%CalculatePerformanceMetric
%Last?modified?21?November?2013
%Matlab?code?by?Bryan?Clarke?b.clarke@acfr.usyd.edu.au?

%This?is?an?implementation?of?the?Optimal?Subpattern?Assignment
%（OSPA）?metric?proposed?by?Schuhmacher?et?al?in?
%Schuhmacher?D.;?Ba-Tuong?Vo;?Ba-Ngu?Vo?“A?Consistent?Metric?for?Performance?Evaluation?of?Multi-object?Filters“?Signal?Processing?IEEE?Transactions?on??vol.56?no.8?pp.34473457?Aug.?2008
%X?is?the?estimated?state?in?the?form?[?[x1;?y1;?vx1;?vy1]?[x2;?y2;?vx2;
%vy2]??...]
%Y?is?the?ground?truth?in?the?form?[?[x1;?y1;?vx1;?vy1]?[x2;?y2;?vx2;
%vy2]??...]
%This?isn‘t?actually?important?as?we?will?swap?the?labels?so?that?X
%is?the?label?of?the?shorter?vector?and?Y?is?the?label?of?the?longer.
%cutoff_c?and?order_p?are?parameters?that?control?the?metric?calculation;
%cutoff?is?a?saturation?threshold?order?controls?how?punishing?it?is?to
%larger?errors?versus?smaller?ones.?See?the?paper?by?Schuhmacher?et?al?to
%get?a?handle?on?these?in?more?detail.
%NOTE:?This?implementation?is?still?a?work?in?progress?and?is?a?bit?buggy.?Use?with?caution.
%NOTE:?We?only?use?2D?OSPA?for?position;?we?don‘t?use?the?velocities.
function?ospa?=?CalculateOSPAMetric（X?Y?cutoff_c?order_p）

????m?=?size（X?2）;%Length?of?vector?X
????n?=?size（Y?2）;%Length?of?vector?Y

????alphas?=?cutoff_c?*?ones（1?n）;%Initialise?to?cutoff?overwrite?if?there?is?a?shorter?value
????bestOMATCost?=?-1;
????bestOMATDataAssoc_i?=?[];
????
????%m?（i.e.?the?length?of?X）?needs?to?be?less?than?or?equal?to?n?（the?length?of?Y）
????if（m?>?n）%Swap?them?if?this?is?not?the?case.?X?and?Y?are?just?labels?that?can?be?applied?to?either?vector;?whichever?one?is?estimate?or?truth?is?not?important.
????????tmpX?=?X;
????????tmpm?=?m;
????????X?=?Y;
????????m?=?n;
????????Y?=?tmpX;
????????n?=?tmpm;
????end
????if（m?>?0）%If?there?are?other?values?we?need?to?find?the?best?data?association.
????????%We?calculate?all?potential?combinations?（ie.?subsampling?without
????????%replacement）
????????comboSize?=?m;
????????valuesSampled?=?1:n;
????????allCombos?=?combnk（valuesSampled?comboSize）;
????????nCombos?=?size（allCombos?1）;
????????
????????%Then?for?each?combination?we?calculate?every?permutation?（i.e.
????????%different?ways?to?order?the?numbers）?to?find?all?possible?data
????????%associations
????????for?i?=?1:nCombos
????????????thisCombo?=?allCombos（i:）;%The?combination?we?are?using
????????????allDataAssocs?=?perms（thisCombo）;
????????????nDataAssocs?=?size（allDataAssocs?1）;
????????????%We?check?all?the?data?associations?for?this?combination
????????????for?j?=?1:nDataAssocs
????????????????thisDataAssoc?=?allDataAssocs（j:）;%An?ordered?list?of?the?indices?of?Y?to?match?them?against?the?values?in?X????????????????
????????????????thisY?=?Y（:thisDataAssoc）;
????????????????thisOMATCost?=?CalculateOMATMetric（X?thisY?order_p）;

????????????????if（bestOMATCost?