Exact Detection Performance for Broadband Correlators

The detection of a broadband plane wave in an isotropic noise field is considered. The detection statistic used is the cross correlation of the sampled output from two sensors where the sampling rate equals the Nyquist rate and the time delay is an integer multiple of the sampling period. By restricting the number of points in the cross correlation to be even, the detection and false-alarm probbilities are obtained in closed form. Numerical results are presented for several special cases.     

Design of Broadband Circular Sonar Arrays Using Linear Programming

The design of a circular acoustic array with uniformly spaced elements is carried out using linear programming. The size of the linear program to be solved is reduced by imposing symmetry conditions on the complex element weights. The cost function used minimizes the beamwidth over a range of frequencies for a specified maximum sidelobe level.     

Active sonar application of a U-D square root PDAF

The probabilistic data association filter (PDAF) is a suboptimal approach to tracking a target in the presence of clutter. In the PDAF implementation, the Kalman measurement update is performed over the set of validated measurements and the Kalman time update is used to propagate the PDAF measurement update. A popular approach to obtaining a numerically stable set of Kalman update equations is to propagate the U-D factors of the covariance in the measurement and time updates. The PDAF measurement update equation is obtained in U-D factored form by applying the modified weighted Gram-Schmidt (MWG-S) algorithm to the three factored terms. The factors of the first two terms are determined from the U-D factors of the a priori and conditional a posteriori covariances. The third term is factored analytically using the Agee-Turner factorization. The resulting U-D square-root PDAF is then applied to the problem of active tracking of a submarine in reverberation using polar coordinates     

Sensor Netting via the Discrete Time Extended Kalman Filter

An implementation is presented of the discrete time extended Kalman filter which the authors have found useful for sensor netting in a variety of tactical radar and ballistic missile defense (BMD) applications. A Potter square root version of the extended Kalman filter is used where vector measurements are processed serially. Both the state and covariance equations are initialized by processing past measurements. The initialization technique and the filter are used in two tactical radar tracking examples.