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Cramér-Rao Bounds For Estimating Range, Velocity, And Direction With An Active Array, Aleksandar Dogandžić, Arye Nehorai
Cramér-Rao Bounds For Estimating Range, Velocity, And Direction With An Active Array, Aleksandar Dogandžić, Arye Nehorai
Aleksandar Dogandžić
We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional …
Estimating Evoked Dipole Responses In Unknown Spatially Correlated Noise With Eeg/Meg Arrays, Aleksandar Dogandžić, Arye Nehorai
Estimating Evoked Dipole Responses In Unknown Spatially Correlated Noise With Eeg/Meg Arrays, Aleksandar Dogandžić, Arye Nehorai
Aleksandar Dogandžić
We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric basis functions. We estimate the dipoles' locations and moments and derive the Cramer-Rao bound for the unknown parameters. We also propose an ML based method for scanning the brain response data, …