16 Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent Chin-Der Wann National Sun Yat-Sen University Taiwan 1. Introduction Kalan filter and its nonlinear extension, extended Kalan filter provide a feasible solution to itigating non-line of sight (NLOS) propagation effects, and therefore iproving accuracy of obile target tracking in indoor wireless environents. Most wireless counication systes for indoor positioning and tracking ay suffer fro different error sources, including process errors, easureent errors, the NLOS propagation effects and dense ultipath arrivals. The errors sources, if not properly eliinated or itigated, generally yield severe degradation of accuracy in ranging, positioning and tracking. Aong the factors that cause perforance degradation, the NLOS effect is considered the ajor error source in indoor location systes using one or ore types of easured location etrics. Accurate indoor positioning and tracking play an iportant role in hoe safety, public services, and other coercial or ilitary applications (Pahlavan et al., 1998). In recent years, indoor localization has drawn increasing interests fro acadeia and industry. There is an increasing deand of indoor localization systes for tracking persons with special needs, such as the elders and children who ay be away fro visual supervision. Other applications need the solutions to tracing obile devices or ovable objects in the covered areas of sensor networks, or localizing accurately in-deand portable equipents in hospitals and laboratories. In public safety and ilitary operations, the tracking systes can be used in navigating and coordinating police officers, fire-fighters or soldiers to coplete cooperative issions inside buildings. Various positioning techniques have been developed in the past few years. Handset-based positioning ethods generally require that a odified handheld device calculate its own position by using a fully or partially equipped global positioning syste (GPS) receiver. The ethod is, however, unfortunately not suitable for any indoor localization applications. Network-based ethods have their advantages in wireless location and indoor positioning. The ethods can be used for location estiation in situations where GPS solutions are not applicable. In the network-based wireless location, various schees using received signal strength indication (RSSI) have also been extensively investigated in the past two decades. In location systes using the RSSI, location estiation is usually obtained fro or augented with the location fingerprinting schee. Though no coplex easureent equipents are involved, the build-up of a radio ap of RSSI ay be tie-consuing.
310 Kalan Filter The RSSI data ay vary fro tie to tie when the layout or environent becoes different fro that when the RSSI data are collected. Due to the liitations of spectral natures of transitted signals in the location systes, accuracy and precision becoe a ajor challenge when applications other than tour-guiding services are targeted. To tackle the probles of obile positioning and tracking in indoor wireless NLOS environents, a variety of techniques and systes have been studied in recent years in the hope of attaining better location accuracy. Tie of arrival (TOA) and tie difference of arrival (TDOA) are two typical tie-related paraeters usually used in pinpointing the location of a obile station. In addition, techniques using angle of arrival (AOA) have also been studied by any researchers. When line of sight (LOS) transission exists between a transitter and a receiver, the signal arrival tie or signal arrival angle ay be correctly obtained if the SNR is high and the ulti-paths fro the propagation channels are resolved properly. In situations where NLOS propagation exists, suitable NLOS itigation techniques are needed for iproving the accuracy of ranging and localization. For applying the TOA and TDOA paraeters in locating obile stations or targets, the true range between a transitter and a receiver in the wireless environent is correctly calculated only when the direct path of signal propagation is present, which ay not always be possible, especially in indoor environents. In ost cases, errors caused by the NLOS effects cannot be ignored in wireless location systes where high accuracy is deanded. Several NLOS itigation techniques for obile positioning systes have been presented in the past few years (Le et al., 003; Najar & Vidal, 003; Wylie & Holtzann, 1996). In (Wylie & Holtzann, 1996), a siple binary hypothesis testing was used for NLOS identification by exploiting the known statistics of the receiver easureent noise. To itigate the NLOS effects, polynoial fitting was applied to all available easured range data for data soothing and variance calculation. Since a whole block of easured data are needed for the process of polynoial fitting, accurate and real-tie obile positioning ay not be possible due to the tie delay in collecting enough data. In other obile location estiation ethods, biased versions of the Kalan filter were used in itigating the NLOS range error (Le et al., 003). A coefficient for adjusting the noise covariance atrix needs to be chosen by experient to obtain good location estiation results. In (Najar & Vidal, 003), a odified Kalan algorith with NLOS error estiation was proposed for UMTS obile positioning. The estiation of range bias in the algorith provided