Data fusion of nonlinear measurement data in the presence of correlated sensor to- sensor errors
Al-Samara, Mansour Mohamed
(1993)
Data fusion of nonlinear measurement data in the presence of correlated sensor to- sensor errors.
PhD thesis, Dublin City University.
Data fusion of nonlinear measurement data in the
presence of correlated sensor-to-sensor errors is
examined. The scenario involves three spatiallydistributed
sensors making three noisy angle-ofarrival
measurements on a signal emitted by a source
whose position is to be estimated. The noisy angleof-
arrival measurements from two of the sensors are
triangulated to form a noisy position measurement in
two dimensions. A second pair of sensor noisy angleof-
arrival measurements are also triangulated to form
a second noisy position measurement. Both of these
noisy position measurements are nonlinear functions
of the noisy angle-of-arrival measurements.
Since there are three sensors SI, S2, and S3, sensor
S2 is common to both triangulation process, causing
a non-zero cross-correlation across both noisy
nonlinear position measurements. Since the position
measurements are nonlinear functions of the angle-ofarrival
measurements, we must use a first-order
approximation to the covariance matrix for each
measurement vector.
The statistics governing the errors on these angle
measurements come from a variety of distributions, namely the uniform, sawtooth, and triangular distributions.
The optimum fusion algorithm applied to the
distributed measurements forms a linear operation on
the measurement vectors. Since the measurements are
nonlinear functions of the parameters, an exact
calculation of the covariance matrix in closed form
is not possible because of the intractable nature of
the mathematics involved. Consequently, these
conditions give sub-optimum conditions for the
algorithm. However it is found that the trace of the
error covariance matrix of the fused measurement is
less than the trace of the error covariance matrix
associated with each individual measurement vector.
Finally, a mathematical high-order approximation to
the covariance matrix is performed. The impact of
these high-order terms is examined through
simulations.