{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T12:22:42Z","timestamp":1784290962770,"version":"3.55.0"},"reference-count":17,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,9,30]],"date-time":"2015-09-30T00:00:00Z","timestamp":1443571200000},"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>A hyperbolic positioning method with antenna arrays consisting of  proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters). A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system.<\/jats:p>","DOI":"10.3390\/s151025157","type":"journal-article","created":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T02:15:03Z","timestamp":1443665703000},"page":"25157-25175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization"],"prefix":"10.3390","volume":"15","author":[{"given":"Kenjirou","family":"Fujii","sequence":"first","affiliation":[{"name":"Hitachi Industrial Equipment Systems Co., Ltd., 3 Kanda-neribei-cho, Chiyoda-ku,  Tokyo 101-0022, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yoshihiro","family":"Sakamoto","sequence":"additional","affiliation":[{"name":"Department of Modern Mechanical Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Modern Mechanical Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiroaki","family":"Arie","sequence":"additional","affiliation":[{"name":"Department of Modern Mechanical Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Schmitz","sequence":"additional","affiliation":[{"name":"Department of Modern Mechanical Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shigeki","family":"Sugano","sequence":"additional","affiliation":[{"name":"Department of Modern Mechanical Engineering, School of Creative Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,30]]},"reference":[{"key":"ref_1","unstructured":"Combain Positioning Service. 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