Abstract. In his 2005 paper, S.T. Smith proposed an intrinsic Cramér-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a Lie group. In this case, by choosing ,e.g., the right invariant metric, parallel transport becomes very simple, which allows a more straightforward ...

We here address the classical bearings-only tracking problem (BOT) for a single object, which belongs to the general class of nonlinear filtering problems. Recently, algorithms based on sequential Monte Carlo methods (particle filtering) have been proposed. As far as performance analysis is concerned, the Posterior Cramér-Rao Bound (PCRB) provides a lower bound on the mean square error. Classic...

Let X = (X1, ..., X ˆ n) be a random sample from distribution fθ. Let θ = δ(X) be an estimator of θ. Let T (X) be a su cient statistic for θ. As we have seen already, MSE provides one way to compare the quality of di erent estimators. In particular, estimators with smaller MSE are said to be more e cient. On the other hand, once we know T (X), we can discard X. How do these concepts relate to e...

er-Rao Lower Bound for Blind Signal Separation Henrik Sahlin and Ulf Lindgren Chalmers University of Technology, Department of Applied Electronics, S-412 96 Gothenburg, Sweden, [email protected], Telephone +46 31 772 1845 Abstract This paper considers some aspects of the source separation problem. Unmeasurable source signals are assumed to be mixed by means of a channel system resulting in m...

In this paper, we present a closed-form expression of a Bayesian Cramér-Rao lower bound for the estimation of a dynamical phase offset for a random BPSK sequence in an AWGN channel. The received symbols are disturbed by carrier phase offset which follows a Wiener model. Considering a received observation sequence, we provide a first analytical expression of the Bayesian CRB. Then, we derive an ...

We consider the use of an arbitrary planar array for direction-ofarrival (DOA) estimation, with the commonly used Cramér-Rao Bound (CRB) as a performance measure. By taking advantage of the cosine structure of the array Fisher information matrix (FIM), the FIM is reformulated to be completely represented by three parameters which depend on the array geometry, leading to a new FIM expression tha...

This paper analyses the estimation process for Finite Rate of Innovation (FRI) signals. The main contribution is the derivation of the well known Cramér-Rao Bound (CRB) for the estimation of signal parameters for a pulse stream. Other publications consider the estimation of the signal instead of its parameters or omit the effect of sampling. In this contribution both effect are considered and a...

OF THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science Optical Science and Engineering The University of New Mexico Albuquerque, New Mexico May, 2007

This paper presents a theoretical study on an optimum SAR-GMTI mode that exploits the flexible programmability of modern phased array radars such as RADARSAT-2 (R2) and TerraSAR-X. One major challenge for SAR-GMTI is the considerable re-positioning error owing to large stand-off ranges. A new GMTI mode is proposed that combines the two concepts of antenna tapering with aperture switching betwee...