GPS Consumer Series: The Vertical Component of GPS
By Chuck Gilbert

Introduction
When you read the technical specification for a GPS-based data collection system, you may notice that the specification of vertical accuracy is often conspicuously absent. When discussing GPS accuracy, GPS manufacturers can go on for hours without ever making any reference to whether the numbers they bandy about refer to horizontal accuracy, vertical accuracy or both. As if it were an unloved misfit, the vertical accuracy is typically ignored in discussions of GPS accuracy. Why?
      In short, GPS vertical accuracy is often ignored simply because it is not as good as the horizontal accuracy. This month's column takes a look at vertical accuracy and what users can consider to ensure that the GPS receiver they purchase is able to meet all their accuracy requirements.

Why the difference?
GPS positions, as originally computed by the GPS receiver, always contain three spatial components. This is true for all receivers from all manufacturers. It is important to understand and accept that all GPS positions are always three-dimensional positions. There is a common misconception that if you use less satellites, you can compute a two-dimensional position. This is really a misnomer. Let's look at what really happens.
      To compute a GPS position, the GPS receiver must solve for four unknowns; x, y, z, and time. (The GPS receiver has an internal clock error, this internal clock error is the fourth unknown, referred to as "time.") Therefore, the GPS receiver requires four sources of information in order to solve four unknowns. Generally, the four sources of information are four satellites.
      There are other ways to get four sources of information. It is not uncommon for users to try to use only three satellites and get the fourth variable from another source. One possibility (although it is not common), is for the user to use three satellites and to carry his own atomic clock. The atomic clock will provide a stable time source (to solve for the receiver clock offset) and the three satellites allow the receiver to solve for x, y, and z. This is not a common solution since atomic clocks are expensive. The other way to use three satellites is for the user to supply the fourth parameter.
      For the overwhelming majority of GPS users, when they are using only three satellites, they provide the receiver with the required fourth parameter by simply typing one of the required parameters directly into their GPS receiver. Does this sound like a rather flaky way to compute a precise GPS position? If so, that's because it is. Here is how it works.
      The easiest parameter for the user to estimate is the "z" value. Most users find it easier to accurately estimate their altitude than their latitude or longitude; and it would be quite impossible for the user to continuously estimate the receiver clock error down to better than a millisecond. Therefore, many receivers provide a screen that can be used to enter an estimate of their altitude when only three satellites are being utilized for a position. Essentially, by entering a fixed "z" value, the user is pretending that there is a satellite at the center of the Earth and is guessing at the distance from that satellite to their location. In reality, this is a dangerous trap.
      The first part of the problem is that the GPS receiver does not require the user's height above sea level. The GPS receiver requires the height of the user above a hypothetical ellipsoidal model of the Earth known as WGS-84. Users rarely know their height above the WGS-84 ellipsoid, therefore they guess at their height above sea level. Unfortunately, users usually don't know their height above sea level as accurately as they think (even on a boat, the user could be wrong by several meters due to tidal variations; and the contours on many topographic maps can be inaccurate by several meters). Furthermore, even in the unlikely event that the user does enter the correct height above sea level, the GPS receiver will often use a crude model to convert the height above sea level to a useable height above ellipsoid. The model used to convert from sea level to ellipsoidal height could easily introduce another error of several meters. The result is that the user has little possibility of managing to enter the correct height. When the user enters the wrong height, the GPS receiver will hold the users altitude fixed at that height and will solve for the other three parameters; x, y, and time. When the user's estimate of altitude is wrong by, say, 10 meters; the resulting horizontal position will also have a 10 meter error. This 10 meters is in addition to all other error sources.
      The bottom line is that a GPS receiver requires a minimum of four satellites simultaneously to compute an accurate position. A GPS receiver can compute a position from only three satellites, however, such positions are never likely to be very accurate.

Why is z less accurate than x and y?
Even when four or more satellites are used to compute a position, the vertical component of a GPS position is usually less accurate than the horizontal components. When vertical accuracy is not explicitly stated, a good rule of thumb is to assume that the vertical accuracy is always two to three times worse than the horizontal.
      Why is the vertical typically so much worse than the horizontal? I heard it best described by a salesman with the following anecdote: "When you use your GPS receiver to compute a position, note that the GPS receiver is generally able to receive satellites from all points of the compass. Therefore, it can measure the distance to a particular satellite and get a certain result. Then, when it measures a distance to another satellite on the other side of the sky this second measurement can serve as a partly redundant measurement to check or validate the measurement that was taken from the opposite direction. This same manner of checking can be performed in all horizontal directions because of satellites that are generally available in all directions over the course of a day.
      In the vertical component, however, the best you can hope for is to have a satellite directly overhead. Generally you are not lucky enough to have a satellite directly overhead so you end up using the vertical components of whatever satellites are at fairly high elevations with respect to your location on Earth. However, unlike the horizontal scenario, where you are able to receive redundant measurements from opposite directions, you never receive a signal from a satellite that is directly beneath you! Therefore the vertical component of GPS positions is inherently weaker than the horizontal."

Surveying versus mapping
In the world of surveying and high precision GPS the vertical accuracy is almost always clearly stated right next to the horizontal accuracy. This might be a function of the legal nature of survey work and a professional surveyor's requirement to fully understand what comes out of the GPS receiver. A typical accuracy specification for a survey grade receiver might be something similar to 1 centimeter horizontal and 2 centimeters vertical accuracy.
      However in the world of "mapping" and GIS data collection, virtually every system on the market offers a well defined horizontal accuracy specification and makes no mention of vertical, almost as if vertical data doesn't even exist. If a GPS-based data collection tool (or mapping grade receiver) does not have a clearly stated accuracy specification, then the following table may be of some assistance in estimating the vertical accuracy.

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