Analyzing non-linearity effect for indoor positioning using an acoustic ultra-wideband system

This paper addresses the non-linearity effect when using iterative least-squares (ILS) methods for indoor positioning, where coordinates are to be determined based on estimated/measured ranges. Dealing with non-linear inverse problems, the obtained least-squares estimator is inherently biased and the bias is usually negligible in satellite positioning systems, e.g. GPS, or other large scale systems. However, in indoor systems, the bias can be significant and therefore extra care needs to be taken to properly apply the ILS methods. Special attention is given to the Gauss-Newton method, since it is well suited for solving (small residual) non-linear problems [1] and most commonly applied in positioning. A scheme to test the significance of the bias due to non-linearity is proposed. The validation of the proposed scheme is experimentally supported by an UWB acoustic positioning demonstrator. By scaling the frequencies with a specific factor (the speed of light over the speed of sound), it is possible to observe similar interactions with the environment using audio signals as for radio UWB signals. This well-affordable acoustic UWB positioning demonstrator can be used to investigate the capabilities of UWB radio signals for potential indoor ranging and positioning applications. The non- linearity effect is analyzed with a number of system setups, differing in the positions of transmitters, the position of the receiver, redundancy, the bandwidth used and therefore the range measurement error. Preliminary results show that centimeter level positioning accuracy can be reached using the audio band between 3.6 and 12.1 kHz (corresponding to the full band between 3.1 to 10.6 GHz allowed for UWB radio communications).