  We design statistical hypothesis tests for performing leak detection in water
pipeline channels. By applying an appropriate model for signal propagation, we
show that the detection problem becomes one of distinguishing signal from
noise, with the noise being described by a multivariate Gaussian distribution
with unknown covariance matrix. We first design a test procedure based on the
generalized likelihood ratio test, which we show through simulations to offer
appreciable leak detection performance gain over conventional approaches
designed in an analogous context (for radar detection). Our proposed method
requires estimation of the noise covariance matrix, which can become inaccurate
under high-dimensional settings, and when the measurement data is scarce. To
deal with this, we present a second leak detection method, which employs a
regularized covariance matrix estimate. The regularization parameter is
optimized for the leak detection application by applying results from large
dimensional random matrix theory. This second proposed approach is shown to
yield improved performance in leak detection compared with the first approach,
at the expense of requiring higher computational complexity.
