University of California, Santa Barbara
The Linear Referencing Profile
is one of the message profiles in the LRMS. It communicates a location
by means of what is popularly known as route and offset. The
route is identified by a name or a numeric index; the offset is expressed
as an absolute distance (in decimetres) or normalized distance (percentage
of route length, correct to 0.01%). Our task is to test this profile,
i.e. to evaluate its ability to transmit a message meaningfully and unambiguously
There are a few details about the way the Profile is currently specified, that need revision, e.g. superfluous pad bits, and logical inconsistencies due to typographic errors. These are described in our report, but are not substantive enough to be covered in this summary.
However, there is a concern
about implementation. When route identity is communicated by means
of road name, it assumes that
(a) the road exists in the destination database, with the same endpoints, and is digitized in the same direction, and
(b) the name can be matched to the source database — the Cross Streets Profile report discusses this issue at length, and concludes that database inconsistencies (e.g. US-101 vs Hwy-101; US-101 vs El Camino Real) result in unacceptably poor success rates.
On the other hand, when route identity is communicated by an index, it assumes common indexing between the communicating parties; often (but not always) this would imply that the parties share a common database, in which case interoperability is not an issue. Our evaluation therefore assumes that route is communicated unambiguously, and the only issue to be tested is offset accuracy. Linear references are employed in the Cross Streets Profile as well as the LRP; the findings of this test effort are applicable to the linear meaurement component of both profiles.
Once we assume agreement that a point lies on a given stretch of road between agreed start and end points, the only source of error is due to the digital representation of that stretch of road, i.e. the number and alignment of shape points. In general it is well known and intuitively obvious that the greater the number of shape points, the greater the length of the shape (see Mandelbrot 1967, Douglas-Poiker 1973, Buttenfield 1985). The value of this test effort is to produce quantitative estimates of the errors that would result from LRP deployment using current commercially available databases.
|.||Determine location||Convert to linear||Transfer||Recover 2-d location|
|GIS-T||Class I: DMI error||—||Class IV||—|
|ITS||Class II: GPS error||Class III||Class IV||Class V|
Testing is based on a sample of 15 sections of road in Santa Barbara County, in and near the City of Santa Barbara, as represented in 6 commercial databases, one of which is an engineering scale product. Roads are selected only if they, and the cross streets defining their extremities, are identifiable in all test databases. The sample roads range in length from 800–7500m, and include freeway sections, major roads, minor residential streets and remote winding mountain roads. Because averages are calculated in each of these categories, they are about equally represented in the sample, hence averages for the entire sample may be overly biased towards sinuous roads, relative to the average driving experience.
There are three sets of tests. First, we examine variability in road length, measuring the length of the digital shape as it appears in each database, and comparing it with our own survey using a distance measuring instrument (DMI) and differential GPS. Second, we examine Class III error: we simulate GPS readings along the sample streets, snap each point to the nearest street segment, and examine how accurately it (a) identifies the correct street, and (b) generates an accurate offset. The third test set (Class IV) takes an offset simulated in one database, and transfers it to each other database in turn, and reports the difference in offset.
The severity of DMI errors
is summarized in Table 2; the numbers are based on road observations and/or
algebraic calculations. Clearly the worst errors occur at terminal
points. Proportional errors can accumulate over long distances.
The values quoted in Table 2 are from extreme cases: lane differences are
usually self-compensating because on average roads wind both right and
left; and the effect of weaving is illustrated with respect to road behavior
that would surely invite a traffic citation.
|Terminal error (team effort, 100 km/h)||
|Rounding error (depends on DMI model)||
|Dead stop error (depends on DMI model)||
|Lane (difference between two adjacent lanes, at 200m radius of curvature)||
|Weaving (lane change back and forth every 4-5 seconds)||
|Tire pressure (effect of 25% drop in pressure)||
|Inclines, bumps, rises and falls (1 cycle of a 1m amplitude sine wave over 500m)||
Length measurement from GPS is susceptible to other sources of error. GPS inaccuracy caused by selective availability, and output latency caused by the approximately 1 sec computing time within the GPS unit, cause small inaccuracies. In general, at a speed of about 75 km/h, length calculation based on differential GPS tracking should be within 1–2% of driven distance.
With the above instrumental
limitations in mind, we measure driven distance along 15 roads, using DMI
and differential GPS, and compare these values to the measured road lengths
in our 6 databases. In general, GPS, DMI and the engineering database
measurement are within 0.1–0.5% of each other, which amounted to about
10m on the sampled road sections. The other databases are typically
in error by 5–15%, translating to about 100–150m error. There are
two reasons for this. The first is the density and positional accuracy
of shape points (Figure 1). The second is the accuracy with which
end points, particularly intersections of freeway ramps, are positioned
in the databases (Figure 2).
Douglas DH, TK Poiker (formerly Peucker) 1973. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Canadian Cartographer 10:112–22
Mandelbrot BB 1967.
How long is the coast of Britain? Statistical self-similarity and
fractional dimension. Science 156:636–38
The full text of the LRMS Linear Referencing Profile report is available under Technical Reports. VITAL acknowledges the support of the Federal Highways Administration, ITS Joint Program Office, Contract DTFH61-91-Y-30066. The project was executed under contract to Viggen Corporation. Infrastructure development that enabled this research was funded by Caltrans.