Weak Radar Target Detection Methods Based Upon Particle Filters

Weak maneuvering target detection is one of the most important tasks in radar signalprocessing systems. Under the condition of very low signal to noise ratio (SNR), thecoherent or incoherent integrations based on the single frame data are difficult to givereliable detection results. The track-before-detect (TBD) technique is considered to bean effective approach to realize weak maneuvering target detection and tracking. TheTBD technique is a method to implement long time signal integration, which canprocess multiple frames of measurements together and simultaneously perform targetdetection and tracking. However, the early TBD technique is implemented by the Houghtransform, dynamic programming, and maximal likelihood estimation, which prohibit orpenalize deviations from straight line motion. Compared with the now availablemethods, particle filter (PF) has outstanding performance in dealing with thenonlinear/non-Gaussian problem when the statistical information is given. And thecost-reference particle filter (CRPF) performs well in dealing with the nonlinearproblem when the statistical information is unknown. The PF and CRPF are effectivemethods of detection and tracking of weak targets in long integration time. Therefore, itis important to investigate and design the TBD algorithms based upon PF and CRPF forweak maneuvering target detection and tracking.The major works of this dissertation are to investigate and design TBD methods.The proposed methods include the likelihood ratio test based upon the auxiliary particlefilter, the generalized likelihood ratio test based upon the cost-reference particle filter,the existence probability test based on the cost-reference particle filter, and thegeneralized likelihood ratio test with total variation penalty using the forward-backwardcost-reference particle filter. These methods can implement effective detection andtracking of weak maneuvering targets in the case of low SNR.The content of the dissertation is organized as follows:1. Review particle filtering algorithms. By introducing and analyzing the PF andCRPF, two modified versions of the CRPF are presented to improve the capability ofthe state estimation in the case of unknown statistics. In the PFs, such as the sequentialimportance resampling particle filter (SIR) and the auxiliary PF (APF), the posteriorprobability density functions of the states of a dynamic system are approximated by alarge number of weighted particles, based on which the states can be estimated bymeans of different rules. However, the PFs require known statistics of the dynamicsystem including the system noise and measurement noise, which is barely encountered in applications. The CRPF was developed for dynamic systems of unknown statistics,where the user-defined cost and risk functions are used to replace the predicted andupdated posterior probability densities in the PFs for the resampling and updateprocedures. By redefining the improved cost and risk functions, two modified CRPFsare proposed for enhancing the capability of state estimation in dynamic systems ofunknown statistics.2. Likelihood ratio detectors based upon particle filters. By analyzing thedefects of the likelihood ratio detector based on the SIR, the likelihood ratio detectorbased upon the APF and the generalized likelihood ratio detector based upon the CRPFare proposed. Using the unnormalized weights of the APF before resampling toapproximate the likelihood ratio of observation, the APF based likelihood ratio test isproposed, which has better capability in weak maneuvering target detection and trackingthan the SIR based likelihood ratio test. However, the SIR and APF based likelihoodratio test require known statistics of a dynamic system. A CRPF based generalizedlikelihood ratio test is proposed for weak maneuvering target detection and trackingunder the condition of unknown statistics, where the generalized likelihood ratio isconstructed from the estimated state sequence provided by the CRPF.3. Existence probability test based upon particle filter. A CRPF based existenceprobability test is proposed for detection and tracking of weak maneuvering target whenthe dynamic system has unknown statistics. Under the condition of long oberservationtime, a target often enters and leaves a radar resolution cell during the observation. Thus,a detector is sometimes required to report the time instants for a target to enter and leaveexcept for its presence. By adding an existence variable into the state vector to modeltarget presence and absence, the existence probability at each time instant can beestimated, which can be used to measure the target presence or absence in a resolutioncell at each time instant. Moreover, the existence probabilities can show the timeinstants for target to enter and leave the resolution cell. For the dynamic systems ofknown statistics, the existence probability test based upon the SIR performs well inweak maneuvering target detection and tracking. For the dynamic systems of unknownstatistics, by introducing an existence variable and a correlative coefficient to improvethe estimation of the existence probabilities, the existence probability test based uponthe CRPF is proposed for weak target detection and tracking. Moreover, the existenceprobabilities at all the time instant are combined to form a binary test statistic to give abinary decision whether a target is present or absent in a resolution cell.4. Generalized likelihood ratio detector with total variation penalty via the forward-backward CRPF. Aiming at the detection problem of unknown nonlinear FMsignals in noise background, a generalized likelihood ratio test method with the totalvariation penalty based upon the forward-backward CRPF is proposed. In the proposedmethod, a nonlinear FM signal is modeled into piecewise linear FM signals. The centralfrequency, chirp rate, and its change rate of each signal segment form the state vector ofthe signal at this time instant. The evolution of the signal and measurements aremodeled as a nonlinear dynamic system of unknown statistics. By defining new cost andrisk functions, a forward-backward CRPF is proposed to estimate the states and theinstantaneous frequency (IF) curve of a signal. The generalized likelihood ratio teststatistic based upon the estimated states and the total variation of the estimated IF curveare important features to decide whether a nonlinear FM signal exists or not. Therefore,the two features are fused to construct the GLRT detector with total variation penalty.Compared with the two state-of-the-art detectors, the proposed detector providessignificant improvement in detection of unknown nonlinear FM signals.