Covariance shaping least-squares estimation

Covariance shaping least-squares estimation

A new linear estimator is proposed, which we refer to as the covariance shaping least-squares (CSLS) estimator, for estimating a set of unknown deterministic parameters x observed through a known linear transformation H and corrupted by additive noise. The CSLS estimator is a biased estimator directed at improving the performance of the traditional least-squares (LS) estimator by choosing the e...

Recursive Generalized Total Least Squares with Noise Covariance Estimation

We propose a recursive generalized total least-squares (RGTLS) estimator that is used in parallel with a noise covariance estimator (NCE) to solve the errors-in-variables problem for multi-input-single-output linear systems with unknown noise covariance matrix. Simulation experiments show that the suggested RGTLS with NCE procedure outperforms the common recursive least squares (RLS) and recurs...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...

Least-squares inner product shaping

We develop methods that construct an optimal set of vectors with a specified inner product structure, from a given set of vectors in a complex Hilbert space. The optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors. Four special cases are considered. In the first, the constructed vectors are orthonormal. In the s...

Least Squares Estimation