Minimum mean square error estimator for mobile location using the pseudo-range TOA measurements

Source Localization in the non-synchronous mobile system is a very important issue since it only requires synchronized clocks between the based stations (BSs) and can reduce system complexity. There are time-difference-of-arrival (TDOA) and pseudo-range time-of-arrival (TOA) based localization techniques for a non-synchronous mobile system. Although many methods and performance analysis have been proposed for TDOA technique, relatively few studies have been reported on pseudo-range TOA method. This paper proposes a novel localization algorithm based on minimum mean square error estimator (MMSEE) for pseudo-range TOA. The simulations show that the proposed method can reach its CRLB and has the better performance than the TDOA method based on maximum likelihood estimator (MLE). Introduction Location estimation of a mobile station (MS) in wireless communication systemshas gained considerable attention since the Federal Communication Commission passed a mandate requiring cellular providers to generate accurate location estimates for Enhanced-911 services [1]. Conventional geolocation techniques include time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), signal strength (SS) based methods, or a combination of these. Among these location techniques, methods based on TOA and TDOA have attracted much attention due to its high location accuracy [2-3]. The main problem of TOA localization technique is time synchronization. TOA technique uses the absolute time of arrival at a certain base station which requires accurate time synchronization between MS and based stations (BSs). It is almost impossible for a MS to finish such high precision time synchronization with the existing hardware configuration. To overcome the imperfect time synchronization in MS, a non-synchronous mobile location system was developed and widely used in cellular location system and global positioning system. Compared with the TOA technique, the non-synchronous mobile location system only requires synchronized clocks between the BSs, and this characteristic reduces system complexity. Besides the unknown coordinates of MS in synchronous mobile system, there is an additional unknown parameter, i.e., the time offset between the clock at a MS and those at BSs, in a non-synchronous mobile system. The most popular localization method in non-synchronous mobile system is TDOA technique, which eliminates the time offset via linealized least squares using equations obtained by differencing between BSs. Many TDOA location methods have been proposed [4-7]. Chan and Ho [7] propose the two-step weighted least squares (WLS) method based on maximum likelihood estimator (MLE) to improve the location accuracy of the SI method. This method is an unbiased, and can provide an optimum performance and attain the deterministic Cramer-Rao lower bound International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 13 (CRLB) asymptotically. Although many methods and performance analysis have been proposed for TDOA technique, relatively few studies have been reported on another location technique in non-synchronous mobile system called pseudo-range TOA. Compared with the TDOA eliminating the time offset by differencing equations between BSs, the pseudo-range TOA method treated the time offset as an unknown parameter and tried to estimate it. In this paper, a novel pseudo-range TOA method based on minimum mean square error estimator (MMSEE) for non-synchronous mobile system is proposed. Since statistical characteristics of time-offset are used as prior information, the proposed method can provide the better performance than TDOA method based on MLE. System Model Firstly, the basic system model of a non-synchronous mobile system is briefly introduced. Besides the unknown coordinates of MS, there is an additional unknown parameter, i.e., the time offset between the clock at a MS and those at BSs, in a non-synchronous mobile system. There are, broadly, two ways to cope with the time offset: processing pseudo-range measurements directly (pseudo-range TOA method) via linearized least squares or via linealized least squares using equations obtained by differencing between BSs (TDOA method). Consider a non-synchronous mobile system, let } N , , 1 {  = N be the set of indices of the BSs, whose locations } , ) , {( N i y x T i i ∈ are known. The unknown parameters are the MS position ) , ( y x and time-offset τ . The delay time i t is the transmission time between MS and BSi . Denote the measurement with noise of } {∗ as } {∗ . A delay estimate can be approximated as: N i for n t t i i i ∈ + = ,  (1) The delay i t is called as the pseudo-range delay by using the pseudo-range concept: N i for l d c t i i ∈ + = ), ( 1 (2) with i n is a zero mean Gaussian random variable with variance 2 i σ , c is the signal propagation speed, τ c l = is the pseudo-range caused by time-offset τ , and i d is the true distance between the BS i and MS. 2 2 ) ( ) ( y y x x d i i i − + − = (3) The corresponding pseudo-range measurement i r  is model as: i i i i cn l d t c r + + = =   (4) The covariance matrix of i r  can be easily calculated from (4):