This document proposes a neural network architecture called B-PR-F for fusing redundant location estimates from sensors on underwater robots operating in unmodeled noise conditions. B-PR-F models the underwater environment and sensor behaviors, uses contextual anticipation to predict sensor deviations, evaluates sensor reliability, and fuses estimates with weighted sums. Simulations in Gazebo demonstrate how B-PR-F can eliminate noise from virtual sensors by incorporating behavioral context and ordered neighborhood relationships between estimates. Experimental results show B-PR-F outperforms Kalman filters for localizing an underwater robot using sonar and DGPS sensors.

1. Neural network for black-box fusion of underwater
robot localization under unmodeled noise
19 sept 2019

2. Types of underwater vehicle
• Autonomus Underwater
Vehicle (AUV) with minor
or no intervention from
operator
• Remotely Operated
Vehicle (ROV) for
maintainance, repair
operations and sea
inspection

3. undewater environment and sensors
• rapid attenuation of higher
frequency signals and
unstructured nature of
water
• for postion and movement
acoustic, vision ,
accelerometer and
gyroscope sensors are
used

4. need of research
• there should be a neural
technique for sensory data
fusion
• coherently combining of
data(any) to estimation
location with respect to
reference frame

5. Acoustic sensors comparision 1/2
• cost functions (rate, reliability
etc)
• acustonic positioning sensors
provide asynchronous
mesurements
• estimates do not drift over time
in acoustic sensors so long
run measurement more
reliable
• slow signal traveling rate
(1500m/s)

6. acoustic sensory comparison 2/2
• geo refered landmark are
more reliable than acoustic
sensor
• commonly accoustic
(easy) LVS example
• robot have to come to
surface to reduce
localization uncertainty

7. main problem of fusion
• baysian algorithms(kalman
filters) are fine but estimation
perform poorly under
unmodeled noise
• parametric algorithms (MCL)
do multimodal hypothesis with
high computational cost
• problem is to make unimodel
estimates under unmodeled
noise

8. Approches for Problem 's solution 1/2
• model non linearity by
agumenting state representation
(difficult)
• supervied learning methodologies
in training of fusion algorithm for
correcting estimates (alternative)
{but for supervised learning task
condition should not vary in training
and execution time}

9. Approches for Problem 's solution 2/2
• Fusion of redundant
estimates of each sensor
based on error covarience
matrix (inversly or
covarience intersaction)
• fusion process as fuzzy
rule based system
(home example of neural
network training!!!!)

10. Writers' research focus
• developing heuristic and
generic fusion policy for
redundant estimates to
handle unmodeled noise
• proposed architecture
where redundant
estimates are viewed as
black box processes

11. Information fusion (past work same writer)
• principle of contexual information
anticipation for obtaining more
reliable fusion for egocentric
localization
• reliability is evalutated within
processing neighbourhood
(mean and deviation)
• confidence is in context of task
and nodes contrubution accordingly
weighted

12. Theory - Fusion architecture
• blue node has fusion
algorithm and weights
for each estimator
• Reset feature (blue node)
for reducing error (dead
recking replace with global
estimate) and context
transition according to
task

13. thory- fusion arhitecture- Parameter set
• µi(t) is mean state
estimate
• Σi(t) covarience matrix
related to error
• σi(t) is expected deviation
of neighbor node from
mean
• δti(t) is time interval
between two esimates
• i is process and t is time

14. theory - fusion architecture - ordering
arrangements1/2
• fusion node's ordering rule
depends on two
assumption
• A1: Estimates from non
delayed measurements
and follow unimodel
distribution(mean and
covariance matrix)

15. theory - fusion architecture - ordering arrangements
2/2
• A2: reliability in relation to
behaviour profile
(antisymetry, transitivity
and totality)

16. Theory - Modeling of A1 and A2
• assume set of one
dimentional site
arrangement (under B
profile)
• Sb is neighborhood
system
• relationship properties:
-no neighboring to itself
-neighboring relationship
is mutual
clinque left and right

17. Theory- Purpose of neural network
• To model arrangements
under distict behaviour
profile
• weighting information
from redundant
estimates to fusion
process

18. B-PR-F for neighboring arrangements
• Layer B is for behaviour
• Layer P is for prediction
• Layer R is for reliablity
• Layer F is for Fusion

19. B-PR-F layer B
• Task senerios and
conditions(near surface or
seabed) represented by
behavior profile
• cardinality is determined
by k availble behaviour
profiles

