Telecommunication Systems

, Volume 70, Issue 1, pp 97–104 | Cite as

3D WLS hybrid and non hybrid localization using TOA, TDOA, azimuth and elevation

  • Nadhir Ben HalimaEmail author
  • Hatem Boujemâa


In this paper, we propose a Three Dimensional (3D) Weighted Least Square (WLS) estimation of mobile position using Time Of Arrival (TOA), Time Difference Of Arrival (TDOA), Direction of Arrival (DOA) given by azimuth and elevation measurement. We present both hybrid and non hybrid localization techniques. Hybrid localization techniques use a combination of TOA, TDOA and DOA whereas non hybrid localization use only TOA or TDOA or DOA measurement. This is the first paper to tackle the problem of 3D hybrid localization using TOA, TDOA, azimuth and elevation. We also present a theoretical performance analysis of the hybrid localization technique where the covariance matrix of the WLS estimator is derived in closed form expression. The theoretical derivation is valid for any distribution of the observation noise. We show that the WLS estimator is unbiased and equivalent to the Maximum Likelihood estimator when the observation noise is Gaussian. We also optimize the localization accuracy by optimizing the base station location in order to minimize the Mean Square Error. Base station location optimization to enhance localization accuracy has not been yet proposed.


Hybrid localization TOA TDOA DOA Azimuth Elevation 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Authors and Affiliations

  1. 1.College of Computer Science and Engineering at YanbuTaibah UniversityMadinahSaudi Arabia
  2. 2.COSIM Research LaboratoryHigher School of Communications of TunisAryanahTunisia

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