g.
positioning computing, data reading and presenting, performing of
mobile station functions, etc. In this preferred embodiment, second
memory means 6 are used as the data memory and program memory of
the control block 5. It is obvious that the first memory means 3
and the second memory means 6 can also comprise common memory.
Furthermore, the positioning receiver RX1, RX2 comprises means MS
for performing the functions of the wireless device, such as a
second antenna 8, a radio part 9, audio means, such as a codec 12a,
a speaker 12b and a microphone 12c, a display 10, and a keypad
11.
[0025] In the following, the invention will be described in a
positioning system according to an advantageous embodiment of the
invention, as shown in FIG. 2, where a searcher S attempts to find
out the position of an object L to be searched. The object L has a
receiver RX1 and the searcher S has a receiver RX2. These receivers
RX1, RX2 are preferably receivers according to FIG. 1. The example
receivers RX1, RX2 used herein are GPS receivers, but it is obvious
that the invention can also be applied in other types of satellite
positioning systems. Furthermore, the receiver RX1 at the object L
to be searched is not necessarily similar to the receiver RX2 by
the searcher S. Below in this description, it will be presented
which properties these receivers RX1, RX2 should have to apply the
method of the invention. Furthermore, it is assumed herein that the
position of the receiver RX2 of the searcher is known at some
accuracy. This position of the receiver RX2 of the searcher can be
determined for example so that the position is calculated in the
receiver RX2 of the searcher by using as the default value the
position of the base transceiver station BTS of the mobile
communication network NW forming the cell in whose area the
receiver RX2 of the searcher is at the moment of searching. On the
other hand, the position of the receiver RX2 of the searcher can
also be determined, in a way known as such, solely on the basis of
the signals received in the receiver RX2. Of the mobile
communication network NW, only one base transceiver station BTS and
a mobile switching centre MSC are shown as examples in FIG. 2, but
it is known as such that the mobile communication network typically
comprises several base transceiver stations as well as other
functional elements. The mobile communication network NW can be for
example a GSM mobile communication network or a UMTS mobile
communication network.
[0026] Both receivers RX1, RX2 receive signals transmitted from the
same, preferably at least three satellites SV1-SV4. To receive the
signals to be received from the different satellites substantially
simultaneously, each receiver must have at least three, preferably
at least four receiving channels CH1-CH4. On these receiving
channels, the signals to be received from the different satellites
are converted preferably to an intermediate frequency and sampled
to form a digital sample signal. On the basis of these sample
signals, code acquisition and tracking are performed in the
receiver by a method known as such.
[0027] In the method according to a first advantageous embodiment
of the invention, the receivers RX1, RX2 measure pseudo ranges
.rho..sub.i1, .rho..sub.i2 to the satellites from which signals
have been received. After the pseudo ranges .rho..sub.i1 have been
measured in the receiver RX1 of the object to be searched, the
receiver RX1 of the object to be searched transmits these pseudo
ranges .rho..sub.i1 to the receiver RX2 of the searcher, for
example via the mobile communication network NW. Furthermore, the
geometrical distances r.sub.i to these satellites are calculated in
the receiver RX2 of the searcher. In computing the geometrical
distances r.sub.i, one counting point used is the position known in
the receiver RX2 of the searcher, and other counting points are the
positions of the satellites computed on the basis of the
positioning data of the satellites. The positioning data can be
obtained either from the modulation signal transmitted in the
signals received from the satellites, or e.g. from the base
transceiver station BTS of the mobile communication network, if
these positioning data are available in the mobile communication
network. As a difference between the geometrical distances and the
pseudo ranges, correction terms are obtained for the pseudo ranges.
Even though these correction terms can be relatively rough and they
can be even incorrect, if the position data of the searcher is
incorrect, it can still be expected that the correction terms are
usable in the vicinity of the searcher. Consequently, possible
errors in the correction terms are the same at a sufficient
accuracy, also with regard to the position of the object to be
searched. In the receiver RX2 of the searcher, the error of the
pseudo ranges with respect to the geometrical distances can be
calculated with the formula
.epsilon..sub.i=r.sub.1-.rho..sub.i.epsilon. (1)
[0028] At this stage, the receiver RX2 of the searcher knows e.g.
the position of the receiver RX2 of the searcher at some accuracy;
the corrected pseudo ranges between the receiver RX2 of the
searcher and the satellites from which signals have been received
in the receiver RX2 of the searcher for measuring the pseudo
ranges; the corrected pseudo ranges between the receiver RX1 to be
searched and the satellites from which signals have been received
in the receiver RX1 to be searched for measuring the pseudo ranges;
as well as the positions of the satellites which have been used in
the measurement of the pseudo ranges both in the receiver RX2 of
the searcher and the receiver RX1 to be searched. After this, these
calculated errors .epsilon..sub.i in the pseudo ranges are used in
the receiver RX2 of the searcher for correcting the pseudo ranges
.rho..sub.i2 of the receiver to be searched. Thus, it is assumed
here that the errors in the pseudo ranges in the receiver RX1 of
the object to be searched are substantially the same as the errors
.epsilon..sub.i in the pseudo ranges calculated in the receiver of
the searcher. After the corrected pseudo ranges {circumflex over
(.rho.)}.sub.i1,{circumflex over (.rho.)}.sub.i2 have been
determined, it is possible to calculate the coordinates of the
receiver RX1 to be searched by means of the corrected pseudo ranges
{circumflex over (.rho.)}.sub.i2 of the receiver RX2 of the
searcher and the corrected pseudo ranges {circumflex over
(.rho.)}.sub.i1 of the receiver RX1 to be searched. It is then
possible to calculate the direction of the receiver RX1 to be
searched from the receiver RX2 of the searcher, and the distance
between the receivers RX1, RX2.
[0029] Although, in the method presented above, it was assumed that
the position of the receiver RX2 of the searcher is known at some
accuracy, it is not of great significance to the final direction
and distance data of the object to be searched even if the position
data were not fully correct. This is due e.g. to the fact that in
the method, the differences between the positions of two receivers
are calculated by using at both points pseudo ranges determined
from the same satellites and by correcting the determined pseudo
ranges by means of errors calculated at only one point. However, it
is not necessary in this method to determine the absolute position
of the points.
[0030] We shall next describe an algorithm to be used in a method
according to another advantageous embodiment of the invention for
determining the relative position of the receiver to be searched.
In this description, the algorithm used in this embodiment is
called squared equations. The aim of this algorithm is to produce a
difference in coordinates of the object to be searched and the
searcher. The coordinate system used is an earth centered, earth
fixed coordinate system ECEF. Unideal properties of the clocks in
the receivers RX1, RX2 are disregarded in this embodiment. This
will thus require that the moments of measuring the pseudo ranges
in the receiver RX2 of the searcher and in the receiver RX1 to be
searched must be synchronized as accurately as possible to be
simultaneous. When the receivers are well synchronized, it is
possible to eliminate at least some of the common-mode errors and
to determine the direction and distance between the receivers. This
method has e.g. the advantage that no iteration will be needed to
arrive at a solution, wherein it does not require great computing
capacity.
[0031] The receiver RX1 to be searched transmits data on the pseudo
ranges measured by itself to the receiver RX2 of the searcher for
example via a mobile communication network. The receiver RX2 of the
searcher selects from these pseudo ranges those measured to the
satellites to which also the receiver RX2 of the searcher is or has
been measuring the pseudo ranges.
[0032] Let us indicate the position of the receiver RX1 to be
searched with .left brkt-bot.x.sub.L,y.sub.L,z.sub.L.right
brkt-bot., the position of the receiver RX2 of the searcher
correspondingly with .left brkt-bot.x.sub.S,y.sub.S,z.sub.S.right
brkt-bot., and the direction and distance between the receivers
with a direction vector .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z.right brkt-bot.. Let us
indicate the position of the satellites at the moment after
transmission of the signal to be used in the calculation of the
pseudo ranges with .left brkt-bot.x.sub.i,y.sub.i,z.sub.i.right
brkt-bot., in which i=satellite index, and since at least three
satellites have been used, i receives at least the values from one
to three. The pseudo ranges .rho..sub.i1, .rho..sub.i2 can be
calculated by the formulas 1 1 S = ( x 1 - x S ) 2 + ( y 1 - y S )
2 + ( z 1 - z S ) 2 2 S = ( x 2 - x S ) 2 + ( y 2 - y S ) 2 + ( z 2
- z S ) 2 3 S = ( x 3 - x S ) 2 + ( y 3 - y S ) 2 + ( z 3 - z S ) 2
(2a) 1 L = ( x 1 - x L ) 2 + ( y 1 - y L ) 2 + ( z 1 - z L ) 2 2 L
= ( x 2 - x L ) 2 + ( y 2 - y L ) 2 + ( z 2 - z L ) 2 3 L = ( x 3 -
x L ) 2 + ( y 3 - y L ) 2 + ( z 3 - z L ) 2 (2b)
[0033] In this example, only three equations (three different
satellites) are used for clarity, but it is obvious that within the
scope of the present invention, it is also possible to use more
corresponding equations to calculate the pseudo ranges to more than
three satellites.
