Abstract
An accurate 3-D wireless local positioning system (LPS) is a highly demanded tool for increasing safety in, e.g., emergency response and security operations. An LPS is an attractive approach that can meet stringent requirements and can achieve acceptable accuracies for a long time during extended operations in global navigation satellite system (GNSS)-denied environments. In this work, three closed-form (CF) least squares (LS) algorithms were considered, where two of them were adapted to exploit the knowledge about nuisance parameters for accurate 3-D positioning based on time difference of arrival (TDoA) measurements. The algorithms utilize the single set (SS) of the TDoA measurements, an extended SS (ExSS) of the TDoA measurements, or the full set (FS) of the TDoA measurements, and were denoted, respectively, as the CFSSLS, CFExSSLS, and CFFSLS solutions. The performance of the algorithms was investigated with simulations and real-world measurements, where the wireless system transmitters were placed in a quasi-coplanar arrangement. At moderate to high signal-to-noise ratio (SNR) levels, the CFSSLS solution has the best performance, followed by the CFExSSLS solution and then by the CFFSLS solution. At low SNR levels, the CFFSLS algorithm outperformed the other two algorithms. Both the CFSSLS and CFFSLS solutions estimate nuisance parameters that are utilized in refining the vertical position estimate of the receiver. The CFFSLS solution delivers more accurate refined vertical position estimates since it utilizes more nuisance parameters, i.e., more information. The experimental results confirmed the simulation study in which the CFFSLS algorithm outperformed the other two algorithms, where the experimental environment was dominated by total non-line-of-sight (NLoS) conditions and low SNR levels at the receiver to be located. Therefore, it is recommended to use the FS TDoA measurements for 3-D positioning in bad signal conditions, such as high noise levels and NLoS propagation.
Highlights
Determining the position of a receiver based on signal measurements from an array of spatially separated transmitters with well-known locations has been, and is still, an important issue in wireless sensor networks, mobile communications, radar, sonar, and global navigation satellite system (GNSS) applications
Computer simulations were conducted using MATLAB to evaluate the performance of the proposed time difference of arrival (TDoA)-based CF least squares (LS) algorithms in terms of the root mean square error (RMSE) at a range of signal-to-noise ratio (SNR) levels from −5 to 40 dB
We see that the closed-form single set least squares (CFSSLS) algorithm performed best followed by the CFExSSLS algorithm at high SNR
Summary
Determining the position of a receiver based on signal measurements from an array of spatially separated transmitters with well-known locations has been, and is still, an important issue in wireless sensor networks, mobile communications, radar, sonar, and global navigation satellite system (GNSS) applications. New applications increase the demand for positioning systems where the GNSS signals are denied, e.g., indoors. Current local positioning systems (LPSs) may fail to meet the requirements of certain applications such as indoor emergency operations, e.g., fire-fighting, security and military missions, due to the need for a pre-installed radio frequency (RF) infrastructure. RF-based LPSs use wireless technologies to estimate the position of the receiver in areas where no GNSS reception is available. The nonlinear relationships of these measurements with the receiver’s position render positioning a nontrivial task
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