System and method for quantifying anchor placement impact placement on location accuracy
AssigneeTelcordia Technologies, Inc.
InventorsYibei Ling, Richard Lau, Scott Alexander
Life of this patent
Estimating the term…
Abstract
A computer implemented method for determining geometric impact of anchor placement on localization accuracy and the subset of anchors which mitigates the impact of measurement-induced noise.
Claims7
A computer implemented method for determining geometric impact of anchor placement on localization accuracy of a mobile node (MN) over an arbitrary traversal area of a wireless network, said method comprising the steps of:
- determining for a given initial set of anchors (p1, . . . , pm) having known positions and an area Ω;
- a dilution of precision for a position (p) in the area from the following expression
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- p
- )
- =
- 2
- 1
- -
- (
- d
- i
- 2
- +
- d
- j
- 2
- -
-
- p
- i
- -
- p
- j
-
- 2
- 2
-
- d
- i
-
- d
- j
- )
- 2
- ,
- where pi and pj are the positions of anchor pair i and j, and di and dj are the distances from MN at p to the anchors i, j;
- determining an optimal anchor pair from m anchors from the following expression
- g
- m
-
- (
- p
- 1
- ,
- …
-
- ,
- p
- m
- )
-
- (
- p
- )
- =
- min
- 1
- ≤
- i
- ,
- j
- ≤
- m
- i
- ≠
- j
-
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- p
- )
- determining the average elevation of a least vulnerable tomography (LVT) from the following expression
- g
- m
-
- (
- p
- 1
- ,
- …
-
- ,
- p
- m
- )
-
- (
- Ω
- )
- =
-
- 1
-
- Ω
-
-
- ∫
- Ω
-
- g
- m
-
- (
- p
- 1
- ,
- …
-
- ,
- p
- m
- )
-
- (
- x
- ,
- y
- )
-
-
- ⅆ
- x
-
- ⅆ
- y
- =
-
- 1
-
- Ω
-
-
- ∫
- Ω
-
- min
- 1
- ≤
- i
- ,
- j
- ≤
- m
-
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- x
- ,
- y
- )
-
-
- ⅆ
- x
-
- ⅆ
- y
- where |Ω| refers to the area size, gm(p1, . . . , pm)(Ω) denote the average of gm(p1, . . . , pm)(p) over Ω with respect to the m available anchors at pi, i=1, . . . , m;
- and
- outputting an indication of the LVT so determined.
A computer implemented method for determining geometric impact of anchor placement on localization accuracy of a mobile node (MN) over an arbitrary trajectory (F) within a wireless network, said method comprising the steps of:
- determining for a given initial set of anchors (p1, . . . , pm) having known positions a dilution of precision for a position (p) from the following expression
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- p
- )
- =
- 2
- 1
- -
- (
- d
- i
- 2
- +
- d
- j
- 2
- -
-
- p
- i
- -
- p
- j
-
- 2
- 2
-
- d
- i
-
- d
- j
- )
- 2
- ,
- where pi and pj are the positions of anchor pair i and j, and di and dj are the distances from MN at p to the anchors i, j;
- determining an optimal anchor pair from m anchors from the following expression
- g
- m
-
- (
- p
- 1
- ,
- …
-
- ,
- p
- m
- )
-
- (
- p
- )
- =
- min
- 1
- ≤
- i
- ,
- j
- ≤
- m
- i
- ≠
- j
-
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- p
- )
- determining the average elevation of a least vulnerable tomography (LVT) over the trajectory from the following expression
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- Γ
- )
- =
- ∫
- Γ
-
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- x
- ,
- y
- )
-
-
- ⅆ
- s
-
- Γ
-
- where |Γ| refers to the length of Γ and ds is an arc length;
- and
- outputting an indication of the LVT so determined.
A computer implemented method for quantitatively comparing two anchor placements over a given area comprising the steps of:
- for a given two placements p1, . . . , pm and q1, . . . , qn and an area Ω
- determining an average elevation of a least vulnerable tomography (LVT) formed by the anchor placements p1, . . . , pm from the following
- gm(p1, . . . ,pm)(Ω)
- determining an average elevation for an LVT formed by the anchor placements q1, . . . , qn from the following
- gn(q1, . . . ,qn)(Ω)
- determining which of the two anchor placements exhibit the better localization accuracy;
- and
- outputting an indication of the one exhibiting the better localization accuracy.
A computer implemented method for quantitatively comparing two anchor placements over a given area comprising the steps of:
- for a given two placements p1, . . . , pm and q1, . . . , qn and an area Γ
- determining an average elevation of a least vulnerable tomography (LVT) formed by the anchor placements p1, . . . , pm from the following
- gm(p1, . . . ,pm)(Γ)
- determining an average elevation for an LVT formed by the anchor placements q1, . . . , qn from the following
- gn(q1, . . . ,qn)(Γ)
- determining which of the two anchor placements exhibit the better localization accuracy;
- and
- outputting an indication of the one exhibiting the better localization accuracy.
A computer implemented method for minimizing noise-induced impact on localization accuracy of a mobile node (MN) comprising the steps of:
- selecting an optimal anchor pair, where pi, 1≦i≦m is a set of positions of anchors accessible to the MN at p and the optimal anchor pair from m anchors is defined by
- g
- m
-
- (
- p
- 1
- ,
- …
-
- ,
- p
- m
- )
-
- (
- p
- )
- =
- min
- 1
- ≤
- i
- ,
- j
- ≤
- m
- i
- ≠
- j
-
- g
-
- (
- p
- i
- ,
- p
- j
- )
-
- (
- p
- )
- where the function gm(p1, . . . , pm)(p) refers to an anchor pair exhibiting a minimum geometric dilution of precision (GDOP) value among its alternatives;
- determining one from two possible position realizations using a reference position derived from a Least Square Method (LSM) according to
- (
- A
- T
-
- A
- )
-
- (
- x
- (
- 0
- )
- y
- (
- 0
- )
- )
- =
- A
- T
-
- M
- ,
- where
- A
- =
- 2
-
- (
- (
- x
- 2
- -
- x
- 1
- )
- (
- y
- 2
- -
- y
- 1
- )
- (
- x
- 3
- -
- x
- 1
- )
- (
- y
- 3
- -
- y
- 1
- )
- …
- …
- (
- x
- m
- -
- x
- 1
- )
- (
- y
- m
- -
- y
- 1
- )
- )
- ,
-
- M
- =
- (
- d
- ~
- 1
- 2
- -
- d
- ~
- 2
- 2
- +
- r
- 2
- 2
- -
- r
- 1
- 2
- d
- ~
- 1
- 2
- -
- d
- ~
- 3
- 2
- +
- r
- 3
- 2
- -
- r
- 1
- 2
- …
- d
- ~
- 1
- 2
- -
- d
- ~
- m
- 2
- +
- r
- m
- 2
- -
- r
- 1
- 2
- )
- ,
- where AT is the transpose of A, (AT A)−1 is the inverse of (AT A), and ri=√{square root over (xi2+yi2)}, 1≦i≦m;
- and
- returning an indication of the anchor position.
Dependencies are inferred from the claim text.