{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T16:59:13Z","timestamp":1791046753847,"version":"4.1.0"},"reference-count":48,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper investigates the hybrid source localization problem using differential received signal strength (DRSS) and angle of arrival (AOA) measurements. The main advantage of hybrid measurements is to improve the localization accuracy with respect to a single sensor modality. For sufficiently short wavelengths, AOA sensors can be constructed with size, weight, power and cost (SWAP-C) requirements in mind, making the proposed hybrid DRSS-AOA sensing feasible at a low cost. Firstly the maximum likelihood estimation solution is derived, which is computationally expensive and likely to become unstable for large noise levels. Then a novel closed-form pseudolinear estimation method is developed by incorporating the AOA measurements into a linearized form of DRSS equations. This method eliminates the nuisance parameter associated with linearized DRSS equations, hence improving the estimation performance. The estimation bias arising from the injection of measurement noise into the pseudolinear data matrix is examined. The method of instrumental variables is employed to reduce this bias. As the performance of the resulting weighted instrumental variable (WIV) estimator depends on the correlation between the IV matrix and data matrix, a selected-hybrid-measurement WIV (SHM-WIV) estimator is proposed to maintain a strong correlation. The superior bias and mean-squared error performance of the new SHM-WIV estimator is illustrated with simulation examples.<\/jats:p>","DOI":"10.3390\/s21217159","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:52:35Z","timestamp":1635465155000},"page":"7159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Closed-Form Pseudolinear Estimators for DRSS-AOA Localization"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7652-9988","authenticated-orcid":false,"given":"Jun","family":"Li","sequence":"first","affiliation":[{"name":"UniSA STEM, University of South Australia, Mawson Lakes Campus, Mawson Lakes, SA 5095, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3373-6295","authenticated-orcid":false,"given":"Kutluyil","family":"Dogancay","sequence":"additional","affiliation":[{"name":"UniSA STEM, University of South Australia, Mawson Lakes Campus, Mawson Lakes, SA 5095, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hatem","family":"Hmam","sequence":"additional","affiliation":[{"name":"Defence Science & Technology Group, Cyber and Electronic Warfare Division, Edinburgh, SA 5111, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,28]]},"reference":[{"key":"ref_1","first-page":"762","article-title":"Statistical theory of d.f. fixing","volume":"94","author":"Stansfield","year":"1947","journal-title":"J. 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