ISSN: 0018-9545@en

In this paper, a new framework is proposed for least-squares localization based on estimated ranges, covering time-difference-of-arrival (TDoA), time-of-arrival (ToA), and received signal strength (RSS) cases. The multidimensional nonlinear localization problem is first transformed to a lower dimension and then solved iteratively. Within the proposed transformed least-squares (TLS) framework, we introduce a method in which the localization problem is transformed to one dimension (1-D). In this way, compared to the classical nonlinear least-squares (NLS) type of methods, the amount of computations in each iteration is greatly reduced; a reduction of 67% for a 3-D positioning system is shown. Hence, the introduced 1-D iterative (1DI) method is fairly light on the computational load. The way to choose the 1-D parameter is proposed, and theoretical expressions for the convergence rate and the root- mean-squared error (RMSE) of the 1DI estimator are derived. Validation is performed mainly based on actual ultra-wideband (UWB) radio measurements, collected in typical office environments, with signal bandwidths varying from 0.5 to 7.5 GHz. Supplementary simulations are also included for validation. Results show that, in terms of RMSE, the 1DI method performs better than the linear least-squares (LLS) method, where the solution is obtained noniteratively, and performs similarly as NLS, especially in TDoA cases.@en

A statistical model for the range error provided by TOA estimation using UWB signals is given, based on UWB channel measurements between 3.1 and 10.6¿GHz. The range error has been modeled as a Gaussian random variable for LOS and as a combination of a Gaussian and an exponential random variable for NLOS. The distance and bandwidth dependency of both the mean and the standard deviation of the range error has been analyzed, and insight is given in the different phenomena which affect the estimation accuracy. A possible application of the model to weighted least squares positioning is finally investigated. Noticeable improvements compared to the traditional least squares method have been obtained.@en

In this paper, ranging based on UWB signals is investigated for indoor dense multipath environments. To this end, a large set of time domain measurements covering the 3.1-10.6 GHz frequency band is carried out. Different approaches to detect the time of arrival of the first path are evaluated. Ranging results based on time estimation are compared to those based on signal strength. Additionally, the effect of the bandwidth on the range estimates is analyzed. Generally, the results show that high ranging accuracy can be achieved for both LOS and NLOS propagation when UWB is used. Analysis of the data points out that additional delay introduced by propagation through walls is the main source of range error in NLOS indoor environments.@en