IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 3, MARCH 2011 1075 Least Squares Estimation and Cramér–Rao Type Lower Bounds for Relative Sensor Registration Process Stefano Fortunati, Student Member, IEEE, Alfonso Farina, Fellow, IEEE, Fulvio Gini, Fellow, IEEE, Antonio Graziano, Maria S. Greco, Fellow, IEEE, and Sofia Giompapa Abstract—An important prerequisite for successful multisensor integration is that the data from the reporting sensors are trans- formed to a common reference frame free of systematic or regis- tration bias errors. If not properly corrected, the registration er- rors can seriously degrade the global surveillance system perfor- mance by increasing tracking errors and even introducing ghost tracks. The relative sensor registration (or grid-locking) process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. In this paper, we consider all registration errors involved in the grid-locking problem, i.e., attitude, measurement, and posi- tion biases. A linear least squares (LS) estimator of these bias terms is derived and its statistical performance compared to the hybrid Cramér–Rao lower bound (HCRLB) as a function of sensor loca- tions, sensors number, and accuracy of sensor measurements. Index Terms—CRLB, grid-locking process, HCRLB, multi- sensor system, sensor registration, target tracking. I. INTRODUCTION I NTEREST in integrating a set of stand-alone sensors into an integrated multisensor system has been increasing in the last few years. Rather than to develop new sensors to achieve more accurate tracking and surveillance systems, it is more useful to integrate existing stand-alone sensors into a single system in order to obtain performance improvements [1], [2]. However, an important prerequisite for successful multisensor integration is the sensor registration process. The problem of sensor registration arises when a set of data coming from two or more sensors must be combined. This problem involves the coordinate transformation and the reciprocal alignment among the various sensors: streams of data from different sen- sors must be converted into a common coordinate system (or frame) and aligned before they could be used in a tracking or Manuscript received July 20, 2010; revised October 13, 2010; accepted November 12, 2010. Date of publication December 06, 2010; date of current version February 09, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Biao Chen. S. Fortunati, F. Gini, and M. S. Greco are with the Department of Ingegneria dell’Informazione, University of Pisa, 56122, Pisa, Italy (e-mail: stefano.fortu- nati@iet.unipi.it; f.gini@iet.unipi.it; m.greco@iet.unipi.it). A. Farina, A. Graziano, and S. Giompapa are with the SELEX Sistemi Inte- grati, 00123, Roma, Italy (e-mail: afarina@selex-si.com; agraziano@selex-si. com; sgiompapa@selex-si.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2010.2097258 surveillance system. If not corrected, the registration errors can seriously degrade the global system performance by increasing tracking errors and even introducing ghost tracks. In naval system, the process of automatic registration is often referred as “grid-locking” process. For brevity, in the following, we use such term to define a general registration process regardless of the particular application. A first basic distinction is usually made between rela- tive grid-locking and absolute grid-locking. The relative grid-locking process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. The problem is that, actually, also the local sensor is affected by biases that cannot be corrected by means of this approach. The absolute grid-locking process assumes that all the sensors in the scenario are affected by errors that must be corrected. One source of registration errors is represented by the sensor calibration (or offset) errors, also called measurement errors. Although the sensors are usually initially calibrated, the calibration may deteriorate over time. There are three measurement errors, one for each component of the measurement vector, i.e., range, azimuth, and elevation. Another kind of registration errors are the attitude or orientation errors. Attitude errors can be caused by biases in the gyros of the inertial measurement unit (IMU) of the sensor. There are three possible attitude errors, one for each body-fixed rotation axis. The last source of registration errors is represented by the location (or position) errors caused by bias errors in the navigation system associated with the sensors. Various algorithms for sensor bias estimation have been proposed in the literature, both for relative and absolute grid-locking process. These algorithms fall into two main classes. A first class formulates the grid-locking problem as a track association problem. Two examples of this class of algorithms can be found in [3] and [4]. In [3], a registration algorithm for two radars is proposed, whereas in [4] a similar procedure is applied to a scenario composed by an active sensor and a passive sensor. The scenario with two active sensors is not investigated in [4]. A second class of algorithms does not use a track-level data, but simply a plot-level data. To estimate the registration errors, such algorithms need only a set of common detections (i.e., each radars in the system must detect the same target at the same time). Since the algorithm derived in this paper falls into this second class, in the following a detailed summary of the existing algorithms for this class is provided. 1053-587X/$26.00 © 2010 IEEE