• airborne radar
• atmospheric turbulences
• covariance matrix estimation.
• grid-locking
• Multiradar system
• sensor registration
• tracking
• tropospheric error correction

In the last few years Homeland Security (HS) has gained a considerable interest in the research community. From a scientific point of view, it is a difficult task to provide a definition of this research area and to exactly draw up its boundaries. In fact, when we talk about the security and the surveillance, several problems and aspects must be considered. In particular, the following factors play a crucial role and define the complexity level of the considered application field: the number of potential threats can be high and uncertain; the threat detection and identification can be made more complicated by the use of camouflaging techniques; the monitored area is typically wide and it requires a large and heterogeneous sensor network; the surveillance operation is strongly related to the operational scenario, so that it is not possible to define a unique approach to solve the problem [1].
Information Technology (IT) can provide an important support to HS in preventing, detecting and early warning of threats. Even though the link between IT and HS is relatively recent, sensor integration and collaboration is a widely applied technique aimed to aggregate data from multiple sources, to yield timely information on potential threats and to improve the accuracy in monitoring events [2]. A large number of sensors have already been developed to support surveillance operations. Parallel to this technological effort in developing new powerful and dedicated sensors, interest in integrating a set of stand-alone sensors into an integrated multi-sensor system has been increasing. In fact, 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
In this dissertation, a notional integrated multi-sensor system acting in a maritime border control scenario for HS is considered. In general, a border surveillance system is composed of multiple land based and moving platforms carrying different types of sensors [1]. In a typical scenario, described in [1], the integrated system is composed of a land based platform, located on the coast, and an airborne platform moving in front of the coast line. In this dissertation, we handle two different fundamental aspects.
In Part I, we focus on a single sensor in the system, i.e. the airborne radar. We analyze the tracking performance of such a kind of sensor in the presence of two different atmospheric problems: the turbulence (in Chapter 1) and the tropospheric refraction (in Chapter 2). In particular, in Chapter 1, the losses in tracking accuracy of a turbulence-ignorant tracking filter (i.e. a filter that does not take into account the effects of the atmospheric turbulences) acting in a turbulent scenario, is quantified. In Chapter 2, we focus our attention on the tropospheric propagation effects on the radar electromagnetic (em) signals and their correction for airborne radar tracking. It is well known that the troposphere is characterized by a refractive index that varies with the altitude and with the local weather. This variability of the refractive index causes an error in the radar measurements. First, a mathematical model to describe and calculate the em radar signal ray path in the troposphere is discussed. Using this mathematical model, the errors due to the tropospheric propagation are evaluated and the corrupted radar measurements are then numerically generated. Second, a tracking algorithm, based on the Kalman Filter, that is able to mitigate the tropospheric errors during the tracking procedure, is proposed.
In Part II, we consider the integrated system in its wholeness to investigate a fundamental prerequisite of any data fusion process: the sensor registration process. The problem of sensor registration (also termed, for naval system, the grid-locking problem) arises when a set of data coming from two or more sensors must be combined. This problem involves a coordinate transformation and the reciprocal alignment among the various sensors: streams of data from different sensors must be converted into a common coordinate system (or frame) and aligned before they could be used in a tracking or surveillance system. If not corrected, registration errors can seriously degrade the global system performance by increasing tracking errors and even introducing ghost tracks. A first basic distinction is usually made between relative 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 bias. Chapter 3 of this dissertation is dedicated to the solution of the relative grid-locking problem. Two different estimation algorithms are proposed: a linear Least Squares (LS) algorithm and an Expectation-Maximization-based (EM) algorithm. The linear LS algorithm is a simple and fast algorithm, but numerical results have shown that the LS estimator is not efficient for most of the registration bias errors. Such non-efficiency could be caused by the linearization implied by the linear LS algorithm. Then, in order to obtain a more efficient estimation algorithm, an Expectation-Maximization algorithm is derived. In Chapter 4 we generalize our findings to the absolute grid-locking problem.
Part III of this dissertation is devoted to a more theoretical aspect of fundamental importance in a lot of practical applications: the estimate of the disturbance covariance matrix. Due to its relevance, in literature it can be found a huge quantity of works on this topic. Recently, a new geometrical concept has been applied to this estimation problem: the Riemann (or intrinsic) geometry. In Chapter 5, we give an overview on the state of the art of the application of the Riemann geometry for the covariance matrix estimation in radar problems. Particular attention is given for the detection problem in additive clutter. Some covariance matrix estimators and a new decision rule based on the Riemann geometry are analyzed and their performance are compared with the classical ones.

[1] Sofia Giompapa, “Analysis, modeling, and simulation of an integrated multi-sensor system for maritime border control”, PhD dissertation, University of Pisa, April 2008.
[2] H. Chen, F. Y. Wang, and D. Zeng, “Intelligence and security informatics for Homeland Security: information, communication and transportation,” Intelligent Transportation Systems, IEEE Transactions on, vol. 5, no. 4, pp. 329-341, December 2004.