Error Bound Analysis towards Fingerprint-based Positioning System Involving Grid Size Information

Most of the representative lower positioning error bound (LPEB) derivation works of Wireless Local Area Network(WLAN) fingerprint-based positioning system are on the basis of Cramr-Rao Lower Bound (CRLB). However, there are some limitations, i) to the best of our knowledge, all existed works have not investigated the impact of grid size, which is one of the factors affecting the location accuracy; ii) traditional CRLB-based derivation takes the user's location coordinate as the basic estimated parameter vector, which is not exact because we actually estimate the nearest reference point (RP) to the user rather than estimating the user's location directly; iii) CRLB-based derivation has a fundamental premise that the signal obeys a specific signal distribution so as to formulate Probability Density Function (PDF) clearly, but for an irregular scenario, the signal may not obey one specific signal distribution and the PDF is unknown, which means CRLB is not available. Motivated by these limitations, this paper firstly constructs a new derivation model which takes grid size information into account, and revises the basic estimated parameter vector as the nearest RP's location. Then we deduce the LPEB in terms of the proposed new derivation model under two situations. Specifically, for a regular scenario with specific signal distribution, we re-deduce LPEB based on CRLB. Moreover, for an irregular scenario with non-specific signal distribution, we transform the observations into a linear pattern expression and apply the Gaussian-Markov theorem to conduct the LPEB derivation. Finally, the simulations and experiments are presented to support our claims.