Stochastic approximation methods for fusion-rule estimation in multiple sensor systems
- Oak Ridge National Lab., TN (United States)
A system of N sensors S{sub 1}, S{sub 2}, ..., S{sub N} is considered; corresponding to an object with parameter x {element_of} {Re}{sup d}, sensor S{sub i} yields output y{sup (i)} {element_of} {Re}{sup d} according to an unknown probability distribution p{sub i}(y{sup (i)}{vert_bar}x). A training 1-sample (x{sub 1}, y{sub 1}), (x{sub 2}, y{sub 2}), ..., (x{sub l}, y{sub l}) is given where y{sub i} = (y{sub i}{sup (1)}, y{sub i}{sup (2)}, ..., y{sub i}{sup (N)}) and y{sub i}{sup (j)} is the output of S{sub j} in response to input x{sub i}. The problem is to estimate a fusion rule f : {Re}{sup Nd} {yields} {Re}{sup d}, based on the sample, such that the expected square error I(f) = {integral}[x - f(y{sup (1)}, y{sup (2)}, ..., y{sup (N)})]{sup 2}p(y{sup (1)}, y{sup (2)}, ..., y{sup (N)}{vert_bar}x)p(x)dy{sup (1)}dy{sup (2)} ... dy{sup (N)}dx is to be minimized over a family of fusion rules {Lambda} based on the given l-sample. Let f {element_of} {Lambda} minimize I(f); f* cannot be computed since the underlying probability distributions are unknown. Three stochastic approximation methods are presented to compute {cflx f}, such that under suitable conditions, for sufficiently large sample, P[I({cflx f}) - I(f*) > {epsilon}] < {delta} for arbitrarily specified {epsilon} > 0 and {delta}, 0 < {delta} < 1. The three methods are based on Robbins-Monro style algorithms, empirical risk minimization, and regression estimation algorithms.
- Research Organization:
- Argonne National Lab., IL (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 103003
- Report Number(s):
- CONF-9404137--; ON: DE94017694
- Country of Publication:
- United States
- Language:
- English
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