For a fixed satellite distance matrix, the closest squared-pseudorange vector that keeps the augmented Euclidean distance matrix at the right embedding dimension is characterized by a rank condition and found by one-dimensional root finding.
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A note on Global Positioning System (GPS) and Euclidean distance matrices
For a fixed satellite distance matrix, the closest squared-pseudorange vector that keeps the augmented Euclidean distance matrix at the right embedding dimension is characterized by a rank condition and found by one-dimensional root finding.