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Modern passive emitter-location systems are often based on joint estimation of the time-difference of arrival (TDOA) and frequency-difference of arrival (FDOA) of an unknown signal at two (or more) sensors. Classical derivation of the associated Cramér-Rao bound (CRB) relies on a stochastic, stationary Gaussian signal-model, leading to a diagonal Fisher information matrix with respect to the TDOA and FDOA. This diagonality implies that (under asymptotic conditions) the respective estimation errors are uncorrelated. However, for some specific (nonstationary, non-Gaussian) signals, especially chirp-like signals, these errors can be strongly correlated. In this work we derive a "conditional" (or a "signal-specific") CRB, modeling the signal as a deterministic unknown. Given any particular signal, our CRB reflects the possible signal-induced correlation between the TDOA and FDOA estimates. In addition to its theoretical value, we show that the resulting CRB can be used for optimal weighting of TDOA-FDOA pairs estimated over different signal-intervals, when combined for estimating the target location. Substantial improvement in the resulting localization accuracy is shown to be attainable by such weighting in a simulated operational scenario with some chirp-like target signals.Index Terms-Chirp, conditional bound, confidence ellipse, frequency-difference of arrival (FDOA), passive emitter location, time-difference of arrival (TDOA).

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Abstract. We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of (power) values to the vertices, so that for each edge one of its endpoints has value as high as the demand, and the total sum of power values assigned is minimized. We investigate how this generalization affects the parameterized complexity of Vertex Cover. On the positive side, when parameterized by the value of the optimal P , we give an O * (1.274 P )-time branching algorithm (O * is used to hide factors polynomial in the input size), and also an O * (1.325 P )-time algorithm for the more general asymmetric case of the problem, where the demand of each edge may differ for its two endpoints. When the parameter is the number of vertices k that receive positive value, we give O * (1.619 k ) and O * (k k )-time algorithms for the symmetric and asymmetric cases respectively, as well as a simple quadratic kernel for the asymmetric case. We also show that PVC becomes significantly harder than classical VC when parameterized by the graph's treewidth t. More specifically, we prove that unless the ETH is false, there is no n o(t) -time algorithm for PVC. We give a method to overcome this hardness by designing an FPT approximation scheme which gives a (1+ )-approximation to the optimal solution in time FPT in parameters t and 1/ .

The approximability of multi-criteria combinatorial problems motivated a lot of articles. However, the non-approximability of this problems has never been investigated up to our knowledge. We propose a way to get some results of this kind which works for several problems and we put it into practice on a multi-criteria version of the traveling salesman problem with distances one and two (T SP (1, 2)). Following the article of Angel et al. [1] who presented an approximation algorithm for the bi-criteria T SP (1, 2), we extend and improve the result to any number k of criteria.

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