Study On Configuration Estimation For Airborne Distributed Aperture Radars

To overcome the shortcomings inherited from traditional large-aperture radars,such as the poor battlefield survivability,expensive maintenance cost,and low efficacy-to-expenditure ratio,Lincoln Laboratory proposes the concept of distributed aperture radars,which include multiple small-aperture unit radars and a central control processing system,with the aim of reaching the identical or better detection performance compared to traditional counterparts.In comparison to traditional counterparts,distributed aperture radars possess the advantages of flexible deployment,excellent expandability,and high angular resolution.However,the application of distributed aperture radars into practice is tough,especially airborne multi-platform ones.On this occasion,relative platform positions are hard to be fixed,even to be measured precisely,and the signals from clocks and local oscillators(LOs)cannot be transferred via optical fibers,inducing the synchronization among unit radars appears more difficult.For the purpose of signal coherence on some/all observed directions,the time and phase synchronization among unit radars along with accurate knowledge of relative platform positions is required.The time and phase unsynchronization among unit radars originates from inconsistency of unit radar LOs and clocks,which can resort to the satellite bidirectional transferring technique in many cases.However,flying control errors make the radar configuration quickly time-varied and further configuration estimation challenging.Additionally,the measurement devices,such as navigation systems,cannot provide the enough radar positioning accuracy as signal coherence requires.Thus,given that several auxiliary devices are adopted,the utilization of direct path waves or echoes from targets for configuration estimation may be an effective way.At this time,the configuration estimation accuracy is primarily limited by the number and placement of auxiliary devices and unit radars,referred to as the parameter identifiability condition.This dissertation concentrates on the parameter identifiability conditions and algorithms for configuration estimation in airborne distributed aperture radars.The main contributions of this work are four-folded:1.The parameter identifiability analysis for configuration estimation under different signal utilization cases is investigated and designing requirements on airborne distributed aperture radars are given.When inter-radar signals are assumed,the Bayesian Cramer-Rao lower bound(BCRLB)for configuration estimation is derived,which serves as the discriminant tool for parameter identifiability.It declares that,accurate configuration estimation must introduce auxiliary devices.Accordingly,several ground auxiliary receivers at exactly known locations are used to collect the signals from radars.The parameter identifiability conditions for configuration estimation,when the signals from radars to auxiliary receivers are used,are derived,which is followed by the derivation concerning the optimal auxiliary receiver placement in accordance with the determinant optimization criterion.To alleviate the computational burden for a large-scale scheme,the parameter identifiability condition for partial configuration estimation using inter-radar signals is given,promising that some configuration parameters are known a priori.It is worth noting that the contents concerning parameter identifiability conditions herein provide theoretical support for the subsequent algorithms from several aspects,such as the choices of number and placement of auxiliary receivers.2.A configuration estimation algorithm based on direct path waves by unit radars and by auxiliary receivers is proposed.In the scenario where some auxiliary receivers are applied,the proposed algorithm takes advantage of the maximum likelihood estimator(MLE)to obtain range measurements from direct path waves in the first stage and then resorts to the iterative weighted least squares(IWLS)technique for obtainment of the closed-form solution concerning radar positions in the second stage.Since the configuration estimation problem is nonlinear owning to the existence of second-order position error terms and to the coupling of position errors between radars in range measurement equations,the devised algorithm introduces the novel idea of auxiliary ranges and iterative fashion to convert the nonlinear configuration estimation problem into a pseudo-linear parameter estimation one.Both theory and simulation reflect that,in the process of linearizing range measurement equations,the devised scheme does not neglect nonlinear terms of position errors and hence,it still works well under a critical scenario such as a disappointed initial guess of position errors deviating from the true solution.3.A joint target localization and configuration estimation algorithm is devised based on direct path waves and echoes,which are received by unit radars and by auxiliary receivers.In the scenario where some auxiliary receivers and single target are present,the direct path wave and echo signal model by unit radars and by auxiliary receivers are established.The hybrid Cramer-Rao lower bound(HCRLB)for joint target localization and configuration estimation is developed,followed by the simplified parameter identifiability analysis.Then a two-stage weighted least squares(TSWLS)algorithm is given for joint target localization and configuration estimation on the basis of the range measurements extracted from direct path waves and echoes,where the nonlinear problem of actual unknowns is converted into a pseudo-linear one concerning nuisance parameters(NPs)and actual unknowns in the first stage.The NPs are defined to be the coupling terms of radar and target positions,and oneway distances between them.Afterwards,the proposed scheme refines the estimates of actual unknowns by using the dependency between the NPs and actual unknowns in the second stage.It is also expanded to generalize to a multi-target scene.Both theory and simulation indicate that,the proposed algorithm is capable of reaching the optimal target localization and configuration estimation performance,given that measurement noises are sufficiently small and position errors are much small compared to one-way distances.4.The configuration estimation algorithms are given based on direct path waves and prior posture information of unit radars.When no auxiliary devices are available,the direct path wave signal model,where the receiving planar arrays of unit radars have flying postures,is established.It is assumed that the flying postures of receiving planar arrays are obtained from the inertial navigation system(INS).To relieve the phenomenon of range and angle measurement accuracy deterioration due to the limited signal sampling frequency at radar receiving ends,a phase tracking method on the basis of polynomial iteration is advocated,where the quadratic parabola fitting is implemented several times around the rough signal pulse front obtained from peak picking for refining measurements.Relying on the set of refined measurements,a coordinates-based linear transformation algorithm is devised to estimate the configuration,where the relation between nominal and true radar positions in different Cartesian coordinate systems is taken into account.To reduce the computational complexity from the nearest algorithm,an offsets-based linear transformation algorithm is proposed,where radar position error estimation is obtained by subtracting nominal relative coordinate offsets from true relative coordinate ones of all radars in different Cartesian coordinate systems.Besides,the joint signal envelope and phase grid searching around the results obtained from any one of the two configuration estimation algorithms enables the performance improvement.Experiments conclude that,the two configuration estimation methods along with joint signal envelope and phase grid searching are able to significantly alleviate the configuration estimation inaccuracy due to phase ambiguity,thereby leading to the better performance.