| Summary: | Positioning systems are used in a wide range of applications which require determining the position of an object in space, such as locating and tracking assets, people and goods; assisting navigation systems; and mapping. Indoor Positioning Systems (IPSs) are used where satellite and other outdoor positioning technologies lack precision or fail. Ultra-WideBand (UWB) technology is especially suitable for an IPS, as it operates under high data transfer rates over short distances and at low power densities, although signals tend to be disrupted by various objects. This paper presents a comprehensive study of the <i>precision</i>, <i>failure</i>, and <i>accuracy</i> of 2D IPSs based on UWB technology and a pseudo-range multilateration algorithm using Time Difference of Arrival (TDoA) signals. As a case study, the positioning of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>×</mo><mn>4</mn><mspace width="3.33333pt"></mspace><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> area, four anchors (transceivers), and one tag (receiver) are considered using bitcraze’s Loco Positioning System. A Cramér–Rao Lower Bound analysis identifies the convex hull of the anchors as the region with highest <i>precision</i>, taking into account the anisotropic radiation pattern of the anchors’ antennas as opposed to ideal signal distributions, while bifurcation envelopes containing the anchors are defined to bound the regions in which the IPS is predicted to <i>fail</i>. This allows the formulation of a so-called <i>flyable area</i>, defined as the intersection between the convex hull and the region outside the bifurcation envelopes. Finally, the static bias is measured after applying a built-in Extended Kalman Filter (EKF) and mapped using a Radial Basis Function Network (RBFN). A debiasing filter is then developed to improve the <i>accuracy</i>. Findings and developments are experimentally validated, with the IPS observed to <i>fail</i> near the anchors, <i>precision</i> around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>3</mn><mspace width="3.33333pt"></mspace><mi>cm</mi></mrow></semantics></math></inline-formula>, and <i>accuracy</i> improved by about <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>15</mn><mspace width="3.33333pt"></mspace><mi>cm</mi></mrow></semantics></math></inline-formula> for static and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mspace width="3.33333pt"></mspace><mi>cm</mi></mrow></semantics></math></inline-formula> for dynamic measurements, on average.
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