Junlin Yan

A Framework for Low Complexity Least-Squares Localization With High Accuracy

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.

Model of distance and bandwidth dependency of TOA-based UWB ranging error

In this paper, a statistical model for the range error provided by TOA estimation using UWB signals is given. To this purpose, a large set of UWB channel measurements covering the bandwidth between 3.1 and 10.6 GHz has been collected and processed. By analyzing the measurement results, 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 propagation. The distance and bandwidth dependency of both the mean and the standard deviation of the range error has been investigated, and an insight in the different phenomena which affect the estimation accuracy, is provided. It is shown that both the signal bandwidth and the distance between the transmitter and the receiver, significantly affect the range error characterization. From the proposed model, the estimation accuracy achieved by TOA-based UWB ranging on the global set of measurements has been derived and compared with the data. For LOS, using the full bandwidth, the range error is at centimeter level; it increases in NLOS due to the additional delay introduced by the propagation through dielectric materials and to the more dense multipath.

Feasibility of Gauss-Newton method for indoor positioning

This paper addresses the feasibility of using iterative least-squares (ILS) methods for indoor positioning, where coordinates are to be determined based on estimated/measured ranges. Special attention is given to the Gauss-Newton method, since it is well suited for solving (small residual) non-linear problems and most commonly applied in positioning. Dealing with non-linear inverse problems, the parameter estimation possibly features local minima next to the sought for global one, and the position estimator is inherently biased. In satellite positioning systems, e.g. GPS, or other large scale systems, an initial guess that leads the iterative method to a global convergence is not hard to obtain, and the bias due to non-linearity is negligible. However, in indoor systems, both effects can become problematic, and therefore extra care needs to be taken to properly apply the ILS methods. Two schemes are proposed in this paper, one to obtain a good initial guess and the other to test the significance of the bias due to non-linearity. The validation of the proposed schemes is supported by simulations as well as by experimental results obtained with an UWB acoustic positioning system, which achieves centimeter level positioning accuracy with LoS propagation and full bandwidth between 3.6 and 12.1 kHz (with equal wavelength compared to the radio signals with the bandwidth between 3.1 to 10.6 GHz allowed for UWB radio communications). The proposed schemes are validated with a number of system setups, differing in the positions of transmitters, the position of the receiver, redundancy, the bandwidth used and therefore the range measurement error.

Modeling distance and bandwidth dependency of TOA-based UWB ranging error for positioning

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 themodel to weighted least squares positioning is finally investigated. Noticeable improvements compared to the traditional least squares method have been obtained.

An Ultra-Wideband Positioning Demonstrator Using Audio Signals

UWB technology has been recognized as an ideal candidate to provide positioning information in indoor environments. However, demonstrators useful to test UWB positioning algorithms are still difficult to realize due to the hardware requirements of this technology and the scarceness of components available in the market. For this reason, the use of an acoustic demonstrator is proposed. By scaling the frequencies with a specific factor, it is possible to obtain the same wavelengths for the audio signals as for the radio signals. In this way, similar interactions with the environment can be observed. A validation of this technique is provided, by analyzing and comparing the large scale statistics and the RMS delay spread of the channel impulse response obtained with the two types of signals, and the similarities and differences are underlined. Finally, first results on the TOA estimation accuracy for different propagation conditions and on the positioning performance achievable using audio signals are shown. With the proposed audio demonstrator an accuracy at centimeter level can be achieved for LOS propagation.

A low-complexity UWB receiver concept for TOA based indoor ranging

In this paper, a new low-complexity TOA estimation strategy for UWB signals is proposed. It is shown that the TOA of the first peak of the received signal can be obtained with a simple analog receiver implementation which requires sampling rates in the order of only a few tens of MHz; at the same time, the achieved range error standard deviation is at centimeter level. A link budget evaluation under the power requirements imposed by the FCC shows that, with the suggested set of system parameters, maximum coverage of this solution is of a few hundreds of meters in LOS, making this approach ideal for low-cost, short to medium range systems which require centimeter positioning accuracy.