[0034] In the next step, these equations (2a), (2b) are squared. In
this case, the squaring will not cause a loss of information,
because the pseudo range terms are known to be positive. 2 1 S 2 =
( x 1 - x S ) 2 + ( y 1 - y S ) 2 + ( z 1 - z S ) 2 2 S 2 = ( x 2 -
x S ) 2 + ( y 2 - y S ) 2 + ( z 2 - z S ) 2 3 S 2 = ( x 3 - x S ) 2
+ ( y 3 - y S ) 2 + ( z 3 - z S ) 2 (3a) 1 L 2 = ( x 1 - x L ) 2 +
( y 1 - y L ) 2 + ( z 1 - z L ) 2 2 L 2 = ( x 2 - x L ) 2 + ( y 2 -
y L ) 2 + ( z 2 - z L ) 2 3 L 2 = ( x 3 - x L ) 2 + ( y 3 - y L ) 2
+ ( z 3 - z L ) 2 (3b)
[0035] The squaring is followed by subtraction of the equations of
formula (3a) from the equations of the formula (3b) related to the
same satellites; i.e. in the above example, the first equation of
the formula (3a) is subtracted from the first equation of the
formula (3b), the second equation of the formula (3a) is subtracted
from the second equation of the formula (3b), and the third
equation of the formula (3a) is subtracted from the third equation
of the formula (3b). Thus, the following equations are obtained: 3
1 L 2 - 1 S 2 = - 2 x 1 x + x L 2 - x S 2 - 2 y 1 y + y L 2 - y S 2
- 2 z 1 z + z L 2 - z S 2 ( 4 )
[0036] in which the direction vector .left
brkt-bot..DELTA.x,.DELTA.y,.DEL- TA.z.right brkt-bot. thus
indicates the difference in the ECEF coordinates of the receiver to
be searched and the receiver of the searcher .left
brkt-bot.x.sub.L-x.sub.S,y.sub.L-y.sub.S, z.sub.L-z.sub.S.right
brkt-bot.. The next step is to eliminate unknown terms, such as
x.sub.L.sup.2, x.sub.S.sup.2, from the formula (4). This can be
performed preferably by subtracting from the first line of the
formula (4) the second line, from the second line the third line,
and from the third line the first line. By indicating
.rho..sub.iL.sup.2-.rho..sub.iS.sup.2={haec- k over
(.DELTA.)}.sub..rho.i, the new set of equations formed on the basis
of the subtractions can be presented as follows: 4 1 - 2 = - 2 ( x
1 - x 2 ) x - 2 ( y 1 - y 2 ) y - 2 ( z 1 - z 2 ) z 2 - 3 = - 2 ( x
2 - x 3 ) x - 2 ( y 2 - y 3 ) y - 2 ( z 2 - z 3 ) z 3 - 1 = - 2 ( x
3 - x 1 ) x - 2 ( y 3 - y 1 ) y - 2 ( z 3 - z 1 ) z ( 5 )
[0037] This is thus a linear set of equations in which the number
of unknown variables .DELTA.x, .DELTA.y, .DELTA.z is equal to the
number of equations, wherein the set of equations can be solved and
the direction vector can be found out. Thus, in this method, it is
not necessary to find out the coordinates of the receiver RX1 to be
searched, errors in the measured pseudo ranges, and even the
coordinates of the receiver RX2 of the searcher do not need to be
accurately known. The requirement is, however, that the searcher
and the object to be searched are relatively close to each other,
preferably within a radius of less than 20 km. Furthermore, if the
measured pseudo ranges are not corrected, it is thus not necessary
to measure the geometrical distances either.
[0038] If sets of more than three equations are used, the method to
be applied in solving them is essentially the same as that
presented above, Thus, the final, overdetermined set of equations
corresponding to the formula (5) is solved by using preferably the
least squares method.
[0039] In the following, we shall describe an algorithm for
determining the relative position of the receiver to be searched,
to be used in a method according to a third advantageous embodiment
of the invention. This algorithm is based on Taylor's method of
linearization. Also in this embodiment, the position of the
searcher is assumed to be known at some accuracy, and the
coordinates of the position of the object to be searched are not
calculated but a direction vector .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z.right brkt-bot. from the
searcher to the object to be searched. This direction vector
corresponds to the residual vector known from Taylor's calculation
formulas. In this embodiment, the calculation of the direction
vector can be iterated, if necessary, to achieve better
accuracy.