20. B-PR-F Layer P (imp noise)
• contextual anticipation b/w
neighborhood arrangements
• neurons here encode parameter
σi(t)
• σi(t) is expected deviation from
sorrounding µi(t) where estimate of
process i should fall
• activation becomes stronger and
uncertainty increasess as task
progesses (with motion of robot and
time pass)

21. B-PR-F Layer R
• encode confidence on
nodes's estimate in relation
to predicted value
• node passes the test and
related node is re-initialized
• cardinality is of PR layers
depends upon Behaviour
and estimators

22. B-PR-F Layer F
• contains fusion weight
for estimaters
• cardinality is determined
by n number of estimaters
• global estimated is
calculated by these
weighted sum

23. B-PR-F - Network parameters
• Wbp condition the activity of
PR layer according to B profile
• Wpp represent lateral
connection of layer P to model
the changes(due to B profile)
-no Interaction then Wpp is
identity otherwise
-f(arbitary func) is defined
according to task and estimator
parameters

24. B-PR-F - Network parameters
• Wpr connectivity between neighborhood
• ς is high magnitude assigned to
unrelated neighbors (inhibation)
• Wy is ordered arrangements of
nodes(according to B profile)
analytically stronger weights to clinque ,
excitatory weights to left and inhibitory
weights to right neighbor
• Wℵ(kxn) is provided by system designer
which tells reliability along behavior
profile
system configuration matrix
difference tells ordered
arrangements

25. B-PR-F Network parameters
• Wrf obtains from row of
system desinger matrix
• correspondance b/w sites
established through
maping function
(represented in PR and
estimators)

26. B-PR-F Layers(Behaviour) activation
• Winner takes all policy
• only one behavior at a
time
• arbitary function (self
defined that behaviour is
1 or 0)

27. B-PR-F Layers(Prediction) activation
• Activation of neurons in
layer P
• reset function cosider
reliability test applied to
right neighbor
• time scaling factor is
representing by heuristic
parameter
reset
function
time change
heuristic
parameter
** P node contains
deviation

28. B-PR-F Layers(Reliability) activation
• information is determined by left
neighbor's parameters
• activation of layer R
indication of new
estimator(given instant)
threshold
value
obtained from
left estimator

29. B-PR-F Layers(fusion) activation
• weighting the n estimators’
output proportionally to the
activation of Layer F (for u
and Σ )

30. Simulations -
Materials and methods
• simulation in Gazebo
• oceans waves senerio in robot
operating system
• dataset is of way point
trajectory
• robot to pass near way points
with particle physics engine(to
model dynamics from equatic
medium)
• Data generated is passed to GNU

31. Simulation - sensory details
• Predefined trajectory with
exploration mission of
shallow and deep water
• IMU for linear acceleration
and rotational rate(surface)
• DVL is more sophisticated in
deep water
• USBL and DGPS are
positioning sensors (in deep
water only usbl)

32. simulation results
• ALT for switching Behavior
profile
• IMU for near surface and
DVL for Deep water
produce precise result
• USBL can face issues (like
physical interference)
• BPRF eliminate noise of
virtual usbl sensor

33. Simulation results (behaviour 2)
• Principle of contextual
anticipation within ordered
neighborhood (only XY
axis)
• boundary of anticipated
region
{ r = p6(t)Σ2(t) i } encode
deviation of E3 with respect
to E2 estimate

34. simulation - Activation of layers
• evolution of layers for above
anticipated trajectory
• if usbl is within anticipated region
then reset signal for coresponding
node of P(anticipation in stand
deviation unit)
• neighbor arrangements and
evolution of info is encoded by
network
• F can reject unexpected
disturbance

35. simulation - activation of layers -
lateral connection role
• Wpp is set according to
two different condition
(identity and behavior
change)
• define sparse
encoding matrix (which
maps Behaviour a units to
Behviour z's)

36. Experience
• travelled 396 in 61 minutes
• Sonar tilt is 0 regarding horizon
• it can cover 130 horizon and 50
meters
• 19992 grayscale 16-bits images by
the SONAR
• 3663 leading values of compass
• 3662 positions by DGPS
• 1450 by USBL

37. Experimental Fusion of sensor

38. Experimental - localization -
scan matching motion estimation
• relative motion is from
multibeam sonar(no need
of correction)
• parameter of interest
• dead recking is obtained
by integrating relative
displacement over time

39. Experiment - Kalman filter
• F is state transition model
• x is estimated state vector
• B is control input model
• u is control control vector
• e is random gaussian
vector that model
uncertainties introduced by
state transition
• posterior state is corrected
by x P y S K
predicted state
estimate and
covariance