Robust State Estimation in Uncertain Environments Using Point Process Models

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The objective of state estimation is to mitigate the effects of noise in sensor measurements and extract the fixed or time-varying parameters of an object of interest using certain system and measurement models. Noise mitigation is necessary not only because no sensor is perfect, but also because our knowledge or model assumptions about any unknown system and its parameters are imprecise. The estimator considers the model uncertainties and noise statistics in order to optimally estimate the parameters of the subject of interest to some optimality criterion. While state estimation typically considers only the effects of system (or model) noise and measurement noise, in estimating the state of a moving object over time, target tracking considers additional measurement-origin uncertainties due to missing detections, false alarms, and interference from other objects of interest. In target tracking, the objective of state estimation is then to mitigate the effects of model and sensor noise and those of measurement-origin uncertainties. With the emergence of affordable sensors (e.g., cameras, sonobuoys, satellite receivers), sensor processing with the objective of state estimation and target tracking has become common. The ubiquitous and affordable nature of these sensors results in additional uncertainties that have not been addressed properly in the literature to date. In sensor processing where expensive radar systems with only one or a handful of sensors are used, systemic errors such as sensor biases, clutter, electronic countermeasures, and other interference have been effectively modeled and addressed. But, given the large number of heterogeneous sensors available, these additional sources of uncertainties have not been modeled or addressed optimally. This situation provides the motivation for the proposed work. Specifically, we will address the following problems: 1) mitigating and taking advantage of various environmental conditions to improve tracking results; 2) track-before-detect for low-observable targets in the presence of heavy clutter; 3) integration of state estimation with sensor management; and 4) constrained state estimation and prediction with the aid of uncertain external data sources (e.g., maps, terrain data). Our solution methodology is based on Point Process models and the Analytic Combinatorics (AC) formalism, which provide an efficient mechanism for working with a wide range of uncertainties in large-scale problems. To provide a comprehensive solution, we will model various forms of uncertainties that are internal and external to sensors, develop robust algorithms to minimize the efforts of sensors, and quantify the performance of the new algorithms using extensions to the AC formalism. In addition to advancing the state-of-the-art, the project will also produce a number of highly qualified personnel in areas of critical importance to Canada.