LAMBDA

The Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method [Teunissen, 1993] is an essential tool in my software. Prior to LAMBDA, finding the “best” integer ambiguity vector was a very computationally-intensive process. The decorrelation procedure of LAMBDA allows for an efficient search to be performed and has become widely accepted in the GNSS community. A faster search process does not however mean a shorter time to resolve ambiguities...

 

LAMBDA is essentially forming linear combinations of ambiguities that are less correlated than the original ones. Since decorrelation often leads to smaller standard deviations for the ambiguities, we could assume that LAMBDA improves ambiguity resolution. Not so fast… You can easily verify that LAMBDA will return the same integer vectors (with the same ambiguity residuals) as the integer least-squares solution without decorrelation.

 

Other than speeding up the search process, LAMBDA could be beneficial when:

  1. using rounding or bootstrapping for fixing ambiguities instead of integer least-squares.
  2. doing partial fixing since it allows identifying  a subset of decorrelated ambiguities that are more easily fixable. (For example, we all know that fixing only the widelane ambiguities is usually more likely to succeed than fixing all ambiguities on L1/L2.)

Remember that if you wish to fix all ambiguities using integer least-squares, LAMBDA, the widelane combination, or any linear combination for that matter, is not helping you.


Reference

Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities. Tech. rep., LGR Series 6, Delft Geodetic Computing Centre, Delft University of Technology, Delft, The Netherlands.



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