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Fast method and apparatus for nonlinearly transforming mean and covariance estimates

  • US 5,963,888 A
  • Filed: 10/22/1997
  • Issued: 10/05/1999
  • Est. Priority Date: 10/22/1997
  • Status: Expired due to Fees
First Claim
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1. A signal processing system for generating a mean vector and covariance matrix pair which estimates the result of applying a given nonlinear function f( ) to a given mean vector a and covariance matrix A, where said mean and covariance {a,A} are derived in part from measurements of a physical system or process, where said signal processing system comprises:

  • (1) means for measuring a mean and covariance estimate {a,A} of variables relating to a physical system or process;

    (2) means for generating a first set of m vectors, {x1,x2, . . . ,xm,}, such that a minus 1/m times the sum of the elements of the set is nonzero, and a set of weights (w1,w2, . . . , wm }, the sum of the weights being W, so that a sum of 1 /W*wi *(xi -a)*(xi -a)T, for index i ranging from 1 to m, is equal to A;

    (3) means for determining a second set of vectors by applying a nonlinear function f( ) to each element of the first set of vectors to obtain a second set of vectors, {f(x1),f(x2), . . . , f(xm)};

    (4) means for computing a transformed mean a+ ;

    (5) means for computing a transformed covariance as a sum of 1/W*wi *(f(xi) -a+)*(f(xi)-a+)T, for index i ranging from 1 to m; and

    (6) means for physically responding to a signal relating to the transformed mean and covariance.

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