Differential position determination using satellites

• US 5,148,179 A
• Filed: 06/27/1991
• Issued: 09/15/1992
• Est. Priority Date: 06/27/1991
• Status: Expired due to Fees

• Current Assignee: Trimble Navigation Limited (Trimble Inc.)
• Original Assignee: Trimble Navigation Limited (Trimble Inc.)
• Inventors: Allison, Michael T.
• Primary Examiner(s): BLUM, THEODORE M
• Application Number:
  US07/722,512
• Time in Patent Office: 446 Days
• Field of Search: 342/457, 342/357, 342/352, 342/356, 364/449
• US Class Current: 342/357.31
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

A method for accurately determining the position of a roving signal receiver positioned on or above the Earth'"'"'s surface, relative to the position of a reference receiver whose position is known with sufficient accuracy, using ranging information, transmitted at a pair of predetermined carrier signal frequencies and received from each of n satellites (n≧4). Pseudorange double differences are formed, between each of the two receivers and each of a first satellite and the other three satellites, using pseudorange information obtained from either one of the two signal frequencies. Phase correction information, in the form of estimates of integer lane wavelength ambiguities, is then obtained from the pseudorange double differences and from certain measurable phase differences. This products n-1 simultaneous equations that can be solved for the roving receiver position cordinates. The method can be adapted to provide roving receiver position when signals carried by both of the two carrier frequencies are encrypted, where a separate non-encrypted signal is available on one of the two carrier frequencies.

Claims

1. A method for determining the position of a radio signal receiver located on or above the Earth'"'"'s surface, the method comprising the steps of:

(1) providing a roving receiver whose position is to be determined at a sequence of predetermined times;

(2) providing a reference receiver whose position is known with sufficient accuracy at the sequence of predetermined times;

(3) providing a plurality of n satellites (n≧

4), numbered j=1,2, . . . , n, at predetermined heights above the Earth'"'"'s surface, where each satellite transmits a predetermined signal at a predetermined sequence of times at each of two carrier frequencies f=f_L1 and f=f_L2 ;

(4) determining a plurality of n theoretical distance values R₁,1,R₂,1, . . . , R_n,1 from each of the satellites to the roving receiver at the sequence of predetermined times, where each theoretical distance value is determined from a knowledge of the position of a satellite and an approximate knowledge of the position of the roving receiver;

(5) determining a plurality of n theoretical distance values R₁,2,R₂,2, . . . , R_n,2 from each of the satellites to the reference receiver at the sequence of predetermined times, where each theoretical distance value is determined from a knowledge of the position of a satellite and of the position of the reference receiver, where the position of the reference receiver is known with sufficient accuracy at each of the predetermined sequence of times;

(6) forming theoretical range double difference values Δ

R_i,i'"'"';

j,j'"'"' (i,i'"'"'=1,2;

i=i'"'"';

j,j'"'"'=2,3,4;

j=j'"'"'), defined by the relations

space="preserve" listing-type="equation">Δ

R.sub.i,i'"'"';

j,j'"'"' =(R.sub.i,j -R.sub.i'"'"',j)-(R.sub.i,j'"'"' -R.sub.i'"'"',j'"'"')

for the pair of satellites i and i'"'"' and the pair of receivers j and j'"'"';

(7) determining a characteristic wavelength λ

Δ

=c/(f_L1 -f_L2), where c is the velocity of light;

(8) measuring first and second phase variables, denoted β

_a,b;

Lk (k=1 and

     2) from observations of the phase of a signal sent by transmitter number a and received by receiver number b (a=i or i'"'"';

b=j or j'"'"') with carrier frequency f=f_Lk ;

(9) forming a third phase variable β

.sub.Δ

a,b =β

_a,b;

L1 -β

_a,b;

L2 ;

(10) forming a fourth phase variable φ

.sub.Δ

i,i'"'"';

j,j'"'"' defined by the relations

space="preserve" listing-type="equation">φ

.sub.Δ

i,i'"'"';

j,j'"'"' =(β

.sub.Δ

i,j -β

.sub.Δ

i'"'"',j)-(β

.sub.Δ

i,j'"'"' -β

.sub.Δ

i'"'"';

j'"'"')

for the pair of satellites i and i'"'"' and the pair of receivers j and j'"'"';

