Uniform Versus Nonuniform Sampling when Tracking in Clutter X. ZHANG, Student Member, IEEE P. WILLETT, Fellow, IEEE Y. BAR-SHALOM, Fellow, IEEE University of Connecticut Many target tracking subsystems have the ability to schedule their own data rates; essentially they can “order” new information whenever they need it, and the cost is in terms of the sensor resource. But among the unmanaged schemes, uniform sampling, in which a new measurement is requested periodically and regularly, is the most commonly-used sampling scheme; deliberately nonuniform schemes are seldom given serious consideration. In this paper, however, we show that such schemes may have been discarded prematurely: a nonuniform sampling can have its benefits. Specifically, the nonuniform and uniform sampling schemes are compared for two kind of trackers: the probabilistic data association filter (PDAF), which updates its track based on a single scan of information at a time; and N-D assignment (an optimization-based implementation of the multi-hypothesis tracker (MHT)), in which the sliding window involves many scans of observations. We find that given the ground rule of maintenance of the same overall scan rate (i.e., the same sensor effort) uniform sampling is always optimal for the single-scan tracker in the sense of track life. However, nonuniform sampling can outperform uniform sampling if a more sophisticated multi-scan tracker is used, particularly when 1) the target has a high process noise, and/or 2) the false alarm density is high, and/or 3) the probability of detection is high. Manuscript received June 1, 2002; revised June 6 and September 9, 2005; released for publication October 15, 2005. IEEE Log No. T-AES/42/2/876417. Refereeing of this contribution was handled by W. D. Blair. This research was supported by AFOSR under Contract F49620-97-1-0198 and by ONR under Contract N00014-97-1-0502. This paper is a modified version of [14]. Authors’ address: Dept. of Electrical and Computer Engineering, U-2157, University of Connecticut, 371 Fairfield Rd., Storrs, CT 06269, E-mail: (willett@engr.uconn.edu). 0018-9251/06/$17.00 c ° 2006 IEEE I. INTRODUCTION The basic tracking problem is that of state estimation for a linear system from measurements corrupted by Gaussian observation noise. The optimal (in essentially every sense) solution in this case is the Kalman filter. However, in target tracking the obfuscation in the measurement system, previously modeled only as the introduction of an additive Gaussian observation disturbance, now additionally incorporates measurement-origin uncertainty. That is, there can be false alarms, and also the “true” (i.e., target-generated) measurement may be missed. Consequently the measurement “scan” delivered from the sensor to the tracking subsystem can be null (detection missed and no false alarms), single (perhaps true, but also may be a false alarm with the true measurement missed), or multiple (the true measurement, if present at all, is not labeled as such among those delivered). The key tracking issues are hence how to determine which measurement, if any, is true, and how to reflect the resulting uncertainty in the tracker’s self-assessment. Many sensor systems operate autonomously, and deliver their measurement scans on a fixed-interval basis–most sonar systems work this way, as do conventional “rotator” radars. Some electronically steered radar systems, however, allow for the tracking user to request scans of data on an adaptive, or at least an agile, basis. Interestingly, Daum in [4] has suggested that sampling times, and possibly jittered versions of these, ought to be considered as parameters in the optimization of tracking systems. Notwithstanding, it appears that most tracking designers remain more comfortable with the original regular delivery of scans; irregular scans are an unwanted extra dimension of freedom, and it is easiest to ignore them. Here we explore the more general case of nonuniform sampling. Suppose we have a uniform sampling interval T. The kind of nonuniform sampling considered here is that the system samples at interval T 1 and T 2 alternatively; but to make the overall sampling rate equal, and to have a fair comparison, we must have T 1 + T 2 =2T. To be concrete, we may consider that a periodic-scan system can request measurements each second (T = 1), and that an alternative (but comparable in terms of radar resource cost) scheme requests a pair of scans separated by 0.1 s, with each pair separated by 1.9 s (T 1 =0:1 and T 2 =1:9). See Fig. 1 for an illustration. The timing just discussed, and that to be explored in this paper, is the result of a deliberate staggering of measurement sampling times–basically, this is an option for a radar resource management system. But there is another sort of nonuniform sampling that is not deliberate, that arising from data fusion from asynchronous sensors. Consider Fig. 2, in which centralized processing is accomplished based on 388 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 42, NO. 2 APRIL 2006