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Track-Before-Detect Procedures for Low PRF Surveillance Rader Xiaobo Deng 1 * , Yiming Pi 1 , Mark Morelande 2 , Bill Moran 2 * Presenter 1. University of Electronic Science and Technology of China, Chengdu, 610054, China 2. The University of Melbourne, Parkville, VIC 3010, Australia In this paper we present a dynamic programming (DP) based tracking-beforedetect (TBD) procedures with reference to a low pulse repetition frequency (PRF) surveillance radar framework. In order to avoid nonlinear transformation and meanwhile preserve the ambiguous Doppler information which is eliminated in most of the literature, we model the target dynamics in the range-Doppler domain. The target state evolutions in the ambiguous range-Doppler domain are considered as a hybrid system with the ambiguous number deemed as mode variable. Ambiguity number (or mode) transitions are governed by guard conditions that are state-dependent. We present a DP based method for joint maximum a posteriori (MAP) estimation of target’s trajectory in the ambiguous range-Doppler maps and the corresponding ambiguity sequence, both assumptions of known and unknown nuisance parameters are considered. The detection and tracking performance of the proposed procedure is investigated under several system settings. The effect of the prior uncertainty of the nuisance parameters (target power and noise variance) on the performance is also studied. 1. Introduction Early detection and trajectory estimation of moving targets from remote surveillance radars is a very challenging problem. The detection and tracking strategy should be power efficient to deal with the targets in low signal-to-noise ratio (SNR), while the complexity should not hamper the process of early decisions. The stringent detection specification is well met by track-before-detect (TBD) approaches. TBD procedures allow simultaneous detection and tracking using unthresholded data and, shows superior detection performance over the conventional methods. Early studies on TBD methods mainly focused on its application in optical and infrared sensors as in [1-5]. Extensions of TBD methods to pulse-Doppler radar system have been considered in [6-8]. Unlike in the infrared and optical scenarios, TBD approaches operate on a sequence of twodimensional grey-scale images, in radar scenario, TBD approaches might apply to a sequence of threedimensional data sets, defined by azimuth, range and Doppler (radial velocity), making the complexity requirement much more stringent. Another difference is that, in radar applications, the inherent properties of the azimuth- range-Doppler data space can be fully exploited to improve detection and tracking performance. For example, in [6], a method for using TBD procedure in pulse-Doppler radars is described, wherein the author exploits the Doppler information to define which range cell a target would have been in the previous frame, and thus greatly simplify the search process involved in the Viterbi algorithm. However, there is a drawback with this method if the observed Doppler is ambiguous, which is the case when the radar under our consideration works with a low pulse repetition frequency (PRF). In [7], the authors maximize the data set over the observed apparent Doppler shifts, and then employ a Viterbi-like tracking algorithm in the range-azimuth domain. In [8], the authors have also suggested taking advantage from the structure of the range-Doppler domain to efficiently perform Viterbi-like tracking of multi-target. However, since the observed Doppler is ambiguous, it’s also eliminated as in [7]. In order to exploit the Doppler information more effectively, we treat it in a more subtle way. The observed Doppler is a modulo-PRF version of the true Doppler, and thus we represent the Doppler information using observed apparent Doppler and the corresponding ambiguity number. The ambiguity number is deemed as a mode variable. In order to avoid the nonlinear transformation between the target’s state and measurement (defined in the ambiguous range-Doppler domain), the target states are defined in the ambiguous range-Doppler domain. The evolutions of target state in successive range-Doppler maps are analyzed and modeled as a hybrid (or multiple-model) system [9, 10
10]: The transitions of target locations (defined by range and apparent Doppler) are governed by the ambiguity number, i.e., mode variable, while the ambiguity number transitions are state-dependent. Exploiting the admissible transitions of target locations and ambiguity number, we have proposed a dynamic programming (DP) based method for joint maximum a posteriori (MAP) estimation of target’s trajectory in the ambiguous range-Doppler maps and the corresponding ambiguity number sequence. The proposed method is investigated under both known and unknown nuisance parameters (target power and noise variance). The detection and tracking performances of the proposed algorithm are studied with respect to different system settings. Moreover, the effect of the prior uncertainty of the nuisance parameters on the detection and tracking performance is also investigated. 2. Signal processing model for low PRF surveillance radars The physical scenario considered here is shown in Fig.1. A low PRF surveillance radar is used for monitoring a given area with an electronically scanned antenna. The surveillance area is divided into small angular regions, visited by the antenna at a constant revisit intervalT R . For many long range targets, passing from one elevation beam to another during several scans happens infrequently due to the geometric constraints; however, crossing azimuth beams happens much more frequently. Therefore, each angular region is composed of a single elevation and N a azimuthal beam-pointing positions. The azimuthal beamwidth is Δ a . The pulse repetition time is T p and the number of train pulses coherently processed is Nd . At each visit, say, the kth , the radar provides a multi-dimensional data map (with four dimensions of range, azimuth, elevation and Doppler), each pixel is the reflected power out of a signal processing unit, e.g., discrete Fourier transform(DFT), of a surveillance radar. Fig.1. Radar surveillance zone illustration The conventional signal processing method for surveillance radar first thresholds the data maps to extract target plots (range, azimuth, elevation and Doppler locations), and then performs tracking based on these plots. For targets of high SNR, this method works well, however, for targets of relative low SNR, such as stealthy military aircraft and cruise missiles, thresholding throws away potentially useful information, causing missing detections. Besides, since we are concerned with low PRF radar, the Doppler plots are ambiguous; it’s hard to resolve the Doppler ambiguity under low SNR in the framework of conventional methods. The TBD algorithms use several successive unthresholded data maps to jointly determine the presence of a target and its trajectory (if present). TBD methods exploit all the useful information among several scans and are especially preferred when encountering low SNR targets. Besides, Doppler ambiguity is also implicitly resolved in the framework of TBD methods. To simplify the exposition, we assume that the azimuth and elevation information are obtained through antenna processing. The only relevant coordinates are range and Doppler. In an actual implementation, one can choose to process azimuth-elevation and range-Doppler maps separately. 11
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