Research On Compuatioanlly Efficient Localization Methods Based On Phase Interferometers

Fast and accurate source localization using an array of sensors is an important topic due to its applications in various areas ranging from wireless communications,radars,sonars,microphone arrays,radio astronomy,seismology,to medical diagnosis and treatment.Source localization is implemented by sampling the fields of incident waves from different directions using an array of sensors.This dissertation establishes a methodology for source localization through transformation of the localization problem from the spatial domain to the spectral domain.Firstly,the spectral-domain interferometer equation(SDIE)is established exploiting integral transforms,mapping the localization problem from the spatial domain to its corresponding spectral domain.The dependence of localization parameters on the spatial domain is transformed to the dependence in the corresponding spectral domain,and hence separating the two-dimensional(2-D)direction of arrival(DOA)for a far-field target and the three-dimensional(3-D)localization parameters for a near-field target.In order to extract the localization-related spectrums,evaluation of spectrums by discrete samples is then developed.SDIEs are thereafter adopted in the circular array(CA),elliptical array,and spherical array(SA),realizing separable variables and hence establishing algebraic relations between the localization parameters and the phase samples.The method is computationally efficient since the localization parameters are estimated through explicit and analytical calculations.For the CA and SA in particular,spectral-domain expressions are first developed,decoupling the two angular parameters.Fourier series are applied as basic functions to the acquisition of spectrums,giving analytical formulations for the two angular parameters by discrete samples around a circular or spherical aperture.Fourier sampling theorem ensures the minimum element number for 2-D DOA estimation.Cramér-Rao lower bound(CRLB)is derived and compared with theoretical accuracy analysis,showing the achievement of an optimum estimation.Mathematical insights into the relation between the estimation accuracy and the element number are observed by employing Parseval's theorem in the Fourier domain.Numerical examples and experimental results are provided to verify the proposed method.It is well known that high DOA estimation accuracy can be obtained from large apertures.However,the measurement of phase difference can only be made modulo of 2?,which leads to an ambiguity in determining the localization of the source.Two methods for ambiguity resolution are proposed,one of which is addressed in the Fourier domain by finding the missing spectrum of ambiguity numbers through integer search.The other method is based on the high-order difference invariance(HODI)property of a CA,by exploiting the rotational symmetry of a CA to realize a virtually smaller radius without DOA estimation accuracy loss.Ambiguity resolution is then addressed by the HODI,giving analytical and simultaneous procession for both ambiguity resolution and DOA estimation.The probability of correct DOA estimation via the HODI is studied.Finally,numerical simulations and experimental measurements are provided to verify the effectiveness and appealing performance of the proposed algorithm.Apart from direction finding of far-field sources,a sensor array is also utilized in 3-D localization,where the range of the source is obtained in addition to 2-D DOA,employing the characteristics of spherical wavefronts of the near field.An analytical method for estimating the 3-D localization with a CA interferometer is presented based on the SDIE.The 3-D parameters are decoupled to different spectrums in the spectral domain and algebraic relations are established between the 3-D localization parameters and the Fourier spectrums.Fourier sampling theorem ensures the minimum element number for 3-D localization of a single source with a CA.Numerical simulations and experimental results are provided to verify the effectiveness of the proposed 3-D localization algorithm.The above-mentioned localization methods require simultaneous sampling of field distributions by static arrays,and hence a considerable number of sensors and associated receivers.In contrast,a moving array,i.e.an array whose element positions vary over time,can be exploited to tradeoff between processing time and hardware cost by time-divided sampling rather than simultaneous sampling as in static arrays.This dissertation essentially focuses on parameter estimation of multiple sources with time-varying parameters,e.g.2-D DOA and signal sorting,with a low-cost circular synthetic array(CSA)consisting of only two rotating sensors.The basic idea is to decompose the received data,which is a superimposition of phase measurements from multiple sources into decoupled groups and separately estimate the DOA associated with each source.Motivated by joint parameter estimation,the expectation maximization algorithm is adopted,which involves two steps,namely,the expectation-step(E-step)and the maximization(M-step).In the E-step,the correspondence of each signal with its emitting source is found.Then,in the M-step,the maximum-likelihood(ML)estimates of the DOA parameters are obtained.These two steps are iteratively and alternatively executed to jointly determine the DOAs and sort multiple signals.Closed-form DOA estimation formulae are developed by ML estimation based on phase data,which realize an optimum estimation.Directional ambiguity is also addressed by another ML estimation method based on received complex responses.The CRLB is derived for understanding the estimation accuracy and performance comparison.The verification of the proposed method is demonstrated with simulations.