Wireless Localization in the Absence of GPS

In this thesis, wireless localization is investigated based on multiple noisy estimates of the time-difference of arrival (TDOA) at each pair of the n \u3e= 4 sensors with different but known locations using WiFi opportunistic signals. Our work is comprehensive and includes channel estimation, symbol detection, TDOA estimation, and location estimation. To mitigate the multipath issue induced by wideband signals, such as WiFi, frequency-division is employed to decompose the wideband RF signal into multiple non-overlapping narrowband signals. To minimize the adverse effects of the clock drift, time-division is proposed to divide the signal into multiple non-overlapping signals in the time domain. In addition, Kalman filtering is proposed, assuming the wide-sense stationary and uncorrelated scattering (WSSUS) channel and the first order auto-regressive (AR) model are used. Because of the multiple TDOA estimates at each pair of the WiFi receiver sensors, an efficient algorithm is developed to estimate the target location. The localization technique developed in this thesis can also be extended to other radio frequency (RF) signals, as shown in our simulation study for out-door localization. The simulation results in our thesis show the effectiveness of the wireless localization, although further work is needed to resolve the nonlinear estimation problem involved in localization based on TDOA estimates

System Identification Based on Errors-In-Variables System Models

We study the identification problem for errors-in-variables (EIV) systems. Such an EIV model assumes that the measurement data at both input and output of the system involve corrupting noises. The least square (LS) algorithm has been widely used in this area. However, it results in biased estimates for the EIV-based system identification. In contrast, the total least squares (TLS) algorithm is unbiased, which is now well-known, and has been effective for estimating the system parameters in the EIV system identification. In this dissertation, we first show that the TLS algorithm computes the approximate maximum likelihood estimate (MLE) of the system parameters and that the approximation error converges to zero asymptotically as the number of measurement data approaches infinity. Then we propose a graph subspace approach (GSA) to tackle the same EIV-based system identification problem and derive a new estimation algorithm that is more general than the TLS algorithm. Several numerical examples are worked out to illustrate our proposed estimation algorithm for the EIV-based system identification. We also study the problem of the EIV system identification without assuming equal noise variances at the system input and output. Firstly, we review the Frisch scheme, which is a well-known method for estimating the noise variances. Then we propose a new method which is GSA in combination with the Frisch scheme (GSA-Frisch) algorithm via estimating the ratio of the noise variances and the system parameters iteratively. Finally, a new identification algorithm is proposed to estimate the system parameters based on the subspace interpretation without estimating noise variances or the ratio. This new algorithm is unbiased, and achieves the consistency of the parameter estimates. Moreover, it is low in complexity. The performance of the identification algorithm is examined by several numerical examples, and compared to the N4SID algorithm that has the Matlab codes available in Matlab toolboxes, and also to the GSA-Frisch algorithm

A graph subspace approach to system identification based on errors-in-variables system models

System identification based on the errors-in-variables (EIV) system model has been investigated by a number of people, led by Söderström and others. The total least-squares (TLS) algorithm is now well known, and has been effective for estimating the system parameters. In this paper, we first show that the TLS algorithm computes approximate maximum likelihood estimate (MLE) of the system parameters. Then we propose a graph subspace approach to tackle the same EIV identification problem, and derive a new estimation algorithm that is more general than the TLS algorithm. Two numerical examples are worked out to illustrate the proposed estimation algorithm for the EIV-based system identification