Position calculation method and storage medium storing a program therefor
View Patent ↗A position calculation method includes a step of calculating error degradation quantities about respective measurement results (“distance-ranging results”) on distances between respective reference stations and a detection-target station from the respective distance-ranging results and positions of the respective reference stations, a step of calculating weight-assigning factors about the respective distance-ranging results based on the respective error degradation quantities, a step of checking the number of valid distance-ranging results, and a step of calculating the position of the detection-target station based on the respective distance-ranging results, the positions of the respective reference stations, and the respective weight-assigning factors.
1. A position calculation method, comprising the steps of:
receiving radio signals between a plurality of respective reference stations and a detection-target station by either said plurality of reference stations or said detection-target station, said plurality of reference stations being radio devices whose positions have been already known, said detection-target station being a radio device whose position has been unknown,
measuring physical quantities about distances thereby to measure absolute distances or relative distances between said plurality of respective reference stations and said detection-target station, respectively, and
calculating position of said detection-target station based on distance-ranging results and positions of said respective reference stations, said distance-ranging results being said respective distances measured,
wherein said calculating step comprises the steps of:
calculating respective error degradation quantities ΔEi from said respective distance-ranging results Ri and said positions Pi of said respective reference stations, said respective error degradation quantities being quantities of respective errors by which said respective distance-ranging results influence minimum value of square error function to solve the position of said detection-target station,
evaluating said respective distance-ranging results based on said respective error degradation quantities, and updating weight-assigning factors Wi about said respective distance-ranging results, and
calculating said position P of said detection-target station based on said respective distance-ranging results, said positions of said respective reference stations, and said respective weight-assigning factors updated.
2. The position calculation method according to claim 1 , wherein said error degradation quantities ΔE i are defined using
ΔE i =E 0 −E i0 , i= 1, . . . , n
where Eo is the minimum value of said square error function using all measurements, n is a number of measurements, and Eio is a minimum value of square error function E not including distance-ranging result R.
3. The position calculation method according to claim 2 , wherein said error degradation quantities ΔE i are determined using variable values P and T acquired using
E
0
=
min
P
,
T
(
E
(
P
,
T
)
)
,
E
(
P
,
T
)
=
∑
k
=
1
n
W
k
{
R
k
+
c
T
-
P
k
-
P
}
2
E
i
(
P
,
T
)
=
∑
k
=
1
k
≠
i
n
W
k
{
R
k
+
c
T
-
P
k
-
P
}
2
,
i
=
1
,
…
,
n
E
i0
=
min
P
,
T
(
E
i
(
P
,
T
)
)
,
i
=
1
,
…
,
n
where P is a position, T is offset of a clock selected as the reference, W k are weight-assigning factors, c is a speed of the radio waves, and R k are distance-ranging results.
4. The position calculation method according to claim 2 , wherein said error degradation quantities ΔE i are determined using variable values P and T acquired using
E
0
=
min
P
,
T
(
E
(
P
,
T
)
)
,
E
(
P
,
T
)
=
∑
k
=
1
n
W
k
{
R
k
+
c
T
-
P
k
-
P
}
2
E
i
(
P
,
T
)
=
∑
k
=
1
k
≠
i
n
W
k
{
R
k
+
c
T
-
P
k
-
P
}
2
,
i
=
1
,
…
,
n
E
i0
=
E
i
(
P
0
,
T
0
)
,
E
(
P
0
,
T
0
)
=
E
0
,
i
=
1
,
…
,
n
where P is a position, T is offset of a clock selected as the reference, Po and To are P and T providing Eo, W k are weight-assigning factors, c is a speed of the radio waves, and R k are distance-ranging results.
5. The position calculation method according to claim 3 , wherein said step of updating said weight-assigning factors is a step of updating values of said weight-assigning factors based on comparisons between said respective error degradation quantities and a threshold value determined in advance.
6. The position calculation method according to claim 5 , wherein said step of updating said weight-assigning factors about said distance-ranging results is a step of updating said values of said weight-assigning factors to zero if said error degradation quantities about said distance-ranging results have exceeded said threshold value determined in advance.
7. The position calculation method according to claim 6 , wherein, before executing said step of calculating said position of said detection-target station, a step of checking the number of valid distance-ranging results is executed in order to judge possibility or impossibility of said execution of said position calculating step.
8. The position calculation method according to claim 7 , wherein said checking of the number of said valid distance-ranging results is a checking based on a comparison between the number of said weight-assigning factors which become non-zero with respect to said respective distance-ranging results and a threshold value determined in advance.
9. The position calculation method according to claim 1 , further comprising a step of calculating Dilution of Precision after having executed said step of calculating said position of said detection-target station, and judging success or failure of said position calculation of said detection-target station in accordance with a calculation value of said Dilution of Precision.
10. A computer-readable storage medium for storing a position calculation program for implementing a position calculation method in a position calculation apparatus,
said position calculation apparatus, comprising:
an input unit for inputting physical quantities about distances,
a processing unit, and
an output unit, said physical quantities about said distances being measured such that radio signals between a plurality of respective reference stations and a detection-target station are received by either said plurality of reference stations or said detection-target station, said plurality of reference stations being radio devices whose positions have been already known, said detection-target station being a radio device whose position has been unknown,
said position calculation method being executed by said processing unit, comprising the steps of:
calculating, from said physical quantities about said distances, absolute distances or relative distances between said plurality of respective reference stations and said detection-target station, respectively, and
calculating position of said detection-target station based on distance-ranging results and positions of said respective reference stations, said distance-ranging results being said respective distances measured,
wherein the calculating step includes the steps of:
calculating respective error degradation quantities from said respective distance-ranging results and said positions of said respective reference stations, said respective error degradation quantities being quantities of respective errors by which said respective distance-ranging results influence least square error,
evaluating said respective distance-ranging results based on said respective error degradation quantities, and updating weight-assigning factors about said respective distance-ranging results, and
calculating said position of said detection-target station based on said respective distance-ranging results, said positions of said respective reference stations, and said respective weight-assigning factors updated.