Discover the importance of Geometric Dilution of Precision (GDOP) in GPS technology. This article delves into how GDOP impacts positioning accuracy, the factors that contribute to its variation, and practical tips for minimizing its effects to enhance navigation and surveying precision.
Loran-C Position Determination and AccuracyEquation in this Loran-C Position Determination and Accuracyarticle of the main text enables calculation of the fix accuracy (2 drms) in terms of the bearings from the user to the master and two secondary stations, the common standard deviation of each TD, the correlation coefficient between the two TDs, and the gradient of the LOPS along the baseline.
Introduction
To recapitulate, 2 drms is the radius of the fix area with probability content of at least 95 %. That is, at the given point in the coverage area, at least 95 % of the apparent fixes would be within a circular area of radius 2 drms.
It is given by the equation:
where:
- A, B, C – angles defined in Figure 1;
- ρ – correlation coefficient between the measured TDs, generally taken to be 0,5;
- K – baseline gradient, 491,62 ft/usec, and;
- σ – common value for the standard deviation of each TD, generally taken to be 0,1 usec for accuracy calculations.
Referring to Figure 1, angle A is the angle between the first secondary and the master station (viewed from the user’s position) and angle B is that subtended by the master and the other secondary. The actual TDs are shown by the dashed lines which are bisectors of angles A and B.

The crossing angle, C, for the three station fix is:
The parameter ρ in equation (1) is the correlation coefficient between the two TDs. The three individual signals from the master and two secondaries are assumed to be independent and uncorrelated because the timing of each signal is derived from separate cesium oscillators. However, the two TDs are correlated to some degree because both are based upon a common master signal. The correlation coefficient varies throughout the coverage area, but is typically given the value 0,5 in chain coverage calculations.
Numerical Examples
In the illustration, angle A is approximately 89 degrees, and angle B is approximately 70 degrees and angle C = 8 912+7 012 = 79,5 degrees. Because the crossing angle is quite large, it is to be expected that the value of 2 drms at this location in the coverage area would be relatively small. This conjecture is shown to be correct: substitution of these angles and other constants given results in a value of 2 drms of approximately 235 ft – quite accurate indeed.
If the vessel (or aircraft) in the illustration were to move away from the master in a generally northeast direction until angle B were 20 degrees and angle A were 30 degrees (thus, angle C = 25 degrees), then the value of 2 drms would increase to approximately 1 922 ft.
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Equation (1) can be used to calculate 2 drms for a three-station loran fix anywhere within the coverage area. Table 1 shows how 2 drms varies with angles A and B. This quantity grows quite large whenever either or both of these angles are small. Figure 2 shows contours of equal value of 2 drms.

In general, as shown in Figure 2, the value of 2 drms is a function of the placement of the master and secondary stations,the user’s location relative to these stations, and the common standard deviation of the TDs.

According to Swanson (1978), the greatest possible accuracy (minimum value of 2 drms) will occur with four stations, each subtending a 90 degree angle with the adjacent station so as to form two orthogonal (at right angles) and uncorrelated LOPS.
The optimal accuracy for this configuration, 2 drms*, is given by the equation:
given the assumed values for each of these parameters.
The geometric dilution of position (GDOP) is defined as the ratio of the actual value of 2 drms corresponding to equation (1) divided by this “best” value, or:
In essence, GDOP measures the ratio of the actual value of 2 drms corresponding to the user’s location in the coverage area of a loran triad to the best possible accuracy of the best possible loran stations. GDOP is a normalized 2 drms, which takes into account the effects of the system geometry and the user’s location.

Table 1 shows the correspondence between GDOP and 2 drms. The specified absolute accuracy of Loran-C is 0,25 NM (1 519 ft), which is equivalent to a GDOP of 10,92.
Table 2. Correspondence between 2 drms and GDOP | |
---|---|
GDOP | 2 drms |
1,0 | 139 |
1,5 | 209 |
2,0 | 278 |
2,5 | 348 |
3,0 | 417 |
3,5 | 487 |
4,0 | 556 |
4,5 | 626 |
5,0 | 695 |
6,0 | 834 |
7,0 | 973 |
8,0 | 1 112 |
9,0 | 1 251 |
10,0 | 1 390 |
12,0 | 1 668 |
14,0 | 1 946 |
16,0 | 2 224 |
18,0 | 2 503 |
20,0 | 2 781 |