By Thyagaraju Damarla

This ebook offers all facets of situational wisdom utilizing acoustic indications. It begins by way of offering the technological know-how in the back of figuring out and interpretation of sound indications. The ebook then is going directly to offer quite a few sign processing suggestions utilized in acoustics to discover the path of sound resource, localize gunfire, music autos and realize humans. the required mathematical historical past and diverse type and fusion thoughts are offered. The booklet comprises majority of the issues one would have to approach acoustic signs for all elements of situational know-how in a single position. The booklet additionally provides array concept, that is pivotal to find the course of arrival of acoustic indications. moreover, the publication provides ideas to fuse the knowledge from a number of homogeneous/heterogeneous sensors for higher detection. MATLAB code is equipped for majority of the true program, that's a necessary source in not just figuring out the idea yet readers may also use the code as a spring-board to advance their very own program established software program code.

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35) can be written as p (x|y, θ) = p (x|θ) . 36) Hence, Eq. 37) We now prove the convergence of EM algorithm; first consider the following theorems: Definition: Let f be a real valued function defined on an interval I = [a, b]. f is said to be convex on I if for all x1 , x2 ∈ I , λ ∈ [0, 1], f (λx1 + (1 − λ)x2 ) ≤ λ f (x1 ) + (1 − λ) f (x2 ). f is said to be strictly convex if the inequality is strict. Theorem 1 (Jensen’s inequality): Let f be a convex function defined on an intern λi = 1, val I .

20) The maximum likelihood estimations of θ1 , θ2 , . . , θk are obtained by maximizing Λ or L. 20), or by solving the simultaneous equations given by ∂Λ = 0, j = 1, 2, . . 21) ∂θ j The following example illustrates the maximum likelihood method using a normal distribution. Example: Let z 1 , z 2 , . . , z m be the independent samples from a Gaussian (Normal) distribution N μ, σ 2 where μ and σ 2 are unknown. We use the maximum likelihood estimation method to determine their values. 18) is given by L z 1 , z 2 , .

The receiver operating characteristic (ROC) curves (Eqs. 25)) for different SNRs are plotted in Fig. 5. 1 Neyman-Pearson Criterion In the previous section, concepts on probability of detection, probability of missed detection and probability of false alarm are presented. The concept of cost function and minimization of cost function to optimize the correct probability of detection are also presented. However, to minimize the cost function, one would often require the priors p0 and p1 . In majority of the cases, the priors are not readily available.