This is a Matlab code suite for sensor network localization and graph realization in 2D.
You need SDP solver SEDUMI to run them.


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These codes take a point set and generate a unit-disk graph with noises and first m points of PP 
as anchors, and localize the rest of points:

    [PP,dd,m,r,nf, Xiter] = ESDP(PP,m,n,r,nf,degree)
    or
    [PP,dd,m,r,nf, Xiter] = ESDPDual(PP,m,n,r,nf,degree)
    Test SDP-based Sensor Localization System
    Input
    PP: 2xn matrix representing all point on 2D
    n : the number of total points
    m : the number of anchor points; the first m columns of PP
    r : the radio range
    nf: noisy factor
    degree: the limit on the number of edges connected to any sensor point, typically set it to 5-10

    Output
    PP: 2xn matrix representing all point on 2D, the last m columns are anchors
    dd: the uppertriangle distance matrix from PP(:i) to PP(:,j), i<j.
    Xiter: position estimation for all n-m unknown points made by the method

This code take a point set and generate a unit-disk graph with noises and use first m points as
anchors to generate a sparse noisy distance matrix as output:  
  
    [PP,dd,m,r]=generateD(PP,m,n,Radius,nf,degree)
    Input
    same as above

    Output
    PP: 2xn matrix representing all point on 2D, the last m columns are anchors
    dd: the uppertriangle distance matrix from PP(:i) to PP(:,j), i<j.
    for codes take a distance matrix as input

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These codes take a sparse and noisy distance matrix dd and last m points of PP as anchors, and 
localize the rest of points:

    [Y_opt,Xiter]=FULLSDPD(PP,m,dd);
or
    [Y_opt,Xiter]=FULLSDPDr(PP,m,dd);

    Xiter = ESDPD(PP,m,dd)

    Xiter = ESDPDualD(PP,m,dd)

    Sensor Localization Solvers
    Input 
      PP  : 2xn matrix representing all point true locations on 2D
      where n is the number of total sensor and anchor points
      m   : the number of Anchor points; last m columns of PP; it should be at least 3
      dd : the sparse (and noisy) distance matrix between PP(:,i) and PP(:,j)
    Output
      Xiter: position estimation for all n-m unknown points made by the method
      Y_opt: SDP matrix representing the second moment of estimation 
    
The difference between FULLSDPD and FULLSDPDr is in the
SDP objective function. A regularization term is added
in FULLSDPDr to handle high level noise problems; see
“Semidefinite Programming Approaches for Sensor Network Localization with Noisy Distance Measurements,” 
(Pratik Biswas, Tzu-Chen Liang, Kim-Chuan Toh, Ta-Chung Wang and Yinyu Ye), 
IEEE Transactions on Automation Science and Engineering, 3:4  (2006) 360-371.

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This code is traking moving sensors:

    [PP,dd,m,r,nf,Xiter] = ESDPDtracking(PP,m,n,r,nf,degree,movingspeed)
    Test SDP-based Sensor Localization and Tracking System
    Input
    PP: 2xn matrix representing all point on 2D
    n : the number of total points
    m : the number of anchor points; the first m columns of PP
    r : the radio range
    nf: noisy factor
    degree: the limit on the number of edges connected to any sensor point, typicallu set it to 5-10
    movingspeed: the moving distance of every sensor per snapshot, typically 1-3% of the diameter of the region
      
    Output
    PP: 2xn matrix representing all point on 2D, the last m columns are anchors
    dd: the uppertriangle distance matrix from PP(:i) to PP(:,j), i<j.
    Xiter: position estimation of the last snapshot for all n-m unknown points made by the method    

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    Developed and maintined by Zizhuo Wang, Song Zheng, Boyd, Yinyu Ye, Zhisu Zhu for Demonstration;
    and the steepest descent code is due to Biswas, Toh and Ye;
    see paper http://www.stanford.edu/~yyye/relaxationsdp6.pdf
    Edge based decompositionThree test SDP relaxaion models for sensor network localization in 2-D: