Multi-estimate extraction for SMC-PHD

Posted on Jul 17, 2019

A RFS (random finite sets) variable is a r.v. that takes values as unordered finite sets. The cardinality of a RFS variable $X$ is random and modelled by a discrete distribution $\rho(n)=\Pr(\vert X\vert=n)$. The RFS $X$ is specified entirely by its cardinality distribution $\rho(n)$ and a family of symmetric joint dist. $p_n(x_1,\ldots,x_n)$ that characterize the distribution of its elements over the state space, conditioned on the set cardinality $n$.

The PDF of an RFS variable $X$ is denoted $f(X)$ and defined as

$f(\{x_1,\ldots,x_n\})=n!\cdot\rho(n)\cdot p_n(x_1,\ldots,x_n)\,.$

target state: $x_k=[p_{x,k},\dot p_{x,k},p_{y,k},\dot p_{y,k}, w_k]^T$

coordinated-turn state transition model:

$x_k = F(\omega_{k-1}) + G\nu_{k-1}$
F = @(a)[1 sin(a(5,:)*T)/a(5,:)      0    -((1-cos(a(5,:)*T))/a(5,:)) 0
0 cos(a(5,:)*T)             0    -sin(a(5,:)*T)              0
0 (1-cos(a(5,:)*T))/a(5,:)  1    sin(a(5,:)*T)/a(5,:)        0
0 sin(a(5,:)*T)             0    cos(a(5,:)*T)               0
0       0                   0    0                           1]*a;
Noise.vel = [15; 15];
Noise.turn= pi/180;


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