1.3.1 Biased Ranges

INTRODUCTION

An important issue is "what is a bias"? The variety of possible GPS positioning modes are all essentially different strategies for accounting for "biases" in GPS measurements. In this text range biases are defined as those influences, both instrumental (or "internal") and system origin (or "external"), on the observations which cause the measured distance to be different from the true distance by a systematic amount.

In section 2.4.1 and section 6.2.1 the distinction between a "measurement bias" and a "measurement error" will be made clearer.

There are different types of biases, but the focus shall be those biases that have the following well defined characteristics:

Range biases that affect all measurements taken at a ground station by a similar amount:

• the station dependent biases.
  

Range biases that affect all measurements made to a particular satellite by a similar amount:

• the satellite dependent biases.
  

Range biases that are unique to a particular receiver-satellite observation:

• the observation dependent biases.

   

In the case of GPS measurements, the sources of the biases can be basically partitioned into the above three categories section 6.2.1. The dominant biases are those due to the station and satellite clocks, and the geometric nature of the high precision measurement used in the GPS survey reductions. They have the following additional features:

• the station and satellite clock errors affect the respective measurements by the same amount.
• the observation dependent ambiguity in carrier phase measurements is assumed to be a constant for an extended period of uninterrupted tracking.

Before discussing biased ranges further it is necessary to introduce a more precise definition for a "clock" and for the "clock error".

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© Chris Rizos, SNAP-UNSW, 1999