9.4.3 Modifying the Stochastic Model

AN EMPIRICAL METHOD OF DETERMINING VCV SCALE FACTORS FOR GPS BASELINE SOLUTIONS

The method makes use of repeat baseline results. The following procedure may be used (based on an approach suggested by JONES, 1995):

• Baselines which have been measured more than once are grouped according to baseline length, for example: 1-5km, 5-10km, 10-15km, 15-25km, 25-50km, >50km.

   

• For each baseline, associated with a pair of stations k-j, the mean values of the baseline component estimates are determined B^mx_kj, B^my_kj, B^mz_kj, together with the associated mean variance terms _m²_xkj, _m²_ykj, _m²_zkj (computed from applying the Law of Propagation of Variances to the individual variance terms _i²_xkj, _i²_ykj, _i²_zkj from the diagonal elements of the VCV matrices).

   

• Compute the component differences for each individual baseline estimate i with respect to the mean values: Bⁱx_kj = B^mx_kj - Bⁱx_kj, Bⁱy_kj = B^my_kj - Bⁱy_kj, Bⁱz_kj = B^mz_kj - Bⁱz_kj.

   

• Compute the corresponding variance factors for the component differences of the individual baseline estimate i with respect to the mean values (applying the Law of Propagation of Variances): _i²_Dxkj = _i²_xkj + _m²_xkj, _i²_Dykj = _i²_ykj + _m²_ykj, _i²_Dzkj = _i²_zkj + _m²_zkj.

   

• The "standardised" differences for each baseline k-j (baseline estimate i) are computed by dividing the component differences by the formal error estimates (standard deviations):

   

• For each baseline group an average variance factor is computed:

(9.4-2)

where m is the number of baselines in the group (the summation being taken over all baselines k-j, each observed a minimum of two times).

The size of the scale factors is dependent on the instrumentation, processing software and observing conditions. Examples of scale factors determined, as a function of baseline length, are (JONES, 1995):

Leica/SKI:

- 0-5km	-- 400	(Tropical (1995) and Mediterranean (1992) climate)
- 5-10km	-- 800	(Tropical (1995) and Mediterranean (1992) climate)
- 10-20km	-- 800	(Mediterranean (1992) climate)

Trimble/GPSurvey:

- 0-2km	-- 25	("rapid static": 5-20 minutes)
- 0-2km	-- 49	(conventional static: 180 minutes)
- 2-4km	-- 36	("rapid static": 5-20 minutes)
- 2-4km	-- 49	(conventional static: 180 minutes)
- 4-8km	-- 81	(conventional static: 180 minutes)
- 8-15km	-- 121	(conventional static: 180 minutes)
- 15-30km	-- 225	(conventional static: 180 minutes)

A similar procedure may be used for any group of baselines determined using a particular hardware/software system. Though care must be taken to ensure that they are truly representative of different observing environments.

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© Chris Rizos, SNAP-UNSW, 1999