New math solves a stubborn engineering problem that has plagued signal processing
Researchers have proven that a fundamental statistical tool used to analyze complex systems produces identical results no matter how engineers organize their input and output data. The finding eliminates guesswork from a process engineers use thousands of times daily in fields from telecommunications to manufacturing quality control.
Originaltitel: On the equivalence of repartitioned MIMO IV parameter estimators
<p>This paper concerns a particular property of the basic instrumental variable (IV) estimator that is useful for multiple-input multiple-output (MIMO) modeling problems where it is not obvious how to partition the available signals between the sets of inputs and outputs. In general, a repartitioning of the input and output signals will result in a different model compared to the original input-output choice. It is important to distinguish cases where a repartitioning results in an algebraically equivalent model and cases where the resulting model transformation is more complex and depends also on particular system and signal properties. The latter situation typically occurs when models are estimated from data. We here show that the basic IV estimator is an exception since it provides algebraically equivalent estimates regardless of true system structure, noise properties, or amount of data. This equivalence result is illustrated in two simulation examples.&lt;br /&gt; (c) 2026 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</p>