By Thyagaraju Damarla

This e-book offers all facets of situational understanding utilizing acoustic signs. It starts off through featuring the technology at the back of knowing and interpretation of sound indications. The booklet then is going directly to offer quite a few sign processing concepts utilized in acoustics to discover the course of sound resource, localize gunfire, tune automobiles and observe humans. the required mathematical history and diverse category and fusion recommendations are offered. The ebook comprises majority of the issues one would have to strategy acoustic signs for all facets of situational know-how in a single situation. The booklet additionally provides array conception, that's pivotal find the course of arrival of acoustic indications. furthermore, the ebook offers thoughts to fuse the data from a number of homogeneous/heterogeneous sensors for higher detection. MATLAB code is equipped for majority of the genuine program, that's a worthwhile source in not just realizing the speculation 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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K ) = p (z i |θ1 , θ2 , . . 18) i=1 The logarithmic likelihood function is given by m ln p (z i |θ1 , θ2 , . . 05 0 −10 −8 −6 −4 Fig. 05 0 −10 −8 −6 −4 −2 0 Z −−> 2 4 6 8 10 Fig. 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.

43) = Q θ|θ(k) + E X |y,θ(k) − log p X |y, θ(k) where we used the definition of Q-function given in Eq. 32). Substituting Eqs. 45) h X |y, θ(k) = E X |y,θ(k) − log p X |y, θ(k) . 45) is the lower bound on L (θ). We note that the only term in Eq. 45) that is dependent on θ is Q θ|θ(k) . Now, consider right-hand side of Eq. 47) L θ(k) The theorem assumes Q θ|θ(k) ≥ Q θ(k) |θ(k) and using Eqs. 48) = L θ(k) Hence L(θ) ≥ L θ(k) . 5 Expectation Maximization Algorithm 41 which, in turn, implies that L(θ)(k+1) ≥ L θ(k) .

10) is called the normal equation. 1 Least Squares Estimator 31 or ˜ L S = 0. 13) is said to be unbiased. 14) P = σ 2 (H T H )−1 . 16) Weighting function is used to emphasize or de-emphasize some of the measurements. The optimal choice for the weighting matrix W is the covariance matrix [87] of the measurement errors (noise) W = Ce−1 . 17) is referred to as the best linear unbiased estimator (BLUE) or Gauss-Markov estimator. 3 Maximum Likelihood Estimator Given a set of observations Z and probability density function p(Z|θ), the maximum likelihood estimator is the one that maximizes the probability distribution that makes the observed data most likely.