Near Field Source Localization Using Evolutionary Technique

There are many challenges in far field and near field source localization in multiple narrow band source environment.To analyze the performance of source localization,the commonly observed challenges are snapshots of array output,joint estimation of unknown parameters,pair matching of unknown parameters,computational complexity,robustness to noise,distance estimation of sources from the array,array perturbations and multi-dimensional direction of arrivals(DOAs).Some of the challenges described here can be fixed in system modeling such as the array geometry,separation between array elements and number of sources to be localized and other challenges can be catered on the algorithm level.The inspiration for choosing near field narrow band source localization is due to the growing applicability such as in indoor communication and source localization,ultrasonic imaging,electronic surveillance,radio frequency identification(RFID)communications,under water source localization and seismic exploration.In this dissertation,one of the main contributions is to localize narrow band sources in the near field of the array using only a single snapshot of array output to estimate the unknown parameters,which makes it possible to use in real time applications.Also,we are jointly estimating ranges and DOAs without any pair matching by taking advantage of evolutionary computing.Array geometries like uniform linear array(ULA)and L-type array are used because of their cost effective,computationally efficient and easy to employment nature.The main contributions of this dissertation are briefly summarized as follows:1.Statistical analysis and modeling of a uniform linear array(ULA)for near field narrow band source localization(1D DOAs and ranges).When the narrow band sources are present in the Fresnel zone(near field)of the array,the source localization problem becomes more complex.The wave fronts impinging from the sources become spherical and range information of sources is also required with angle of arrival to localize the sources accurately.This doubles the number of unknown parameters to be estimated jointly and also complicates the process of computation.A massive number of snapshots of array output are required by the existing models for near field narrow band source localization.Also,most existing models could not estimate the unknown parameters jointly and require one by one estimation.This prevents the use of such methods in real time applications.To overcome the requirement of a huge number of snapshots,an evolutionary technique named as differential evolution is proposed and mean square error is adopted as a fitness evaluation function.The proposed methods is efficient enough to manage to use only a single snapshot of array output to jointly estimate the unknown parameters for near field narrow band source localization using a uniform linear array.Statistical analysis of proposed technique is performed by a large number of Monte-Carlo simulations.Simulations results show that the proposed method is nearer to the Cramer-Rao bound and approaches the bound with increase of signal to noise ratio.Furthermore,results show that the performance is effected when the source moves away from the array in accordance with the theory of wave transition to an infinite range in the far field.Also,the proposed method does not work when the number of sources is more than the number of array sensors used as it becomes an underdetermined problem.2.Enhanced modeling of a uniform linear array with sensor position perturbations and statistical analysis of the performance of near field narrow band source localization in the presence of array sensor position perturbations.Normally,in array signal processing,sensor positions are assumed to be exactly known.In practical scenarios,external factors and fabrication accuracy limitations induce errors in sensor positions known as the array perturbations.By using an array with sensor position perturbations degrades the performance and accuracy of parameter estimation.Some existing models perform array pre-calibration to know the sensor positions exactly and then perform source localization.To avoid the need for array pre-calibration,a uniform linear array is modeled for near field narrow band source localization when the sensor positions are subject to random errors.The number of unknown parameters is more than twice the number of sources in this scenario.To lessen the complexity,the process is split up in three steps.First,the ranges and DOAs are jointly estimated assuming there are no errors in sensor positions.These estimated parameters will not be accurate as in actual there are sensor position errors.In the second step,the sensor position perturbations are estimated by using ranges and DOAs estimated in the first step as calibration sources.Then,the DOAs and ranges of near field narrow band sources are updated with considering the sensor position uncertainties estimated in the second step.Differential evolution with mean square error as fitness function is taken as the global optimizer because of its competence,effectiveness and ease in application and its single snapshot requirement to convergence to optimum result.The effectiveness of proposed method is presented by a large number of Monte-Carlo simulations and their statistical analysis.The results of proposed method are compared with other methods and the Cramer-Rao bound.The results show that the proposed method outperforms other methods even in the presence of sensor perturbations and tends to approach Cramer-Rao bound.3.Statistical analysis and modeling of extension of a uniform linear array to an L-type array geometry for joint estimation of range and 2D DOAs of near field narrow band sources without using any pair matching.Over several decades,two-dimensional direction of arrival estimation has received significant consideration.Existing 2D array geometries include circular arrays,planar arrays,spherical arrays etc.As the dimensionality of DOA estimation increases,the complexity of computation of the estimation process is persistently affected by the geometry of array and pair matching of the DOAs become essential,which may result in pair matching inaccuracy and poor angle estimation performance.Existing models for 2D DOA estimation require pair matching algorithms which comprise of 2D searching and nonlinear optimization.To overcome the difficulty of pair matching and to jointly estimate the range and 2D DOAs(i.e.elevation and azimuth angles)of near field narrowband sources an L-type planar array,composed of two uniform linear arrays attached orthogonally from end of each ULA is proposed.L-type array is advantageous in terms of coverage area and employment as it needs less number of array elements as compared to rectangular and circular arrays.Another advantage of deploying L-type array is to obtain the 2D DOAs by decoupling the array into two ULAs and independently estimating DOA for each subarray.Differential Evolution with mean square error as a fitness evaluation function is applied to optimize the estimation process as it does not need spectrum peak search or additional angle pair matching procedure and converges in a single snapshot making it useful in real time applications.Theoretical analysis and experimental results show that the proposed method outperforms other methods and tends to reach the Cramer-Rao bound for elevation and azimuth angles and range estimations even the number of unknown parameters is thrice the number of sources.