[0040] Also in this embodiment, the receiver RX1 to be searched
transmits data on the pseudo ranges measured by itself to the
receiver RX2 of the searcher e.g. via a mobile communication
network. In the receiver RX2 of the searcher, it is possible to use
all the received pseudo ranges or to select from these pseudo
ranges those measured to the satellites to which also the receiver
RX2 of the searcher is or has been measuring the pseudo ranges.
[0041] The position of the searcher and the object to be searched
in the ECEF coordinate system can be expressed with the following
formulas which, excluding the time term, correspond to the formulas
(2a) and (2b). 5 i = ( x i - x L ) 2 + ( y i - y L ) 2 - ( z i - z
L ) 2 + ct L = f ( x L , y L , z L , t L ) , i = 1 , , n ( 6 )
[0042] where c is the speed of light, n is the number of signals of
satellites used in the search and received in both receivers.
[0043] Let us indicate the estimated position of the receiver RX1
to be searched with a vector .left brkt-bot.{circumflex over
(x)}.sub.L,.sub.L,{circumflex over (z)}.sub.L,{circumflex over
(t)}.sub.L.right brkt-bot.. The real position of the receiver RX1
to be searched can thus be expressed with the formula 6 x L , y L ,
z L , t L = x ^ L , y ^ L , z ^ L , t ^ L + x , y , z , t ( 7 )
[0044] in which .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot. is the
error in the estimated position. The linear approximations of the
pseudo range formulas in the estimated position can be determined
by selecting the linear terms of Taylor series at point .left
brkt-bot.{circumflex over (x)}.sub.L,.sub.L,{circumflex over
(z)}.sub.L,{circumflex over (t)}.sub.L.right brkt-bot.. According
to Taylor's theorem on multi-variable functions, the linear
equations can be written as follows: 7 f ( x ^ L + x , y ^ L + y ,
z ^ L + z , t ^ L + t ) = f ( x ^ L , y ^ L , z ^ L , t ^ L ) + f (
x ^ L , y ^ L , z ^ L , t ^ L ) x x + f ( x ^ L , y ^ L , z ^ L , t
^ L ) y y + f ( x ^ L , y ^ L , z ^ L , t ^ L ) z z + f ( x ^ L , y
^ L , z ^ L , t ^ L ) t t ( 8 )
[0045] Thus, the error in the estimated position .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot. can be
calculated by using in this case at least four linearized pseudo
range equations. Since it has been assumed herein that the searcher
and the object to be searched are relatively close to each other,
the position of the searcher .left brkt-bot.{circumflex over
(x)}.sub.S,.sub.S,{circumfle- x over (z)}.sub.S,{circumflex over
(t)}.sub.S.right brkt-bot. can be taken as a starting point for
determining the position .left brkt-bot.{circumflex over
(x)}.sub.L,.sub.L,{circumflex over (z)}.sub.L,{circumflex over
(t)}.sub.L.right brkt-bot. of the object to be searched, further
assuming that the receiver RX2 of the searcher has no clock error,
i.e. {circumflex over (t)}.sub.L=0. In this method according to
another advantageous embodiment of the invention, the
above-presented formula (8) is solved to obtain an error .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot. in the
estimated position, which is simultaneously the difference between
the positions of the searcher and of the object to be searched,
i.e. the direction vector.
[0046] The solution can be deduced as follows. By substituting the
position of the seacher in the above formula (8) and by calculating
the partial derivatives, the following set of equations is
obtained: 8 iL = iS - x i - x S S x - y i - y S S y - z i - z S S z
+ c t , i = 1 , , n ( 9 )
[0047] From this set of equations (9), it is possible to solve the
unknown direction vector .left
brkt-bot..DELTA.x,.DELTA.y,.DELTA.z,.DELTA.t.right brkt-bot..
[0048] Next, the direction vector can be converted to a
searcher-centered xyz coordinate system, in which x-axis points to
the East and y-axis to the North, and z-axis points upwards. Such a
coordinate system can also be called East North Up (ENU). The
distance, direction and height difference of the receiver RX1 to be
searched can thus be calculated relative to the receiver RX2 of the
searcher.
[0049] Even though time was one variable in the formulas presented
above, the corresponding calculations can also be made without the
time data. All the time terms are thus excluded from the formulas
presented above.
[0050] The above-presented calculations can also be iterated,
wherein at each iteration time, the results of the previous
calculation time are used e.g. as the new estimated position. By
increasing the number of iterations, the calculation precision can
further be improved. The number of iterations can, however, be kept
relatively small, because in the present invention, the starting
estimate used for the position to be searched is existing data on
the position of the searcher and not a random position as is used
in many positioning systems of prior art. The display 10 can be
used e.g. to display the direction and distance information to the
searcher S.
