6.2.1 Measurement Biases and Errors

INTRODUCTION

All GPS pseudo-range and carrier phase measurements are affected by a variety of biases and errors (see Figure below). To appreciate the impact of measurement biases on GPS data quality (and ultimately on the positioning accuracy and reliability that is obtained), the level of measurement noise should be kept in mind.

"Rule-of-Thumb": < STRONG>Measurement resolution is possible at the level of 1%, or better, of the wavelength. This is therefore the level of measurement noise.

For the two basic GPS range-like measurements, the implications are:

Pseudo-range "noise":

• C/A code "wavelength" is approximately 300m, hence 3m is the range resolution or range measurement noise.
  (There is, however, a trend to instrumentation with submetre C/A code resolution.)
• P code "wavelength" is approximately 30m, hence 0.3m is the range resolution, or range measurement noise.

Carrier phase "noise":

• L1 carrier wavelength is approximately 0.19m, implying millimetre resolution, or carrier measurement noise.
• L2 carrier wavelength is approximately 0.24m, implying millimetre resolution, or carrier measurement noise.

Measurements are also biased by: atmospheric refraction clock errors site and instrumental effects Selective Availability effect phase is biased by unknown ambiguity

Biases may be defined as being those effects on the measurements that cause the true range to be different from the measured range by a systematic amount, and which must be accounted for in the measurement model used for data processing. As well as entering through incorrect or incomplete observation modelling, biases can also enter through imperfect knowledge of constants (for example, any "fixed" parameters such as the satellite orbit data, station coordinates, speed of light, etc.). Hence under the heading of "errors" are assembled all unaccounted for measurement effects, as well as any unmodelled or residual biases (see section 2.4). Different GPS applications require different levels of GPS accuracy. There is therefore a different partitioning of "biases" and "errors". At one extreme, in the case of GPS pseudo-range-based point-positioning, all effects with the exception of the receiver and satellite clock "uncertainty" are treated as errors. At the other extreme, GPS baseline determination to accuracies as high as 0.01 parts per million (ppm) for geodesy applications demand that all measurement biases are explicitly accounted for in any solution scheme. In the case of GPS surveying (falling as it does between these two extremes) the following categorisation can be adopted:

BIASES

• Satellite dependent:
  • Ephemeris uncertainties
  • Sate llite clock uncertainties
  • Selective Availability effects
• Receiver dependent:
  • Receiver clock uncertainties
  • Reference station coordinate uncertainties
• Receiver-Satellite (or Observation) dependent:
  • Ionospheric delay
  • Tropospheric delay
  • Carrier phase ambiguity

ERRORS

• Unmodelled, residual biases
• Carrier phase cycle slips
• Multipath disturbance
• Antenna phase centre offset
• Random observation error (noise)

GPS biases and errors.

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© Chris Rizos, SNAP-UNSW, 1999