Method of precise position determination

• US 5,252,982 A
• Filed: 04/23/1992
• Issued: 10/12/1993
• Est. Priority Date: 08/24/1990
• Status: Expired due to Term

• Current Assignee: Leica Heerbrugg AG (Hexagon AB)
• Original Assignee: Leica Heerbrugg AG (Hexagon AB)
• Inventors: Frei, Erwin
• Primary Examiner(s): Sotomayor, John B.
• Application Number:
  US07/849,065
• Time in Patent Office: 537 Days
• Field of Search: 342/357, 342/352, 342/450, 342/451, 342/463, 342/464, 342/465
• US Class Current: 342/357.27
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

The method of precise position determination, in particular for geodetic positioning by means of carrier-frequency phase-difference measurement on GPS satellites, uses a double difference (Δφ₁₂^nm (k)) of a measured phase values, forms an initial solution for a position vector (x_jc) by means of a compensation calculation, and actual phase ambiguities (x_jN) and then integer alternative phase ambiguities (x_jA).

A rapid reduction in the number of alternative phase ambiguities (x_jA) to be processed and automatic statistical protection of the results is achieved by means of special statistical selection tests, using a corresponding cofactor matrix (Q_xxj) and an a posteriori rms error (m_0s) of the initial solution.

In this way, the required number of satellites (4 to 5) observed and the observation duration (a few minutes) can be reduced considerably, likewise the computer cost. Operator decisions are eliminated.

Claims

1. A method of precise position determination

a) of a first receiver (R₁) at a measurement location (r₁) relative to

b) a second receiver (R₂) at a reference location (r₂),

c) using a number of transmitters (Sⁿ) of electromagnetic radiation, which is received by the receivers (R₁ R₂) and whose position is known relative to one another and relative to the two receives (R₁, R₂) at a time of a measurement with a certain accuracy,

d) each receiver (R₁, R₂) producing a measured phase value (φ

_iⁿ (k)) per transmitter (Sⁿ) for a number of time epochs (E_k), which measured phase value, except for an additive complete phase ambiguity (n_ifⁿ (k)), determines quotients of a transmitter-receiver distance (|r_iⁿ |) and a wavelength (λ

_f) of the electromagnetic radiation precisely and

e) the measured phase values (φ

ⁿ (k)) and the position of the transmitters (Sⁿ) stored for each epoch (E_k) and supplied to an automatic data processing installation wherein they are processed in a program-controlled manner,

f) an initial solution produced using a compensation calculation unit by forming a double difference (Δ

φ

₁₂^nm (k)) of measured phase values (φ

_iⁿ (k)) for each pair of transmitters (Sⁿ, S^m),

fa) a solution vector (x_j) of which initial solution contains as components (x_ji) approximate values for 3 components of the position vector to be determined (x_jc) and actual approximate values of all phase ambiguities (x_jN) and which, at the same time, provides

fb) a corresponding cofactor matrix (Q_xxj) and

fc) an a posteriori rms error (m_0j);

g) according to which, integer alternative phase ambiguities (x_jAi) are formed within an interval characterized by the a posteriori rms error (m₀) around each actual phase ambiguity (x_jNi) and

h) various combinations (x_jA) of alternative phase ambiguities (x_jAi) are used as known variables to determine alternative position vectors (x_jAc) and associated rms errors (m_0j),

i) the alternative position vector (x_sAc;

) with the minimum rms error (m_0s) is determined;

wherein

j) combinations (x_jA) of alternative phase ambiguities (x_jAi) formed are subjected to a statistical selection test which takes into account a correlation of the phase ambiguities (x_jAi), which is characterized by a corresponding cofactor matrix (Q_xxj) and a posteriori rms error (m₀, and

k) only the combinations (x_jA) of alternative phase ambiguities (x_jAi) which have passed the selection test are used as known variables to determine alternative position vectors (x_jAc) and associated rms errors (m_0j);

l) the minimum rms error (m_0s) is tested to determine whether

1a) the associated alternative position vector (x_sAc) can be statistically combined with the position vector (x_jC) of the initial solution and

1b) the minimum rms error (m_os) can be statistically combined with an a priori variance (σ

₀) of the initial solution, and

1c) the difference with respect to the second smallest rms error (m_0s'"'"') is statistically significant,

m) in the presence of these conditions for the minimum rms error (m_0s), the alternative position vector (x_sAC) having the minimum rms error (m_0s) is produced as the measured value of the precise position determination.

