Fusion rule estimation in multiple sensor systems with unknown noise distributions
A system of N sensors S{sub 1},S{sub 2},{hor_ellipsis},S{sub N} is considered; corresponding to an object with parameter x {epsilon} R{sup d}, sensor S{sub i} yields output y{sup (i)} {epsilon} R{sup d} according to an unknown probability distribution p{sub i}(y{sup (i)}{vert_bar}x). A training l-sample (x{sub 1},y{sub 1}),(x{sub 2},y{sub 2}),{hor_ellipsis},(x{sub l},y{sub l}) is given where y{sub i} = (y{sub i}{sup (1)}, y{sub i}{sup (2)},{hor_ellipsis},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:R{sup Nd} {yields} R{sup d}, based on the sample, such that the expected square error I(f) = {integral}[x {minus} f(y{sup (1)},y{sup (2)}, {hor_ellipsis},y{sup (N)})]{sup 2}p(y{sup (1)},y{sup (2)}, {hor_ellipsis},y{sup (N)}{vert_bar}x)p(x)dy{sup (1)}dy{sup (2)}{hor_ellipsis}dy{sup (N)}dx is to be minimized over a family of fusion rules {Lambda} based on the given l-sample. Let f{sub *} {epsilon} {Lambda} minimize I(f); f{sub *} cannot be computed since the underlying probability distributions are unknown. Using Vapnik`s empirical risk minimization method, we show that if {Lambda} has finite capacity, then under bounded error, for sufficiently large sample, f{sub emp} can be obtained such that P[I(f{sub emp}) {minus} I(f{sub *}) > {epsilon}] < {delta} for arbitrarily specified {epsilon} > 0 and {delta}, 0 < {delta} < 1. We identify several computational methods to obtain f{sub emp} or its approximations based on neural networks, radial basis functions, wavelets, non-polynomial networks, and polynomials and splines. We then discuss linearly separable systems to identify objects from a finite class where f{sub emp} can be computed in polynomial time using quadratic programming methods.
- Research Organization:
- Oak Ridge National Lab., TN (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 10115913
- Report Number(s):
- CONF-931245--1; ON: DE94005466; CNN: Grant IRI-9108610
- Country of Publication:
- United States
- Language:
- English
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