[0051] The invention can also be applied by combining different
methods mentioned above e.g. by determining the corrected pseudo
ranges by the method according to the first advantageous embodiment
of the invention and by then determining the direction vector by
the method according to either the second or the third advantageous
embodiment of the invention. Thus, the corrected pseudo ranges can
be used. Yet another alternative is to determine the position of
the searcher, the position of the object to be searched, and then
the direction vector on the basis of these position data. This
alternative is suitable for use e.g. when the receivers do not, for
any reason, receive the signals transmitted by the same
satellites.
[0052] FIG. 2 shows yet, in a principle view, the effect of various
sources of error on the determination of the position of the object
to be searched by a method according to an advantageous embodiment
of the invention. For clarity, FIG. 2 only shows determinations
made according to two satellites. The figure shows the
circumference of a circle indicated with a uniform, single line
TS1, on which the receiver RX2 of the searcher is really located
when viewed from the first satellite SV1 used in the review; that
is, the distance between the satellite and the circumference of the
circle is the same as the true distance between the searcher and
the first satellite. In a corresponding manner, a uniform, single
line TS2 indicates the circumference of a circle on which the
receiver RX2 of the searcher is really located when viewed from the
second satellite SV2 used in the review. A single broken line MS1
indicates the circumference of a circle on which the receiver RX1
of the object to be searched is located on the basis of the
measurements, viewed from the first satellite SV1 used in the
review; that is, the pseudo range between the searcher and the
satellite SV2. A single broken line MS2 indicates the circumference
of a circle on which the receiver RX2 of the searcher is located on
the basis of the measurements, viewed from the second satellite SV2
used in the review.
[0053] A uniform, double line TL1 indicates the circumference of a
circle on which the receiver RX1 of the object to be searched is
really located when viewed from the first satellite SV1 used in the
review; and a uniform, double line TL2 indicates the circumference
of a circle on which the receiver RX2 of the object to be searched
is really located when viewed from the second satellite SV2 used in
the review. Yet a double broken line ML1 indicates the position of
the receiver RX1 of the object to be searched, determined on the
basis of the measurements and viewed from the first satellite SV1
used in the review; and a double broken line ML2 indicates the
position of the receiver RX1 of the object to be searched,
determined on the basis of the measurements and viewed from the
second satellite SV2 used in the review.
[0054] FIG. 2 also indicates the real positions of the receiver RX2
of the searcher and the receiver RX1 to be searched. Furthermore,
reference RX1' indicates the position of the receiver to be
searched, determined by the method according to an advantageous
embodiment of the method, and correspondingly, reference RX1'
indicates the estimated position of the receiver of the searcher.
From the figure, it can be seen, for example, that the direction
and length of the direction vector .DELTA.' determined by the
method of the invention does not significantly differ from the
direction and length of the direction vector .DELTA. according to
the real positions, even though the positions do not necessarily
fully comply with the real situation. When using such a system, it
is not so necessary for the user to know the coordinates
corresponding to his/her own real position or the real position of
the object to be searched, but it is more important to know at
least the direction and preferably also the distance to the object
to be searched.
[0055] Most of the blocks required for implementing the method
according to the first advantageous embodiment of the invention can
be implemented e.g. in a digital signal processor (not shown).
Furthermore, for controlling the operation of the receiver, it is
possible to use a control means, preferably a microprocessor or the
like.
[0056] Although it was presented above that the searcher and the
object to be searched use a receiver which comprises positioning
means, it is obvious that this receiver RX1, RX2 can also be part
of an electronic device with also other functions, such as means
for performing functions of a mobile station. Furthermore, part of
the receiver may comprise common means with the other functions of
such an electronic device, which is known as such.
[0057] In the above-described methods according to an advantageous
embodiment of the invention, the positioning of the receiver RX1 to
be searched was performed in connection with the receiver RX2 of
the searcher. However, the invention can also be applied in such a
way that at least part of the operations described above, such as
the calculation of the direction vector, can also be implemented
e.g. in a computing server CS or the like. Thus, the receiver RX1
to be searched and the receiver RX2 of the searcher transmit the
pseudo range data measured by them to this computing server via a
communication network, such as a mobile communication network NW.
After the computing server has determined the direction vector, the
computing server sends the data on this direction vector to the
receiver RX2 of the searcher, in which e.g. a display device is
used to display data on the distance and direction of the object to
be searched in relation to the searcher.
[0058] Furthermore, the invention can be applied in connection with
other such positioning systems, in which distances are measured to
measuring points whose positions are known.
* * * * *