Sparse reconstruction of equivalence classes of moving targets using single-channel synthetic aperture radar

Abstract—Simultaneously estimating position and velocity ofmoving targets using only phase information from single-channelSAR data is impossible. This paper deﬁnes classes of equivalenttarget motion and solves the GMTI problem up to membershipin an equivalence class using single-channel SAR phase data. Wepresent a deﬁnitions for endo- and exo-clutter that is consistentwith the equivalence classes, and show that most target motioncan be detected, i.e. the set of endo-clutter targets is very small.We exploit the sparsity of moving targets in the scene to developan algorithm to resolve target motion up to membership inan equivalence class, and demonstrate the effectiveness of theproposed technique using simulated data.Index Terms—Radar signal processing, synthetic apertureradar, motion detection, sparse signal recovery I. I NTRODUCTION This paper studies the problem of recovering both thepositions and velocity vectors of moving targets in a distantground scene, a problem referred to as ground moving targetindication (GMTI). A variety of radar-based approaches toGMTI have been proposed including multi-channel phasedarrays [1]–[4], displaced phase center antennas [5], and space-time adaptive processing [6]–[8]. This paper focuses on the ex-ploitation of single-channel synthetic aperture radar (SC-SAR)data for the GMTI problem. Single-channel SAR systems areof interest because they are more available and more readilydeployable on unmanned aerial vehicles and satellites wheresize, weight and power are critically important.Synthetic aperture radar (SAR) systems move a singleantenna through space to mimic the effect of sampling echoreturns using a large distributed array of antennas. Processingalgorithms applied to collected SAR data can produce near-photographic quality, highly-focused imagery of a distantscene [9]–[11]. These imaging algorithms assume that objectsin the scene are stationary over the collection interval. If thescene contains moving objects, then these objects can appearin the image to be defocused and displaced to an extent thatdepends on the speed and direction of the motion [12]–[14].A. Relation to Prior WorkTechniques for single-channel SAR GMTI have been pro-posed by a number of authors. Fineup [15] used image “sharp-ness” as a metric to estimate target motion. Ouchi [16] studiedhow target motion reveals itself in sequences of multi-lookSAR images. Kirscht [17] estimated target velocity by watch-ing target position and signal amplitude across a sequenceof SAR images. Bioucas-Dias et al [18] constructed matchedﬁlters that account for both amplitude and phase of echoesreturned from moving targets. Werness et al [19] assumed thepresence of three prominent point scatters on each target toestimate its motion. Barbarossa [20] applied optimal maximumlikelihood schemes for detecting and focusing moving targets.Samczynski et al [21] applied spectral estimation to estimatethe range component of velocity and applied a variation onmap-drift auto-focus to obtain the along-track component.Marques et al [22] applied digital spotlighting to separatemultiple moving targets before applying motion estimation.A result of Chapman et al [13] establishes ultimate limitson moving target detection and estimation using only phasemeasurements from a single-aperture SAR. SAR inherentlymeasures the two-way range to a target, and for every station-ary target there exist many moving targets having the samerange history, and therefore none of these movers can bedistinguished from the stationary target using the phase historyalone [13]. Thus there are equivalence classes of movingand stationary objects that are indistinguishable. Winkler [14,Chapter 5] provides nice graphical illustrations of these equiv-alence classes and proposes a single-channel SAR GMTIalgorithm that uses contextual information such as roadwaysto remove the class ambiguity. Marques [23] also uses priorknowledge of the road network.B. Contributions of This PaperThe present paper shows that most target motion is actuallydistinguishable from the static background. However, there isambiguity in determining both location and velocity simultane-ously. A technique is proposed to recover moving targets up tomembership in an equivalence class. The proposed techniquesimultaneously estimates an image of the stationary back-ground of the scene as well as the moving target information.The sparsity of moving targets in the scene is exploited in therecovery. The effectiveness of the method is evaluated usingsimulated data.II. D