Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.

Underwater surveillance using passive sonar and track-before-detect technology requires accurate models of the tracked signal and the background noise. However, in an underwater environment, the signal channel is time-varying and prior knowledge about the spatial distribution of the background noise is unavailable. In this paper, an autoregressive model that captures a time-varying signal level caused by multi-path propagation is presented. In addition, a multi-source model is proposed to describe spatially distributed background noise. The models are used in a Bernoulli filter track-before-detect framework and evaluated using both simulated and sea trial data. The simulations demonstrate clear improvements in terms of target loss and improved ability to discern the target from the noisy background. An evaluation of the track-before-detect algorithm on the sea trial data indicates a performance gain when incorporating the proposed models in underwater surveillance and tracking problems.

Network-centric multitarget tracking under communication constraints is considered, where dimension-reduced track estimates are exchanged. Previous work on target tracking in this subfield has focused on fusion aspects only and derived optimal ways of reducing dimensionality based on fusion performance. In this work we propose a novel problem formalization where estimates are reduced based on association performance. The problem is analyzed theoretically and problem properties are derived. The theoretical analysis leads to an optimization strategy that can be used to partly preserve association quality when reducing the dimensionality of communicated estimates. The applicability of the suggested optimization strategy is demonstrated numerically in a multitarget scenario.

Data fusion in a communication constrained sensor network is considered. The problem is to reduce the dimensionality of the joint state estimate without significantly decreasing the estimation performance. A method based on scalar subspace projections is derived for this purpose. We consider the cases where the estimates to be fused are: (i) uncorrelated, and (ii) correlated. It is shown how the subspaces can be derived using eigenvalue optimization. In the uncorrelated case guarantees on mean square error optimality are provided. In the correlated case an iterative algorithm based on alternating minimization is proposed. The methods are analyzed using parametrized examples. A simulation evaluation shows that the proposed method performs well both for uncorrelated and correlated estimates.

This paper addresses the problem of retrieving consistentestimates in a distributed network where the communication between the nodes is constrained such that only the diagonal elements of the covariance matrix are allowed to be exchanged. Several methods are developed for preserving and/or recovering consistency under the constraints imposed by the communication protocol. The proposed methods are used in conjunction with the covariance intersection method and the estimation performance is evaluated based on information usage and consistency. The results show that among the proposed methods, consistency can be preserved equally well at the transmitting node as at the receiving node.

Using sensors to observe real-world systems is important in many applications. A typical use case is target tracking, where sensor measurements are used to compute estimates of targets. Two of the main purposes of the estimates are to enhance situational awareness and facilitate decision-making. Hence, the estimation quality is crucial. By utilizing multiple sensors, the estimation quality can be further improved. Here, the focus is on target tracking in decentralized sensor networks, where multiple agents estimate a common set of targets. In a decentralized context, measurements undergo local preprocessing at the agent level, resulting in local estimates. These estimates are subsequently shared among the agents for estimate fusion. Sharing information leads to correlations between estimates, which in decentralized sensor networks are often unknown. In addition, there are situations where the communication capacity is constrained, such that the shared information needs to be reduced. This thesis addresses two aspects of decentralized target tracking: (i) fusion of estimates with unknown correlations; and (ii) handling of constrained communication resources. 

Decentralized sensor networks have unknown correlations because it is typically impossible to keep track of dependencies between estimates. A common approach in this case is to use conservative estimators, which can ensure that the true uncertainty of an estimate is not underestimated. This class of estimators is pursued here. A significant part of the thesis is dedicated to the widely-used conservative method known as covariance intersection (CI), while also describing and deriving alternative methods for CI. One major result related to aspect (i) is the conservative linear unbiased estimator (CLUE), which is proposed as a general framework for optimal conservative estimation. It is shown that several existing methods, including CI, are optimal CLUEs under different conditions. 

A decentralized sensor network allows for less data to be communicated compared to its centralized counterpart. Yet, there are still situations where the communication load needs to be further reduced. The communication load is mostly driven by the covariance matrices since, in this scope, estimates and covariance matrices are shared. One way to reduce the communication load is to only exchange parts of the covariance matrix. To this end, several methods are proposed that preserve conservativeness. Significant results related to aspect (ii) include several algorithms for transforming exchanged estimates into a lower-dimensional subspace. Each algorithm corresponds to a certain estimation method, and for some of the algorithms, optimality is guaranteed. Moreover, a framework is developed to enable the use of the proposed dimension-reduction techniques when only local information is available at an agent. Finally, an optimization strategy is proposed to compute dimension-reduced estimates while maintaining data association quality.