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:
using rounding or bootstrapping for fixing ambiguities instead of integer least-squares.
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.
Ambiguity resolution and validation are perhaps the most popular GNSS-related research topics. A plethora of methods were developed for this purpose such as the popular ratio test, the difference test, the projector test, the W-test, etc. However, the techniques that worked for short-baseline RTK don’t perform as well for long-baseline RTK or PPP.
The main reason is the presence of the ionosphere. For short-baseline RTK, ambiguity residuals are only correlated with positioning errors. As the baseline length increases, satellite-dependent errors creep in and make the ambiguity validation process much more complex. Partial ambiguity resolution aimed at solving this problem, but knowing which satellites to select/discard is not always a simple task.
My preferred method for ambiguity resolution in kinematic applications is the so-called “BIE” approach. The first paper I know describing it was written by Blewitt [1989], although it was deemed unpractical at the time because of the heavy computational load. The basic idea consists of computing a weighted average of integer vectors. The outcome can be summarized as:
Poorly-defined solution = float solution
Precise solution = fixed solution
Otherwise = somewhere between the float and fixed solutions (generally!)
Hence, BIE offers a nice and smooth convergence to an ambiguity-fixed solution and is valid for short-baseline RTK or PPP. Be aware that BIE can go very wrong if your stochastic model is incorrect… but more on this topic in a subsequent post!
Reference
Blewitt, G. (1989). “Carrier-phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km,” Journal of Geophysical Research, Vol. 94, No. B8, pp. 10187-10203. doi:10.1029/JB094iB08p10187.
