The GNSS integer ambiguities: estimation and validation

Table 4.2: Probabilities Ps = P (ǎ = a), P1 = P (| ˇ b−b| ≤ | ˆ b−b|), P2 = P (| ˜ b−b| ≤ | ˆ b−b|),
and P3 = P (| ˜ b − b| ≤ | ˇ b − b|). Double difference code and phase standard deviations
respectively: σp = σm and σφ = σcm.
σ Ps P1 P2 P3
1.4 0.312 0.526 0.521 0.474
0.8 0.675 0.724 0.708 0.283
0.6 0.859 0.875 0.859 0.205
0.4 0.985 0.983 0.981 0.434
Table 4.3: Mean and maximum approximation errors in ˆz− ˜z 2 Q ˆz . Nz equals the minimum
and maximum number of integers used.
α mean maximum Nz
06 01 10 −16 753-850
10 −12 10 −11 10 −11 347-407
10 −8 10 −7 10 −6 112-155
10 −6 10 −6 10 −5 53-87
06 02 10 −16 4730-4922
10 −12 10 −12 10 −12 2203-2379
10 −8 10 −7 10 −7 785-879
10 −6 10 −6 10 −6 357-442
10 01 10 −16 274-345
10 −12 10 −11 10 −8 80-121
10 −8 10 −7 10 −4 11-31
10 −6 10 −5 10 −2 2-14
10 03 10 −16 44323-45440
10 −12 10 −11 10 −10 14353-15048
10 −8 10 −7 10 −6 2959-3330
10 −6 10 −5 10 −4 1007-1215
80 Best Integer Equivariant estimation