(11) measuring a pseudorange ρ

_a,b;

Lk =c(t^b -t_a), where t_a is the uncorrected time a given signal is transmitted by satellite a,t^b is the uncorrected time the given signal is received by receiver b, c is the speed of light, and the satellite transmits the given signal using the carrier frequency f=f_Lk (a=i,i'"'"';

b=j,j'"'"';

k=1 or

     2);

(12) forming unfiltered pseudorange double difference values Δ

ρ

_i,i'"'"';

j,j'"'"';

Lk defined by the relations

space="preserve" listing-type="equation">Δ

ρ

.sub.i,i'"'"';

j,j'"'"';

Lk =(ρ

.sub.i,j;

Lk -ρ

.sub.i'"'"',j;

Lk)-(ρ

.sub.i,j'"'"';

Lk -ρ

.sub.i'"'"';

j'"'"';

Lk);

(13) determining a fifth phase variable N_i,i'"'"';

j,j'"'"' by the relations

space="preserve" listing-type="equation">N.sub.i,i'"'"';

j,j'"'"' =Δ

ρ

.sub.i,i'"'"';

j,j'"'"';

Lk/λ

Δ

+φ

.sub.Δ

i,i'"'"';

j,j'"'"'

with i=1, j=1 and j'"'"'=2;

(14) determining the values of the n-1 fifth phase variables N₁,i'"'"';

1,2 (i'"'"'=2, . . . , n) for a sequence of samples determined at the predetermined sequence of times;

(15) filtering the sequence of samples of the fifth phase variables N₁,i'"'"';

1,2 for each value of i'"'"'=2, . . . , n to determine a filtered fifth phase variable N₁,i'"'"';

1,2 (f), in order to remove or minimize the effects of noise on the fifth phase variable; and

(16) solving the n-1 simultaneous equations given by

3. The method of claim 1, further comprising the step of choosing said integer n equal to four.

4. The method of claim 1, further comprising the step of performing said step of filtering of said samples of said fourth phase variables by the method of least squares filtering.

5. The method of claim 1, further comprising the step of performing said step of filtering of said samples of said fourth phase variables by the method of Kalman filtering.

6. The method of claim 1, further comprising the step of choosing said carrier frequency for measurement of said pseudorange values ρ

_a,b;

Lk as f_Lk =f_L1.

7. The method of claim 5, further comprising the step of determining at least one of said pseudorange values ρ

_a,b;

Lk for f_Lk =f_L2 by the following sequence of steps;

receiving at said receiver number j a first signal F₁ (t) and a second signal F₂ (t) with the respective carrier signal frequencies f=f_L1 and f=f_L2, respectively, where these two signals are transmitted as identical signals by a satellite number a with the respective carrier signal frequencies f=f_L1 and f=f_L2 ;

forming a cross-correlation signal <

F₁ (t-) F₂ (t-Δ

t)>

=C(Δ

t), and determining the value of Δ

t, denoted Δ

t_max, for which C(Δ

t) achieves its maximum value; and

determining said pseudorange value ρ

_a,b;

Lk for f_Lk =f_L2 by the relation ρ

_a,b;

L2 =ρ

_a,b;

L1 -cΔ

t_max, where c is the speed of light.

8. The method of claim 6, further comprising the steps of:

encrypting said signals transmitted at said carrier frequencies f=f_L1 and f=f_L2 ; and

transmitting a second signal at said carrier frequency f=f_L1 that is not encrypted, and for which said fourth and fifth phase variables and said pseudorange values ρ

_a,b;

L1 (a=i,i'"'"';

b=j,j'"'"') can be determined for use in steps (10)-(16) of claim 1 using this second signal and said signals transmitted at carrier frequencies f=f_L1 and f=f_L2.

