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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.

Time of arrival
(TOA) estimation using ultra-wideband (UWB) signals appears the most suitable
ranging technique for indoor positioning applications which require centimeter-
to decimeter-level accuracy [

The contribution of this letter is to provide a better understanding of the types of range error usually experienced in indoor environments and to propose a novel statistical model for the error obtained by TOA-based UWB range estimation. Unlike in the available literature, the distance and the bandwidth dependency of both the bias of the range error, and its random variations have been investigated and statistically modeled. Finally, a possible application of the model to weighted least squares positioning is analyzed and the improvements compared to the classical least squares approach are evaluated.

The channel
impulse response (CIR) measurements used in this paper were collected using a
time domain technique and cover the bandwidth between 3.1 and 10.6 GHz allowed
by the FCC for UWB radio transmissions. Details of the system setup can be
found in [

The CIR

The range error is expressed as the sum of a bias

In LOS, the bias

Parameters for the characterization of

LOS | 0 | 0.0148 | 0.48 | 0 |

NLOS | 0.019 | 0.027 | 0.47 | 0.013 |

LOS | 0.016 | 1.5 | 0.64 | 0.60 |

NLOS | 0.049 | 1.5 | 0.21 | 0.73 |

The deviation from the mean,

Range error
versus

LOS

NLOS

For the statistical characterization of

NLOS range error behavior.

From the described model, it is possible to derive the
mean and standard deviation of the range error obtained from the total set of
measurements, as a function of

Figure

Mean and standard deviation of the global range error versus

In this
section, a possible application of the proposed model to improve the classical
least squares positioning is investigated. From the total set of measurements,
a subset of

In traditional least squares, the problem is solved by
searching the minimum of the objective function

Final position estimation accuracy for different scenarios.

LOS | LOS | NLOS | NLOS | LOS/NLOS | LOS/NLOS | |
---|---|---|---|---|---|---|

LS | 0.025 (m) | 0.017 (m) | 0.143 (m) | 0.093 (m) | 0.167 (m) | 0.064 (m) |

WLS | 0.025 (m) | 0.017 (m) | 0.091 (m) | 0.068 (m) | 0.054 (m) | 0.024 (m) |

LS | 0.211 (m) | 0.147 (m) | 0.322 (m) | 0.210 (m) | 0.308 (m) | 0.180 (m) |

WLS | 0.180 (m) | 0.102 (m) | 0.235 (m) | 0.160 (m) | 0.207 (m) | 0.121 (m) |

In this letter, a statistical model for the range error obtained by TOA estimation using UWB signals has been proposed. It is shown that both a decrease of the bandwidth and an increase of the distance cause an increase in the mean and standard deviation of the range error due to the more dense multipath which results in these situations. The range error is modeled as a Gaussian random variable for LOS, and as the combination of a Gaussian and an exponential random variable for NLOS. The more complex characterization in NLOS describes the effects on the range error of the dense multipath in this propagation condition, and represents a generalization which includes also the LOS scenario. A possible application of the model to weighted least squares positioning is finally investigated. Improvements compared to traditional least squares are especially evident when there is a significant redundancy or a combination of LOS and NLOS measurements.