LAMBDA

Least Squares Ambiguity Decorrelation Adjustment Algorithm This is a Pythonic translation of Dr P.J. Teunissen's LAMBDA algorithm for fixing integer ambiguities. The original LAMBDA was written in MATLAB by Dr Sandra Verhagan and Dr Bofeng Li, TU Delft / Curtin University. This Pythonic translation employs the default integer least-squares (ILS) with search-and-shrink method. It decorrelates float ambiguities based on the covariance matrix search-and-shrink, and then fixes ambiguities. Although it was intended for GNSS ambiguity fixing, it can fix integers for other applications like InSAR Credits to PJ Teunissen, Jonge, J Tiberius, S. Verhagen, and Bofeng Li.

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FILE DESCRIPTION:

This is the classical LAMBDA method that was originally authored by

Teunissen, Jonge, and Tiberius (1993). The code was later written in

MATLAB by Dr Sandra Verhagen and Dr Bofeng Li. It takes in a vector of

float ambiguities to the integer least-squares problem, and covariance

of the float ambiguities. It then runs the LAMBDA's ILS search-&-shrink

and spits out the ambiguity integers. The other 5 methods in original

LAMBDA MATLAB code are not supported here (feel free to edit the code

and implement it youself!). The default ncands = 2, as per original code.

All support functions from the original MATLAB code (decorrel, ldldecom)

have been nested within the main function as sub functions.

INPUTS:

- ahat : numpy array of float ambiguities

- Qahat : numpy covariance matrix for float ambiguities

- ncands : number of candidates (optional parameter, default = 2)

OUTPUT:

- afixed1 : Best estimated integer candidates

- afixed2 : 2nd best estimated integer candidates

- sqnorm : Distance between integer candidate and float ambiguity

vectors in the metric of the variance-covariance matrix

REMARKS:

Changes to the Python version of this code:

- Everything is identical EXCEPT MATLAB is ones-based indexing.

- Python is zero-based indexing, and range function does not

include the upper limit index. Thus, only indices have changed.

- Example in MATLAB: for i = 1:5 => {1,2,3,4,5}

- Equivalently in Python: for i in range(0,5) => {0,1,2,3,4}

- Indices are thus updated accordingly.

WRITTEN BY:

- Original Authors: Sandra Verhagen / Bofeng Li

- Translated by: Samuel Low, 29-07-2019,

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