Balanced least squares: estimation in linear systems with noisy inputs and multiple outputs
| Title | Balanced least squares: estimation in linear systems with noisy inputs and multiple outputs |
| Publication Type | Conference Paper |
| Year of Publication | 2016 |
| Authors | Vía, J., and I. Santamaría |
| Conference Name | IEEE Workshop on Statistical Signal Processing (SSP) |
| Month Published | June |
| Conference Location | Palma de Mallorca |
| Abstract | This paper revisits the linear model with noisy inputs, in which the performance of the total least squares (TLS) method is far from acceptable. Under the assumption of Gaussian noises, the maximum likelihood (ML) estimation of the system response is reformulated as a general balanced least squares (BLS) problem. Unlike TLS, which minimizes the trace of the product between the empirical and inverse theoretical covariance matrices, BLS promotes solutions with similar values of both the empirical and theoretical error covariance matrices. The general BLS problem is reformulated as a semidefinite program with a rank constraint, which can be relaxed in order to obtain polynomial time algorithms. Moreover, we provide new theoretical results regarding the scenarios in which the relaxation is tight, as well as additional insights on the performance and interpretation of BLS. Finally, some simulation results illustrate the satisfactory performance of the proposed method. |
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