Craomr-Rao Bound of Position Estimation for Underwater Source

The Craomr-Rao Bound (CRB) expression of near-field distance estimation for underwater source is first presented. Furthermore, the CRB of far-field Direction-Of-Arrival (DOA) estimation is deduced. The characteristics and factors of CRB results are shown as following: (1)Both of the distance estimation CRB and the DOA estimation CRB can be divided into two items, one of which is relative to the geometry of array, including array manifold and array aperture, while the other one depends on the signal characteristics, containing source direction, frequency, bandwidth and SNR etc; (2)Both of them are inversely proportional to an item which is composed of bandwidth and spectrum density function; (3)The distance estimation CRB is directly proportional to the forth power of distance; (4)The distance estimation CRB is relative to the position of reference point, while the DOA estimation CRB is not; (5)For Uniform Linear Array (ULA), the distance estimation CRB is close to be inversely proportional to the fifth power of array aperture, and the DOA estimation CRB is close to be inversely proportional to the cube of array aperture; for Uniform Circle Array (UCA), both of them is inversely proportional to the array aperture and independent of source direction. The Monte-Carlo simulation results validate the theoretical analysis and the conclusions. This paper not only presents the best performance of distance estimation and DOA estimation, but also provides the theoretical guidance of array and signal design to achieve the optimum estimation.