TDOA/FDOA And SDOA Estimation In Passive Localization

The dual-satellite passive localization system uses two satellites to receive and process the signal emitted from the target to obtain the location of the target,which has the advantages of simple structure,long distance and strong concealment.With the continuous development of spatial information technology and signal measurement technology,the dual-satellite passive localization system has attracted wide attention.Estimating the parameters of the received signal of two satellites is the basis for target localization.For the narrowband emitted signal,the estimated parameters are the time difference of arrival(TDOA)and the frequency difference of arrival(FDOA)between two received signals of the two satellites.While for the wideband emitted signal,the estimated parameters are the time difference of arrival(TDOA)and the scale difference of arrival(SDOA)between two received signals of the two satellites.The estimation performance of the TDOA /FDOA and the TDOA / SDOA directly affects the accuracy and speed of the target localization.However,the computational cost of existing TDOA /FDOA estimation algorithms and TDOA /SDOA estimation algorithms are large,which is difficult to meet the requirement of real-time processing.The work of this dissertation is carried out aiming at the efficient esimation of TDOA /FDOA and the efficient esimation of TDOA / SDOA for the linear frequency modulated(LFM)signal in the context of the dual-satellite passive localization system.On the basis of priveous work,by analyzing existing TDOA /FDOA estimation algorithms and TDOA /SDOA estimation algorithms,according to the characteristics of LFM signal,this dissertation proposes two fast and accurate TDOA /FDOA estimation algorithms and one fast and accurate TDOA /SDOA estimation algorithms to solve the problem of large computational cost of traditional estimation algorithms.The main work and main research results of this dissertation are summarized as follows:1.The influence of narrowband emitted signal and wideband emitted signal on the received signals of motion satellites is studied,and then the narrowband model and wideband model of the received signals of two satellites are established.The Cramér-Rao lower bound of TDOA and FDOA estimation and the Cramér-Rao lower bound of TDOA and SDOA estimation are introduced.The concepts of narrowband cross ambiguity function,wideband cross ambiguity function and fractional Fourier transform(Fr FT)are given,then the common algorithms for realizing discrete narrowband cross ambiguity function,discrete wideband cross ambiguity function and discrete fractional Fourier transform are discussed.2.Aiming at the problem that the computational cost of two-dimensional searching the peak position of narrowband ambiguity function is large,by analyzing the narrowband ambiguity function of the LFM signal,a TDOA/FDOA estimation algorithm which is one-dimensional searching the peak position of narrowband ambiguity function along the ridge of narrowband ambiguity function is proposed.The main work is listed as follows: The narrowband ambiguity function of the LFM signal is deduced to show the fact that the narrowband ambiguity function of the LFM signal has a ridge which passes through the peak position of the narrowband ambiguity function.Based on this fact,the idea of searching for the peak positon of the narrowband ambiguity function along the ridge is established.Then,we use the decimated ambiguity function to fastly estimate the slope of the ridge and estimate the intersection of the ridge and the frequency axis using Fr FT,thus obtain the position equation of the ridge.When searching the peak position of the narrowband ambiguity function along the ridge,the value at each point on the ridge is obtained once by computating the correlation function of singals,and the TDOA and FDOA are estimated according to the peak position.The proposed method can be realized by fast Fourier transform(FFT),which has high computational efficiency.By comparing with the TDOA/FDOA estimation algorithm,the efficiency of the method is validated.The simulation results show that the proposed method can accurately estimate the TDOA/FDOA and with the increase of the signal-to-noise ratio,the root mean square error is close to Cramér-Rao lower bound.3.The TDOA/FDOA estimation method by searching the peak position along the ridge of narrowband ambiguity function needs to accurately estimate the position equation of the ridge,which still is time consuming.By analyzing the influence of dechirp on the narrowband ambiguity function of LFM signal,a TDOA/FDOA estimation method based on dechirp is proposed.The main work is listed as follows: The narrowband ambiguity function of the dechirped LFM signal is derived and the fact that the peak position of narrowband ambiguity function of LFM signal is changed regularly by dechirp is pointed out.By dechirping two received LFM signals and computating the projection of narrowband ambiguity function of dechirped LFM signals on the frequency axis,an equation for TDOA and FDOA can be established according to the peak position of the projection result.A set of equations can be obtained by dechirping the received LFM signal with multiple angles,then the TDOA estimate and FDOA estimate can be obtained by solving the equation set,which is realized using the least square method.This method transforms the process of searching the peak position of narrowband ambiguity function into the fitting problem of least square,and it can be realized using the FFT.The simulation results show that the proposed method can accurately estimate the TDOA/ FODA and with the increase of the signal-to-noise ratio,the root mean square error is close to the Cramér-Rao lower bound.4.Aiming at the outilers problem in the practical application for the TDOA/FDOA estimation method,two different methods are proposed.The main work is listed as follows: The reason of the outilers is analyzed,and the influence of outliers on TDOA/FDOA estimation is discussed,then the method of using the Mahalanobis distance to eliminate the outliers and the interpolation method to avoid the outliers are proposed.For the interpolation method,the relationship between the interpolation factor and the dechirp angle is deduced,and in order to avoid the outliers,the condition for interpolation factor is derived.The simulation results verify the validity of these two methods.5.Aiming at the problem that computational cost of existing TDOA/SDOA estimation algorithms are too large,a scaling-based TDOA/SDOA estimation method for wideband LFM signal is proposed.The main work is listed as follows: The influence of the scale on the chirp-rate of the LFM signal is deduced,and the idea of estimating the SDOA by estimating the chirp-rates of two received LFM signals is proposed.Then,the fast scaling method for the discrete signal is introduced,and the TDOA/SDOA estimation by directly using the fast scaling method is analyzed.On the basis of the above work,a scaling-based fast algorithm of TDOA/SDOA estimation for wideband LFM signals is proposed.In this method,the Fr FT is first used to estimate the chirp-rates of two received LFM signals and the cascading structure is employed in this process,then the SDOA can be estimated according to the relationship between the SDOA and the and the chirp-rate.Then,using the estimated SDOA,the slice of wideband ambiguity function on the estimated SDOA can be obtained by computating the correlation function of two signals,thus the TDOA can be estimated according to the peak position of the correlation result.Compared with the scaling method,the advantage of this proposed method is that the signal is scaled only once,thus the computational cost is lower.The simulation results show that the proposed method can accurately estimate the TDOA/SDOA and with the increase of the signal-to-noise ratio,the estimated root mean square error is close to the Cramér-Rao lower bound.