Novel Ultra Wideband Low Complexity Ranging Using Different Channel Statistics

UWB technology can reach centimetre level ranging and positioning accuracy in LOS propagation when time of arrival techniques are used. However, in a real positioning system, this accuracy poses high demands on hardware. In this paper, we investigate the possibility of using UWB channel impulse response statistics, other than the TOA, for ranging applications, thus avoiding the costly synchronization between the system nodes. First, models for the total received signal power, for the first path power, and for the mean excess delay of the power delay profile are proposed, based on an extensive UWB measurement campaign conducted in typical office environments. The distance dependency of these statistics is analyzed. These models are subsequently used to obtain a best linear unbiased estimation of the distance. Finally, it is shown how the knowledge of the model of the described statistics, can be used to identify the environment in which the transmitter and receiver are operating. The achieved standard deviation of the range error is 0.35 m, about three times less than obtained with the classical signal strength estimation.

Low complexity ultra-wideband ranging in indoor multipath environments

In this paper, the possibility of using UWB channel impulse response statistics, other than the TOA, for ranging applications, is investigated. Models for the total received signal power and for the first path power are proposed, based on an extensive UWB measurement campaign covering both LOS and NLOS propagation and conducted in typical office environments. The proposed models are subsequently used to estimate the distance between the transmitter and the receiver. The possibility of combining in an optimal way the range estimation provided by each single method, using a best linear unbiased estimator of the distance, is then analyzed. Finally, some implementation issues related to the proposed solution are discussed. First, a low complexity receiver implementation, able to estimate the power of the first path of the channel impulse response is suggested. Second, the bandwidth dependency of the described approach is considered and a model for the achieved standard deviation is proposed. Third, the possibility of using the strongest path power statistic, instead of the first path, is briefly discussed. In LOS, when large bandwidths are used, the first path power represents a reliable statistic, and it is able to achieve a standard deviation of the range error of 0.54 m, about half of that achieved with the classical signal strength estimation. To retrieve this statistic, no synchronization between the system nodes is needed and only modest sampling rates are required. For this reason, this approach represents a viable solution for low complexity positioning systems. In NLOS, the first path power statistic is useful to improve the accuracy provided by the signal strength approach.

A Novel Non-Iterative Localization Solution

In this paper, a new method is proposed for low complexity localization based on measured/estimated ranges. First, it is proved that the method provides a better estimator than the well known non-iterative direct methods documented in literature, i.e. the Spherical Interpolation and the Linear Least Squares method. It does so by exploiting two similar full constrained models. The proposed estimator is better, in the sense that it corresponds to an equal or smaller value of the original least-squares objective function. Second, the method goes without iterations, and therefore requires considerably less computation power than the iterative techniques such as the Gauss-Newton method. Validation is performed based on actual Ultra-WideBand (UWB) radio measurements conducted in typical office environments, with signal bandwidths varying from 1 to 7.5 GHz. Results show that the position estimates obtained with the proposed non-iterative method have lower root mean squared errors than any other tested well-known direct methods.

A new approach to low complexity UWB indoor LOS range estimation

In this paper, the possibility of using UWB channel impulse response statistics, other than the TOA, for ranging applications, is investigated. Models for the total received signal power and for the first path power are proposed, based on an extensive UWB measurement campaign conducted in typical office environments. The use of the models is twofold: to obtain a best linear unbiased estimation of the distance and to identify the environment in which the transmitter and receiver are operating. Finally, the bandwidth dependency of the proposed approach is discussed and compared with that of the signal strength method, and a possible low complexity hardware implementation is suggested. The described strategy does not need synchronization between the system nodes, and only modest sampling rates are required. At the same time, the achieved standard deviation of the range error is 0.40 m, about 2.5 times less than obtained with the classical signal strength estimation.