Swarm Intelligence Techniques Applied to Nonlinear Systems State Estimation - Advances in Heuristic Signal Processing and Applications - page 233

where ξ j is the weight of particle j and is calculated according to:

exp

.

1 ) 2
2 γ 2 N 2

1
γN √ 2 π

(j −

ξ j = − (10.22)

In the above equation, γ is a parameter of the algorithm. When γ is small, the
best solutions are strongly preferred, and when it is large, the PDF becomes more
uniform. Moreover, μ j

i denotes the i th position component of sample j within the
archive and σ i is the average distance of other solutions from sample j , defined as:

N

x i −

x i

λ

σ i =

(10.23)

−

N 1

n = 1

where λ is a parameter of the algorithm; the lower it is, the higher convergence
speed of the algorithm is achieved.

10.4.3.5 Movement of the Ants

During any iteration of the inner loop, ants choose their destinations according to a
state transition strategy similar to ACO R .

10.4.3.6 Computation of Weights

After termination of the inner loop, sample j of the archive is assigned a weight as
follows:

1

w k =

(10.24)

(f k − min j = 1 f k + ε) β

1 is a threshold, β> 1 is a parameter of the algorithm, and f k is the
cost function of sample j at time k .

where 0 ≤ ε ≤

10.4.3.7 State Estimation

In this algorithm, the states are estimated based on the weighted mean of archived
antsasfollows:

N

w j

k x j

ˆ x k =

k .

(10.25)

j = 1