2. The method as claimed in claim 1, wherein in each case two transmitters (Sⁿ, S^m) of different frequencies (L1, L2) assume the same position and the receivers (R₁, R₂) for signals of different frequencies (L₁, L₂) produce separate measured phase values (φ

_iⁿ (k)).

3. The method as claimed in claim 1, wherein a statistical selection test for combinations (x_jA) of the alternative phase ambiguities is carried out in accordance with the condition:

##EQU9##

4. The method as claimed in claim 1, wherein a statistical selection test for the combinations (x_jA) of the alternative phase ambiguities is carried out in accordance with the conditions:

space="preserve" listing-type="equation">P[x.sub.Ni -ξ

.sub.Tf;

1-α

/2 ·

m.sub.xNi ≦

x.sub.ANi ≦

x.sub.Ni +ξ

.sub.Tf;

1-α

/2 ·

m.sub.xNi ]=1-α

space="preserve" listing-type="equation">P[x.sub.Nik -ξ

Tf;

1-α

/2·

m.sub.xNik ≦

x.sub.Anik ≦

x.sub.Nik +ξ

.sub.Tf;

1-α

/2 ·

m.sub.xNik ]=1-α

##EQU10##

5. The method as claimed in claim 4, wherein the statistical selection test additionally comprises the condition:

space="preserve" listing-type="equation">P[x.sub.Lik -ξ

.sub.Tf;

1-α

/2 ·

m.sub.xLik ≦

x.sub.ALik ≦

x.sub.Lik +ξ

Tf;

1-α

/2·

m.sub.xLik ]=1-α

6. A method of precise position determination of a first receiver at a measurement location relative to a second receiver at a reference location using a plurality of transmitters of electromagnetic radiation which is received by the first and second receivers, the method comprising the steps of:

(a) producing a measured phase value for each transmitter for a number of time epochs for each of the first and second receivers, the measured phase values indicating a transmitter-receiver distance and a wavelength of electromagnetic radiation;

(b) supplying measured phase values and transmitter position information for each time epoch to an automatic data processing unit;

(c) producing, in the automatic data processing unit, an initial solution by forming a double difference of measured phase values for each pair of transmitters, a solution vector of the initial solution containing as components approximate values for three components of a position vector being determined and actual approximate values of phase ambiguities, the solution vector providing a corresponding cofactor matrix and an a posteriori rms error;

(d) forming, int eh automatic data processing unit, integer alternative phase ambiguities within an interval defined by a posteriori rms error around an actual phase ambiguity;

(e) determining in the automatic data processing unit, alternative position vectors and associated rms errors using combinations of the alternative phase ambiguities as known variables and determining an alternative position vector with a minimum rms error;

(f) subjecting, in the automatic data processing unit, combinations of the alternative phase ambiguities to a statistical selection test which uses a correlation of phase ambiguities characterized by a corresponding cofactor matrix and a posteriori rms error;

(g) determining, in the automatic data processing unit, alternative position vectors and associated rms errors using combinations of alternative phase ambiguities which have passed the statistical selection test as known variables;

(h) determining, in the automatic data processing unit, whether an associated alternative position vector can be statistically combined with a position vector of the initial solution, whether a minimum rms error can be statistically combined with an a priori variance of the initial solution, and whether a difference associated with a second smallest rms error is statistically significant; and

(i) producing, in the automatic data processing unit, an alternative position vector having a minimum rms error as a measured value of precise position determination.

7. A method as claimed in claim 6, wherein at least two of the plurality of transmitters assume the same position and transmit different frequencies and wherein the first and second receivers produce separate measured phase values for signals of different frequencies.