9. The method of claim 5, further comprising the step of determining at least one of said pseudorange values ρ

_a,b;

Lk for f_Lk =f_L2 by the following sequence of steps;

receiving at said receiver number j a first signal F₁ (t) and a second signal F₂ (t) with the respective carrier signal frequencies f=f_L1 and f=f_L2, respectively, where these two signals are transmitted as identical signals by a satellite number a with the respective carrier signal frequencies f=f_L1 and f=f_L2 ;

forming a cross-correlation signal <

F₁ (t-Δ

t) F₂ (t)>

=C(Δ

t), and determining the value of Δ

t, denoted Δ

t_max, for which C(Δ

t) achieves its maximum value; and

determining said pseudorange value ρ

_a,b;

Lk for f_Lk =f_L2 by the relation ρ

_a,b;

L2 =ρ

_a,b;

L1 +cΔ

t_max, where c is the speed of light.

10. The method of claim 8, further comprising the steps of:

encrypting said signals transmitted at said carrier frequencies f=f_L1 and f=_L2 ; and

transmitting a second signal at said carrier frequency f=f_L1 that is not encrypted, and for which said fourth and fifth phase variables and said pseudorange values ρ

_a,b;

L1 (a=i,i'"'"';

b=j,j'"'"') can be determined for use in steps (10)-(16) of claim 1 using this second signal and said signals transmitted at carrier frequencies f=f_L1 and f=f_L2.

11. The method of claim 1, further comprising the step of choosing said carrier frequency f=f_Lk for measurement of said pseudorange values ρ

_a,b;

Lk as f_Lk =f_L2.

12. The method of claim 1, further comprising the step of replacing said filtered fifth phase variable N_i,i'"'"';

j,j'"'"' (f) by an integer M_i,i'"'"';

j,j'"'"' if the absolute value of the difference |N_i,i'"'"';

j,j'"'"' (f)-M_i,i'"'"';

j,j'"'"' |≦

g, where g is a predetermined positive fraction (0<

g≦

0.5).

13. The method of claim 1, wherein said step of solving said n-1 simultaneous equations comprises the step of solving the n-1 equations

15. The method of claim 13, wherein said step of solving said n-1 simultaneous equations comprises the step of solving the n-1 equations

16. The method of claim 13, further comprising the steps of:

encrypting said signals transmitted at said carrier frequencies f=f_L1 and f=f_L2 ; and

transmitting a second signal at said carrier frequency f=f_L1 that is not encrypted, and for which said fourth and fifth phase variables and said pseudorange values ρ

_a,b;

L1 (a=i,i'"'"';

b=j,j'"'"') can be determined for use in steps (12)-(18) of claim 13 using this second signal and said signals transmitted at carrier frequencies f=f_L1 and f=f_L2.

2. φ

.sub.Δ

1. i'"'"';

1,2 =-Δ

R₁,i'"'"';

1,2 /λ

.sub.Δ

+N₁,i'"'"';

1,2 (f), (i'"'"'=2, . . . , n)

to obtain position coordinates (x₁,y₁,z₁) of the roving receiver when the coordinates (x₂,y₂,z₂) of the reference receiver are known are known with sufficient accuracy.

14. A method for determining the position of a radio signal receiver located on or above the Earth'"'"'s surface, the method comprising the steps of:

(1) providing a roving receiver whose position is to be determined at a sequence of predetermined times;

(2) providing a reference receiver whose position is known with sufficient accuracy at the sequence of m predetermined times;

(3) providing a plurality of n satellites (n≧

4), numbered j=1,2, . . . , n, at predetermined heights above the Earth'"'"'s surface, where each satellite transmits a predetermined signal at a predetermined sequence of times at each of two carrier frequencies f=f_L1 and f=f_L2 ;

(4) determining a plurality of m theoretical distance values R₁,1, R₂,1, . . . , R_m,1 from each of the satellites to the roving receiver at the sequence of predetermined times, where each theoretical distance value is determined from a knowledge of the position of a satellite and an approximate knowledge of the position of the roving receiver;

(5) determining a plurality of m theoretical distance values R₁,2, R₂,2, . . . , R_n,2 from each of the satellites to the reference receiver at the sequence of predetermined times, where each theoretical distance value is determined from a knowledge of the position of a satellieteand of the position of the reference receiver, where the position of the reference receiver is known with sufficient accuracy at each of the predetermined sequence of times;

