Article Figures & Data
Figures
- FIGURE 1
An example network to demonstrate the computation of
- FIGURE 2
Examples of the considered problem with varying selections of fixed anchors White circles indicate the true positions of estimated anchors, filled circles indicate fixed anchors, and lines represent measured distances. (a) GO — Grid with opposite corner selection (b) LC — A cut of ladder class with corner selection (c) RM — Random class with middle selection (d) MO — Measured class with opposite selection
- FIGURE 3
Mean RMS of the estimation error across problem instances (a) Grid — Corner (GC) (b) Grid — Opposite (GO) (c) Grid — Middle (GM) (d) Ladder — Corner (LC) (e) Ladder — Opposite (LO) (f) Ladder — Middle (LM) (g) Measurement — Corner (MC) (h) Measurement — Opposite (MO) (i) Measurement — Middle (MM) (j) Random — Corner (RC) (k) Random — Middle (RM) (l) Legend
- FIGURE 4
Mean RMS of the cost function value across problem instances (a) Grid — Corner (GC) (b) Grid — Opposite (GO) (c) Grid — Middle (GM) (d) Ladder — Corner (LC) (e) Ladder — Opposite (LO) (f) Ladder — Middle (LM) (g) Measurement — Corner (MC) (h) Measurement — Opposite (MO) (i) Measurement — Middle (MM) (j) Random — Corner (RC) (k) Random — Middle (RM) (l) Legend
- FIGURE 5
Selected results of distributed network determination
Rings indicate true positions, filled circles indicate fixed anchors, and crosses indicate estimated positions. (a) Problem LC, N-CSG TBLS solver (b) Problem LC, CSG solver (c) Problem MO, N-CSG TBLS solver (d) Problem GO, N-CSG TBLS solver (e) Problem RM, N-CSG TBLS solver
- FIGURE 6
Mean step sizes across all anchors and random problem instances
The dashed line represents the constant step-size value α0 = 10−3 used by the CSG and N-CSG solvers.
Tables
- TABLE 1
Benchmark Results for Each Problem–Solver Combination
The RMS of the estimation error ε[X] is shown in meters in the left columns. The right columns show the RMS of the cost function value ρ[X] in m2.
ID LM CSG N-CSG N-CSG
BLSN-CSG
TBLSN-CLM ε[X] ρ[X] ε[X] ρ[X] ε[X] ρ[X] ε[X] ρ[X] ε[X] ρ[X] ε[X] ρ[X] GC 1.28 1.05 0.38 3.76 0.32 2.01 0.35 1.98 0.36 1.97 0.38 2.02 GO 1.14 1.09 0.36 3.72 0.28 2.02 0.31 2.00 0.32 2.00 0.34 2.07 GM 1.47 1.01 0.55 3.93 0.45 2.02 0.48 1.97 0.47 1.94 0.47 2.00 LC 1.88 1.02 1.16 30.71 0.61 1.46 0.61 1.41 0.61 1.37 0.62 1.42 LO 1.41 0.99 1.16 30.21 0.61 1.37 0.62 1.34 0.62 1.31 0.63 1.42 LM 1.92 0.92 1.16 30.73 0.59 1.44 0.62 1.37 0.63 1.33 0.65 1.36 MC 1.87 1.00 0.67 3.79 0.60 2.59 0.73 2.39 0.78 2.32 1.17 1.98 MO 1.09 0.92 0.70 3.55 0.83 2.29 0.85 1.68 0.87 1.67 1.04 1.68 MM 1.26 1.01 0.51 3.00 0.50 1.93 0.61 1.56 0.60 1.73 0.62 1.98 RC 1.60 1.01 0.57 3.76 0.47 9.50 0.40 2.35 0.34 2.50 0.48 2.42 RM 1.58 1.04 0.59 3.64 0.53 12.42 0.40 2.40 0.33 2.56 0.49 2.47 Note: Values are rounded to two decimal places. The lowest estimation error and RMS of the cost function value achieved for each problem are shown in bold.
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