Refinement of TOA Localization with Sensor Position Uncertainty in ClosedForm The subject of localization has received great deal attention in the past decades. Although it is perhaps a wellstudied problem, there is still room for improvement. Traditional localization methods usually assume the number of sensors is sufficient for providing desired performance. However, this assumption is not always satisfied in practice. This paper studies the time of arrival (TOA)based source positioning in the presence of sensor position errors. An error refined solution is developed for reducing the meansquarederror (MSE) and bias in small sensor network (the number of sensors is fewer) when the noise or error level is relatively large. The MSE performance is analyzed theoretically and validated by simulations. Analytical and numerical results show the proposed method attains the CramerRao lower bound (CRLB). It outperforms the existing closedform methods with slightly raising computation complexity, especially in the larger noiseerror case.

Direct position determination of multiple radio signals The most common methods for position determination of radio signal emitters such as communications or radar transmitters are based on measuring a specified parameter such as angle of arrival (AOA) or time of arrival (TOA) of the signal. The measured parameters are then used to estimate the transmitteru0027s location. Since the measurements are done at each base station independently, without using the constraint that the AOATOA estimates at different base stations should correspond to the same transmitteru0027s location, this is a suboptimal location determination technique. Further, if the number of array elements at each base station is M, and the signal waveforms are unknown, the number of cochannel simultaneous transmitters that can be localized by AOA is limited to M  1. Also, most AOA algorithms fail when the sources are not well angularly separated. We propose a technique that uses exactly the same data as the common AOA methods but the position determination is direct. The proposed method can handle more than M  1 cochannel simultaneous signals. Although there are many stray parameters, only a twodimensional search is required for a planar geometry. The technique provides a natural solution to the measurements sources association problem that is encountered in AOAbased location systems. In addition to new algorithms, we provide analytical performance analysis, CramerRao bounds and Monte Carlo simulations. We demonstrate that the proposed approach frequently outperforms the traditional AOA methods for unknown as well as known signal waveforms.