(6) forming theoretical range double difference values Δ

R_i,i'"'"';

j,j'"'"' (i,i'"'"'=1,2;

i=i'"'"';

j,j'"'"'=2,3 4;

j=j'"'"'), defined by the relations

space="preserve" listing-type="equation">Δ

R.sub.i,i'"'"';

j,j'"'"' =(R.sub.i,j -R.sub.i'"'"',j)-(R.sub.i,j'"'"' -R.sub.i'"'"',j'"'"')

for the pair of satellites i and i'"'"' and the pair of receivers j and j'"'"';

(7) determining a characteristic wavelength λ

.sub.Δ

=c/(f_L1 -f_L2), where c is the velocity of light;

(8) receiving at receiver b two signals S_a,b;

Lk transmitted from satellite a (a=i,i'"'"';

b=j,j'"'"') with carrier frequency f=f_Lk (k=1 and

     2);

(9) forming the square of the received signal S_a,b;

L2 and determining a phase variable, denoted β

_a,b;

L2.sup.(2), of this squared signal;

(10) determining a phase variable, denoted β

_a,b;

L1.sup.(1), of the signal S_a,b;

L1 ;

(11) forming a third phase variable β

.sub.Δ

a,b =2β

_a,b;

L1.sup.(1) -β

_a,b;

L2.sup.(2) ;

(12) forming a fourth phase variable φ

.sub.Δ

i,i'"'"';

j,j'"'"' defined by the relations

space="preserve" listing-type="equation">φ

.sub.Δ

i,i'"'"';

j,j'"'"' =(β

.sub.Δ

i,j -β

.sub.Δ

i'"'"',j)-(β

.sub.Δ

i,j'"'"' -β

.sub.Δ

i'"'"';

j'"'"')

for the pair of satellites i and i'"'"' and the pair of receivers j and j'"'"';

(13) measuring a pseudorange ρ

_a,b;

L1 =c(t^b -t_a), where t_a is the uncorrected time a given signal is transmitted by satellite a,t^b is the uncorrected time the given signal is received by receiver b, c is the speed of light, and the satellite transmits the given signal using the carrier frequency f=f_L1 (a=i,i'"'"';

b=j,j'"'"');

(14) forming unfiltered pseudorange double difference values Δ

ρ

_i,i'"'"';

j,j'"'"';

L1 defined by the relations

space="preserve" listing-type="equation">Δ

ρ

.sub.i,i'"'"';

j,j'"'"';

L1 =(ρ

.sub.i,j;

L1 -ρ

.sub.i'"'"',j;

L1)-(ρ

.sub.i,j'"'"';

L1 -ρ

.sub.i'"'"';

j'"'"';

L1);

(15) determining a fifth phase variable N_i,i'"'"';

j,j'"'"' by the relations

space="preserve" listing-type="equation">N.sub.i,i'"'"';

j,j'"'"' =Δ

ρ

.sub.i,i'"'"';

j,j'"'"';

L1 /λ

.sub.66 +φ

.sub.Δ

i,i'"'"';

j,j'"'"'

with i=1, j=1 and j'"'"'=2;

(16) determining the values of the n-1 fifth phase variables N₁,i'"'"';

1,2 (i'"'"'=2, . . . , n) for a sequence of samples determined at the predetermined sequence of times;

(17) filtering the sequence of samples of the fifth phase variables N₁,i'"'"';

1,2 for each value of i'"'"'=2, . . . , n to determine a filtered fifth phase variable N₁,i'"'"';

1,2 (f), in order to remove or minimize the effects of noise on the fifth phase variable; and

(18) solving the n-1 simultaneous equations given by

space="preserve" listing-type="equation">φ

.sub.Δ

1,i'"'"';

1,2 =-Δ

R.sub.1,i'"'"';

1,2 /λ

.sub.Δ

+N.sub.1,i'"'"';

1,2 (f), (i'"'"'=2, . . . , n)

to obtain position coordinates (x₁,y₁,z₁) of the roving receiver when the coordinates (x₂,y₂,z₂) of the reference receiver are known with sufficient accuracy.