Research On MDS-based TDOA Localization Schemes Using Subspace Analisys

This dissertation focuses on source localization schemes using TimeDifference-of-Arrival(TDOA)measurements.TDOA localization is one of the four modes of wireless localization techniques which play an important role in localization systems.TDOA localization has the advantages over Time-of-Arrival localization by lower costs,over Direction-of-Arrival localization by wider applications,and over Received-Signal-Strength localization by higher accuracy.As a result,research on TDOA localization is valuable for both theoretical and practical purposes.The strategy of TDOA localization algorithms is to design a cost function with respect to the source position.By minimizing the cost function,we get the estimation of the source position.The most simple cost function is the hyperbolic least squares cost function solved by classic iterative methods.However,it suffers from low localization accuracy,high computational complexity,as well as dependence on initial guesses.Among existing cost functions,the most successful one is the spherical least squares cost function,corresponding to the two-step weighted least squares(2WLS)method published in 1994.The non-ierative 2WLS method rises to fame for its high localization accuracy and low computational complexity,nearly becoming the standard TDOA localization algorithm.However,the 2WLS method needs to invert a measurement matrix,which will become ill-conditioned when the sensor array is quasi-linear in 2 dimensional(2-D)scenarios or quasi-coplanar in 3-D scenarios.As we know,inversion of ill-conditioned matrix will lead to large localization error to cause the algorithm unstable,which is a potential risk of the 2WLS method.Recently,a new cost function is proposed in 2010 by the predecessors,named the multidimensional scaling-based(MDS-based)cost function.However,the existing MDS-based direct-form localization scheme again relies on matrix inversions and faces the ill-conditioning problem.In this dissertation,the subspace properties of the MDS model are studied thoroughly using subspace analysis methods.Based on the subspace properties,the existing direct-form localization scheme is simplified.Besides,two new localization schemes that use an auxiliary line are proposed.Particularly,the contributions of this dissertation include:1.Detailed analysis of the MDS-based cost function is presented.(1)The cost function is simplified from complex field to real field.(2)Four subspace properties of the MDS-based cost function are summarized.Among these properties,Property 1 and 4 are proposed by the predecessors,but is proved by us,whereas Property 2 and 3 are proposed and proved by us.(3)The refined cost function which takes account of the noise distribution is constructed.2.The simplified MDS-based direct-form localization scheme is presented.The linear model proposed by the predecessors is rigorously proved.The calculation of the covariance matrix of the noise vector is simplified substantially.The proposed scheme is non-iterative as the 2WLS method is,and it achives the same performance on localization accuracy and computational complexity as the 2WLS method does.3.Two MDS-based localization schemes using an auxiliary line are proposed.(1)A rough localization scheme using an auxiliary line is proposed.Firstly,subspace analysis of the MDS-based cost function is presented to draw an auxiliary line which goes through the neigbourhood of the source position.Then,the minimizer of the cost function on the auxiliary line is found to be the estimation of the source position.The proposed scheme is stable that it does not need matrix inversion.It is non-iterative that it does not need initial guesses to garrantee the convergence to the right local minimum.It has nearly the same computational complexity as the 2WLS method.However,its localization accuracy is slightly lower than that of the 2WLS method.(2)A refined localization scheme using the auxiliary line is proposed.Firstly,the cost function is modified by taking into consideration of the distribution of the measurement errors using a weighting matrix based on the estimation of the rough localization scheme.Then,the global minimizer of the refined cost function is searched for by classic iterative methods.The proposed scheme has the same localization accuracy as the 2WLS method while keeps being stable,for it does not need matrix inversion.However,its computational complexity is higher than that of the 2WLS method.Note that the most important advantage of the localization schemes using the auxiliary line is stability.The work of this dissertation enriches the properties of the MDS-based cost function of TDOA localization and presents several localization schemes that are designed in a completely different way from the existing methods.The new schemes not only improve the performances of stability,but also pave the way for new thoughts of TDOA localization problems.Future work may include research on localization schemes with sensor position errors or in the presence of synchronization clock bias.Future work may also include research on combination of TDOA with other wireless measurements,and so on.