Skip to main content
Log in

Assessing receiver noise using GPS short baseline time series

  • Original Article
  • Published:
GPS Solutions Aims and scope Submit manuscript


In this contribution, we focus on both the functional and stochastic models of GPS short baseline time series. Biases in the observations can be interpreted as due to an incomplete functional model. Multipath, as a major part of errors, is believed to induce periodic effects on the carrier-phase observations over short time spans (a few minutes). Here, we employ a harmonic estimation method to include a set of harmonic functions in the functional model. Such sinusoidal functions are introduced to compensate for periodic systematic effects in GPS short baselines time series. This guarantees the property of unbiasedness of the least-squares estimators. On the other hand, the covariance matrix of observables is, in practice, generally based on the supposition of uncorrelated observables. A realistic description of the measurement noise characteristics, through the observation covariance matrix, is required to yield minimum variance (best) estimators. We will use least-squares variance component estimation to assess time-correlated noise of GPS receivers. Receiver noise characteristics are traditionally assessed through special zero baseline measurements. With the technique introduced in this paper we demonstrate that we can reach the same conclusions using (ordinary) short baseline measurements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others


  • Amiri-Simkooei AR, Tiberius CCJM (2004) Testing of high-end GNSS receivers. In Granados GS (ed) Second ESA/Estec workshop on satellite navigation user equipment technologies NaviTec2004, Noordwijk, The Netherlands, 8–10 December 2004, WPP-239

  • Bona P (2000) Precision, cross correlation, and time correlation of GPS phase and code observations. GPS Solut 4(2):3–13

    Article  Google Scholar 

  • De Jong C (1999) A modular approach to precise GPS positioning. GPS Solut 2(5):52–56

    Article  Google Scholar 

  • Gourevitch S (1996) Measuring GPS receiver performance: a new approach. GPS World 7(10):56–62

    Google Scholar 

  • Teunissen PJG (1988) Towards a least-squares framework for adjusting and testing of both functional and stochastic model, Internal research memo. Geodetic Computing Centre, Delft, reprint of original 1988 report (2004), No. 26

  • Teunissen PJG (2000) Adjustment theory: an introduction. Delft University Press, Delft., Series on mathematical geodesy and positioning

  • Teunissen PJG, Amiri-Simkooei AR (2006) The theory of least-squares variance component estimation. J Geod (submitted)

  • Teunissen PJG, Simons DG, Tiberius CCJM (2005) Probability and observation theory. Delft University, Faculty of Aerospace Engineering, Delft University of Technology, lecture notes AE2-E01

  • Tiberius CCJM, Borre K (2000) Time series analysis of GPS observables. In Proc. ION-GPS2000, Salt Lake city, Utah, pp 1885–1894

  • Tiberius CCJM, Kenselaar F (2000) Estimation of the stochastic model for GPS code and phase observables. Surv Rev 35(277): 441– 454

    Google Scholar 

Download references


The authors would like to appreciate M. Schenewerk and K. O’Keefe for their comments to improve the presentation of the paper.

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. R. Amiri-Simkooei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amiri-Simkooei, A.R., Tiberius, C.C.J.M. Assessing receiver noise using GPS short baseline time series. GPS Solut 11, 21–35 (2007).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: