Robust Noise Models

M-Estimators

Comparing kernel width

For all comparisons provided yesterday, the kernel width for all m-estimators was fixed at 10. To see how the kernel width affects both the final solution accuracy and convergence time, a comparison was conducted where the only varied parameter was the Cauchy kernel width.

The number of iterations required before L.M. reached a stop criterion and final graph error is shown in the table below.

So, it’s obvious that the kernel width can dramatically affect both the solution accuracy and convergence time. At some point in the future I will run a similar study with all m-estimators.

Robust Graphical Methods

Now, I’m going to move from testing traditional m-estimator weighting schemes to more recent weight schemes developed specifically for navigation applications. These methods include switchable constraints, max-mixture, and Realizing, Reversing, Recovering.

Running g2o with external library

g2o_viewer provides a flag, typeslib, to allow for the easy integration of external libraries.

Example — max-mixtues

$ ~/g2o_viewer -typeslib path-to-max-mixture/lib/libg2o_max_mix_core.so dataset.g2o

Switchable Constraints

Getting switchable contraints to run on Ubuntu 16.04

$ cd ~/git
$ git clone https://github.com/christiankerl/vertigo.git
$ cd vertigo
$ mkdir build; cd build;
$ export G2O_INCLUDE_DIR='~/Documents/git/g2o/g2o/core'
$ export G2O_LIBRARIES='~/Documents/git/g2o/lib'
$
$ EDITOR ~/g2o/g2o/config.h

paste the following lines in config.h 

    #ifndef G2O_CONFIG_H
    #define G2O_CONFIG_H

    #ifdef __cplusplus
        #include <g2o/core/eigen_types.h>
    #endif

    #endif


$ EDITOR max_mixture/CMakeLists.txt

    copy the following line into CMakeLists.txt so that gcc knows to 
    compile the library with c++11. 


    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")

$ cmake ../; make 

Switchable Constraints Test 1

To test switchable constraints, 100 false loop-closure constraints were added to the Manhattan 3500 data-set. The video below shows both the switchable constraints and traditional $L^2$ optimization ( switch constraints is shown on left ) attempting to minimize the graphs total error when the false loop-closures are present.

Max-Mixtues

Getting max-mixtures to run on Ubuntu 16.04

$ cd ~/git
$ git clone https://github.com/agpratik/max-mixture.git
$ cd max-mixture
$ mkdir build; cd build;
$ export G2O_ROOT='~/Documents/git/g2o'
$ EDITOR max_mixture/CMakeLists.txt

copy the following line into CMakeLists.txt so that gcc knows to 
compile the library with c++11. 


set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")

$ cmake ../; make

Max-Mixture Test 1

To test Max-Mixture, 100 false loop-closure constraints were added to the Manhattan 3500 data-set. The video below shows both the max-mix and traditional $L^2$ optimization ( max-mix is shown on left ) attempting to minimize the graphs total error when the false loop-closures are present.

Max-Mixture Vs. Switchable Constraints

A side by side comparision of max-mix and switch constrats was conducted. For this comparision, 1000 false loop-closure constraints were added to the Manhattan 3500 data-set. The video below shows the side by side optimization.

Next Steps

Test RRR algorithm using g2o and manhattan dataset