Multidimensional Algebraic Polynomial Approximation

A computational algorithm to approximate an n-dimensional function of the form F(x,y,z, ...) by an algebraic polynomial in the least square (LSQ) sense is described. The basis of this algorithm is that the n-dimensional function can be approximated by a set of polynomials in each one of the independent variables x,y,z, ... . This technique is illustrated by deriving the algebraic polynomial approximation in the LSQ sense for three-dimensional functions of the form F(x,y,z).     

Omega Lane Ambiguity Resolution Using Methods of Statistical Decision Theory

Lane ambiguity is an inherent problem of navigation systems using phase measurements. A lane ambiguity resolution technique combining methods of hyperbolic and range-range modes of navigation has been developed. The basis of this approach is that the ensemble of received phases at any location forms a unique set and therefore the lane resolution problem reduces to finding a position such that the expected set of phases (or the phase predicted for the position of the navigator) matches the received set. This method of lane resolution is not constrained by lane widths and using the phase data of 10.2, 13.6, and 11? kHz; lane resolution has been accomplished for distances of up to 120 nmi. This method of lane resolution requires phase data from at least four stations at any frequency and is very sensitive to uncompensated propagation phase shifts.