Patent Document ID: 20120084042
Application ID: 13226863
Patent Status: 0

Claim One:
1. A computer-implemented method of predicting sensor output values of a sensor monitoring system, comprising the steps of: providing a set of one or more test input values to a system of sensors, and one or more known sensor output values from said sensor system, wherein other sensor output values are unknown; calculating, for each unknown sensor output value, a predictive Gaussian distribution function P ( y U | x ) = ∏ m ∈ U P ( y m | x ) = 1 ( 2 π ) d / 2  S y U  1 / 2 exp ( - 1 2 ( y U - μ y U ) T S y U - 1 ( y U - μ y U ) ) from the test input values, wherein vector x of dimensionality d represents the test input values, vector y U of dimensionality M represents the set of unknown output sensor values, y m εy U , μ y U is a vector of mean values of the set y U determined by a training phase, S y U is a diagonal covariance matrix of the set y U determined by said training phase; and predicting each unknown output y m from P(y m |x, y O )=∫ y U m P(y m |x, y U m )P(y U |x)dy U m , wherein vector y O represents the known sensor output values, vector y U m represents unknown output sensor values in y U except y m, , and P(y m |x, y U m ) is a conditional Gaussian distribution defined by 
 log P ( y m |x,y U m )=−½ log|K|−½ y U m K −1 y U m T +C ,wherein C=−(0.5 d)log(2π) and K is an N×N kernel matrix defined between pairs of test input values x i , x j wherein N is the number of test input values whose elements K i,j are defined by Gaussian kernel functions K i,j =k(x i , x j |Λ)=exp(−½(x i −x j ) T Λ −1 (x i −x j )), wherein Λ=diag[λ 1 2 ,. .. , λ d 2 ] T whose values λ i are determined by another training phase.