Approximate Diagonalized Covariance Matrix for Signals with Correlated Noise
2016 (English)In: Proceedings of the 19th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2016, 521-527 p.Conference paper (Refereed)
This paper proposes a diagonal covariance matrix approximation for Wide-Sense Stationary (WSS) signals with correlated Gaussian noise. Existing signal models that incorporate correlations often require regularization of the covariance matrix, so that the covariance matrix can be inverted. The disadvantage of this approach is that matrix inversion is computational intensive and regularization decreases precision. We use Bienayme's theorem to approximate the covariance matrix by a diagonal one, so that matrix inversion becomes trivial, even with nonuniform rather than only uniform sampling that was considered in earlier work. This approximation reduces the computational complexity of the estimator and estimation bound significantly. We numerically validate this approximation and compare our approach with the Maximum Likelihood Estimator (MLE) and Cramer-Rao Lower Bound (CRLB) for multivariate Gaussian distributions. Simulations show that our approach differs less than 0.1% from this MLE and CRLB when the observation time is large compared to the correlation time. Additionally, simulations show that in case of non-uniform sampling, we increase the performance in comparison to earlier work by an order of magnitude. We limit this study to correlated signals in the time domain, but the results are also applicable in the space domain.
Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. 521-527 p.
Signal processing, approximate estimation
Control Engineering Signal Processing
IdentifiersURN: urn:nbn:se:liu:diva-130162ISBN: 978-0-9964527-4-8OAI: oai:DiVA.org:liu-130162DiVA: diva2:948531
19th International Conference of Information Fusion, Heidelberg, Germany, July 5-8 2016
FunderSwedish Research Council