Recursive algorithm for the calculation of the adaptive Kalman filter weighting coefficients

The optimal discrete adaptive Kalman filter, as presented by Magill, necessitates the iterative calculation of a weighting coefficient for each value of the quantized parameter space. This correspondence proposes a new recursive algorithm for the calculation of the weighting coefficients and compares it to the weighting coefficient algorithm of Magill. When there are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> elements in the a priori known parameter space, it is shown that the memory and computational savings include 1) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> memory allocations, 2) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> scalar additions per iteration, and 3) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> scalar multiplications per iteration.