Architectures for Particle Filtering - Signal Processing Systems - page 633

Fig. 5 The example of
particle exchange for ( a )RPA
and ( b ) RNA algorithm in
which the groups are formed
from two PEs

a b

N=0 N=13 N=0 N=8

4 4

1 2 1 1 2 2

1

4

4

3 4 3 3 4 4

N=0 N=3 N=0 N=8

and RPA is that in RNA the PEs are grouped in groups of two and they act almost
as separate particle filters. Let us assume that the sums sum i for the PEs 1 to 4 are:
0, 13 16 as in the previous example. Also, let us assume that PE1 and PE2

form one group and PE3 and PE4 form another group as it is shown in Fig. 5 b using
solid lines. The resampling is done inside these groups as if they are separate particle
filters. Since all the probability mass is contained in PE2, it has to send four particles
to PE1. The same happens in the second group, i.e., PE3 sends four particles to PE4.
After resampling, the weights of the particles are not equal as in the RPA algorithm.
They are set to the sum of the weights of the group. In the first group composed of
PE1 and PE2, the sum of the weights is 13

/ 16, 0, 3 /

/ 16 so that the weights of the replicated

particles are 13 16. The implementation of the RPA algorithm with fixed groups is

referred to as 2-2 fixed (Mode 3) configuration.
If the groups are fixed, the weights in one group can become dominant in
comparison to the weights from another group. In the case of unequally distributed
weights, the particle filter performance will deteriorate because only one half
(one group) of particle filter will contribute to the final estimate. This problem is
solved by regrouping the PEs. In Fig. 5 b , new groups are formed from PE1 and
PE3, and PE2 and PE4 shown with dashed lines. Regrouping can be done using
some defined rules or adaptively. The rule that is used in Fig. 5 b is that groups
are formed alternatively as PE1-PE2, PE3-PE4 and PE1-PE3, PE2-PE4. In adaptive
configurations, the groups are formed in a way that the PE with the largest weight is
grouped with the PE with the smallest weight. In this way, weights of particles are
more evenly distributed among the PEs. The implementation of the RPA algorithm
with regrouping with fixed rules is referred to as 2-2 mixed (Mode 4) and with
adaptive regrouping as 2-2 adaptive (Mode 5).
Several additional modes are considered. For a single PE operation (Mode 0), the
resam pling is integrated into each PE and no particle sharing scheme is presented.
Four independent particle filterings with different parameters can be processed
concurrently. Although a single PE mode is supported by the resampling units, a
PE with integrated resampling unit is more efficient in terms of data access and
speed [ 26 ] .
In Mode 1, only two PEs are active. In Mode 2, two fixed groups made of two
PEs each are formed. There is no interaction among these two groups, and therefore
two separate particle filters.

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