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. 2018 Jul 19;18(7):2346. doi: 10.3390/s18072346
CPPS Cyber-physical production system
IIoT Industrial Internet of Things
RFID Radio Frequency IDentification
BoM Bill of Materials
IPS Indoor positioning system
UWB Ultra-Wide Band
BLE Bluetooth Low Energy
MSDF Multi-sensor data fusion
AoA Angle of Arrival
SS Signal Strength
RSS Received Signal Strength
ToA Time of Arrival
p1,,pNp products
m1,,mNm modules
a1,,aNa activities
c1,,cNc components
w1,,wNw workstations
t1,,tNt activity types
A (Np×Na) activities required to produce a product
W (Na×Nw) workstation assigned for an activity
B (Np×Nc) component/part required to produce a product
P (Np×Np) module/part family required to produce a product
C (Na×Nc) component/part built in or processed in an activity
M (Na×Nm) activity required to produce a module
T (Na×Nt) category of the activity
Sw (Na×lw) activity involved over a measured time interval
k index of the production cycle (discrete time)
y^iw(k) estimation of the individual activity times for work station w in the kth production cycle
xw(k) ’efficiency’ of the operator, the vector of the estimated local activity times
x(k) workstation-independent version of xw(k)
s(k) sequence of the timestamps recorded by the active fixture sensors
zw(k) vector of the sum of the activity times that are situated between the two sensors
α index of the first sensor of a fixture-sensor pair
β index of the second sensor of a fixture-sensor pair
qa the set of activities required to produce a specific product
ew serially uncorrelated white-noise vector of observational errors
Rw(k) covariance matrix of observational errors
H(k) time-variable regressors representing the number of activities and built in components
e(k) the set of the serially uncorrelated white-noise vector of observational errors of the workstations
x^(N) estimation error
Q positive-definite weighting matrix defined as Q=R-1
P* inverse of the parameter covariance matrix
A*(k) State-transition matrix in the Kalman filter represented estimation problem (in our case an identity matrix)
K(k) Gain of the Kalman filter/recursive estimator
Lw,cw Representation of the linear inequality constraints
Aew,bew Representation of the linear equality constraints
μj vector of Lagrange multiplier associated with equality
λj vector of Lagrange multiplier associated with inequality constraints