Optimal Placement of Heterogeneous Sensors for Targets with Gaussian Priors CHUN YANG Sigtem Technology, Inc. LANCE KAPLAN U.S. Army Research Laboratory ERIK BLASCH MICHAEL BAKICH Air Force Research Laboratory An optimal strategy for geometric sensor placement to enhance target tracking performance is developed. Recently, a considerable amount of work has been published on optimal conditions for single-update placement of homogeneous sensors (same type and same measurement quality) in which the targets are either assumed perfectly known or the target location uncertainty is averaged out via the expected value of the determinant of the Fisher information matrix (FIM). We derive conditions for optimal placement of heterogeneous sensors based on maximization of the information matrix to be updated by the heterogeneous sensors from an arbitrary Gaussian prior characterizing the uncertainty about the initial target location. The heterogeneous sensors can be of the same or different types (ranging sensors, bearing-only sensors, or both). The sensors can also make, over several time steps, multiple independent measurements of different qualities. Placement strategies are derived and their performance is illustrated via simulation examples. Manuscript received November 21, 2011; revised August 1 and October 17, 2012; released for publication November 6, 2012. IEEE Log No. T-AES/49/3/944602. Refereeing of this contribution was handled by P. Willett. This research is supported in part under Contract FA8650-08-C-1407. Authors’ addresses: C. Yang, Sigtem Technology, Inc., 1343 Parrott Drive, San Mateo, CA 94402, E-mail: (chunyang@sigtem.com); L. Kaplan, Networked Sensing and Fusion Branch, U.S. Army Research Laboratory, Adelphi, MD; E. Blasch and M. Bakich, Air Force Research Laboratory (AFRL), Rome, NY, and Wright Patterson Air Force Base, OH, respectively. 0018-9251/13/$26.00 c ° 2013 IEEE I. INTRODUCTION Target tracking performance is determined by the fidelity of the target mobility model, the tracking sensor measurement quality, and the sensor-to-target geometry. The effectiveness of a sensor update is implicitly dependent on the range to target via the signal-to-noise ratio (SNR) for a ranging sensor, and it is also an explicit function of range for a bearing-only sensor. A tracking sensor manager has choices in sensor placement, sensor selection such as waveform design and type, and filter tuning to control tracking performance for optimization of the track accuracy, target confidence, and sampling timeliness. A user (or sensor manager) can control the mobility models by choosing when to take a measurement sample (e.g., a shorter time between measurements leads to a smaller magnitude in process noise variance and a smaller coupling factor between velocity and position states) and how to capture target movement (e.g., selection of dynamic models that anticipate speed up, slow down, or turning maneuvers). An intelligent sensor manager can further adapt to various operating conditions of sensors, targets, and environments. This paper is concerned with the geometrical aspect of sensor placement so as to optimize the tracking performance. Sensor management is important for effective and efficient target tracking [24] and various strategies highlight information theory [15, 19, 21]. Typically, sensor management is developed in conjunction with many other tradeoffs such as the tracking algorithm [2], the time horizon [7], and the sequence of measurements [8]. Placement of m sensors around a target has recently drawn a considerable amount of attention. Interesting results are summarized in a recent paper [1] where the determinant of the Fisher information matrix (FIM) is maximized so as to obtain necessary and sufficient conditions for optimal placement of ranging sensors, bearing-only sensors, and time-of-arrival (TOA) and time-difference-of-arrival (TDOA) sensors, respectively. In [25] the FIM is used as part of an objective function that also includes sensor survival probability and target detection probability, and the optimal sensor placement problem is solved by a combination of deterministic (a gradient descent algorithm) and randomized (a genetic algorithm) optimization. In [23] the problem of computing the optimal geometric configuration of a mobile surface sensor network to maximize the range-related information available for simultaneous localization of multiple targets in three-dimensional (3-D) space is addressed where tradeoffs involved in the precision with which each of the targets can be localized are handled with Pareto weights. Similarly, the use of the trace of the Cramer-Rao lower bound (CRLB), which is the inverse of the FIM, is considered in [28]—[30] for TDOA measurements. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 49, NO. 3 JULY 2013 1637