## 2 Related Work  
Two types of system configurations can be distinguished by the role of the mobile nodes. In an active LPS, the mobile nodes emit ultrasound (US) and the beacons are receivers. This is for example the case in BAT [4], the pioneer of US LPS, and the recently developed SNoW Bat [5]. On average, scalability of such systems is rather limited because the number of concurrently transmitted signals lowers the SNR. For example, [6] reported that for more than 16 concurrent transmitters the bit error rate was already severely deteriorated and no longer allowed correct transmitter identification. If concurrent access is not (or no longer) possible, the locating rate starts to decay and is inversely proportional to the number of nodes. This has already been discussed in [7] for the Active Bat system where complex workarounds are necessary increasing system complexity and cost. Contrary to the two previous systems, Cricket [8,9], the first BLUPS [10] and other systems [11] use transmitting beacons and receiving nodes. Reported position errors are less than 9 cm for BAT [4], less than 1.5 cm for SNoW BAT [5], 30 cm for Cricket V1 [9], 1 cm for Cricket V2 [9], and 1.5 cm for BLUPS [10]. The time of flight (ToF) method for ranging measurement is used to deliver fine-grained localization in [4,5,8-10]. A System using time differences of arrival (TDoA) is [6]. Robustness to different failures in ToF/TDoA measurements is an important aspect as lightweight obstructions around the receiver will introduce bending and refracting effects and can introduce an error of up to 5% [12]. Non Line of Sight (NLoS) errors with different size of object and position can be between 10% and 100% [12]. It is also known that the traditional least squares multilateration algorithm delivers inaccurate results if there is a single error in measured distances [13]. For example [12] used the least median of squares (LMedS) which delivers improved performance in case of NLOS signals. For achieving high accuracy in a LPS, calibration is of upmost importance because the correct position of beacons will directly influence the accuracy. This is obvious because these positions are used in the formulas for multilateration. Different calibration methods have been proposed: In [14], the ceiling mounted receivers were calibrated by a transmitter moving to at least five known coordinate points. DOLPHIN [15] is a distributed positioning system aimed at ubiquitous computing applications. It applies iterative multilateration techniques where three precise positions of devices have to be defined as initial state. An auto calibration algorithm also requiring three known tests points for the ToF and TDoA case is presented in [11]. Different types of measuring devices as required by [11,14,15] can be used depending on the budget available. If low cost devices are used, e.g., simple measurement tapes, this will almost always reduce the final location accuracy. A lightweight 3D tag system using a calibration device is shown in [16] where the average error was between 19.5 cm and 23.9 cm depending on the method used. An auto calibration algorithm requiring no additional devices developed for LPS [17] is based on multidimensional nonlinear least squares fitting algorithm. In [18] a two-step self-calibration method is proposed which does not require any pre-calibrated positions if relative positions are sufficient. In order to perform that task no additional hardware besides US receivers or transmitters and radio transceivers, which are already available for a WSN, are required. It achieved very good position accuracy in the range of millimeter by simulation. Verification of the calibration by comparing with manual calibration as in [11] is not recommend because of the inability to establish an orthogonal coordinate system. The only quantity, which canbe easily verified, is a point-to-point distance but not the individual coordinates due to the lack of the coordinate system unity vectors. Remarkably, an average deviation of only 2.2 cm has been achieved in [11].