Optimum vs. correlation methods in tracking random signals in background noise
R. C. Davis · Quarterly of Applied Mathematics · 1957
A method of target tracking used exclusively in some applications is that of space diversity reception. We consider a two-dimensional problem with two receivers, although in principle the techniques developed are applicable to a three-dimensional problem utilizing three or more receivers. With N N receivers the computational difficulties increase as N 2 N^2 . The tracking problem considered here is formulated as follows. During a time interval 0 ≤ t ≤ T 0 \le t \le T one observes random processes x 1 ( t ) = s ( t ) + n 1 ( t ) x_1(t) = s(t) + n_1(t) and x 2 ( t ) = s ( t + τ 0 ) + n 2 ( t ) x_2(t) = s(t + \tau _0) + n_2 (t) , and one desires to estimate the unknown value of τ 0 ⋅ s ( t ) , n 1 ( t ) \tau _0 \cdot s(t), n_1(t) , and n 2 ( t ) n_2(t) are continuous, Gaussian, stationary processes with continuous, monotonoid covariance functions and with E s ( t ) n 1 ( t ′