perforance iproveent of location tracking in the NLOS environents. Since ost wireless counications systes used in wireless location ay suffer fro the NLOS and dense ultipath situation, it is an iportant issue to obtain higher accuracy in deterining signal arrival tie for the tie-based location systes. The ultra-wideband (UWB) radio syste, in addition to the usage for counications, can provide users with the abilities of high accurate location estiation and tracking. As a good candidate for lowpower high-speed wireless counications, the ultra-wideband (UWB) radio technology has gained any interests in recent years for its applications in indoor counications. In indoor environents, the UWB systes, based on the spectral characteristics of the signals, are capable of tackling the ultipath effects and providing finer and ore accurate easureents in ranging than other narrow-band systes. With the fine tie resolution, the accuracy of UWB location systes can be within one inch. The UWB systes though provide potentially accurate ranging for indoor positioning and tracking, the NLOS propagation errors caused by blocked LOS paths between a base station and the obile
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 311 station ay still lead to severe degradation of position accuracy, posing a ajor challenge to positioning and tracking. Suitable NLOS identification and itigation techniques are basically required in the systes for achieving better positioning perforance. This chapter will first present the UWB signal odels in LOS and NLOS indoor environents. The data soothing schees using Kalan filter and polynoial fitting technique for identifying the NLOS status of the transission are discussed. To iprove the accuracy of tie-based UWB range estiation, the NLOS itigation techniques using biased Kalan filters will be covered. Soe probles of applying the biased Kalan filtering in the NLOS identification and itigation are addressed, followed by solutions to iproving the correctness of hypothesis tests in the identification stage, and reducing the exceeding negative adjustent effects of biased Kalan filtering in the itigation stage. The applications of extended Kalan filters on wireless positioning and tracking are then presented. A network-based location syste, in which location etrics fro ultiple base stations are used for obile target location estiation is studied. Positioning techniques using hybrid TDOA/AOA (tie difference of arrival/angle of arrival) location etrics in the UWB environents will be presented. Siulation results are included to show the capability of Kalan filter-based architecture in itigating the NLOS errors and iproving the accuracy of target positioning and tracking in the UWB indoor wireless location syste.. Non-line of sight propagation errors.1 Range easureent odel We assue that there are ultiple base stations (BS s) in UWB indoor wireless location systes. In dealing with the non-line of sight propagation effects, the range easureent between a rover (or obile station) and the -th base station, corresponding to the TOA location etrics of the -th base station can be odelled as r ( t ) = L i ( t ) + n i ( t ) + NLOS i ( t ) i (1) where r (t i ) is the easured range at the sapling tie t i, L (t i ) is the true range, n (t i ) is the easureent noise and odelled as a zero-ean additive Gaussian rando variable with standard deviation σ, and NLOS ( t ) is the NLOS error coponent in the received signal. i There will be no NLOS error coponent if the line-of sight propagation path exists, and NLOS ( t ) = 0. The easureent error n (t i ) becoes the only source of range i easured error. In a dense ultipath UWB indoor environent, the estiation of the arrival tie of the first path can be directly related to the easured range data at each base station, as in (1). The IEEE UWB channel odelling subcoittee adopted a odified Saleh-Velenzuela (S-V) odel, which seeed to best fit the UWB channel easureents (Molisch, et al., 003). The S-V odel was used in odelling the ultipath of an indoor environent for wideband channel. The channel easureents showed that ultipath arrivals in clusters rather than in a continuous for (Saleh & Valenzuela, 1987), as shown in Fig. 1. Assue that T 0 is the arrival tie of the first path in the first cluster. The arrival tie T 0 can be related to the positive NLOS error coponent NLOS ( t ) at the tie instant t i. For the LOS cases, we i have T 0 = 0 and NLOS ( t ) = T 0 c = 0, where c is the speed of light. i
31 Kalan Filter The arrival tie T 0 for the NLOS cases can be odelled as an exponential distribution and described by the following equation (Molisch, et al., 003) p( T ) =Λexp[ Λ ( T )] () 0 0 where Λ[1/nsec] is the cluster arrival rate. The ultipath cluster arrival rates under different UWB channel odels, CM1 through CM4, are listed in Table 1. The related paraeters listed by the IEEE UWB channel odelling subcoittee have been used in any siulations and technical designs of a variety of UWB systes. Fig. 1. Multipath delay profile of typical UWB channels UWB Channel CM 1 CM CM 3 CM 4 Tx/Rx separation 0-4 0-4 4-10 >10 Λ (1/nsec) 0.033 0.4 0.0667 0.0667 LOS/NLOS condition LOS NLOS NLOS NLOS Table 1. The cluster arrival rate of ultipath used in UWB channel odels. Non-line of sight identification For the NLOS error probles in obile position location, several NLOS identification and itigation techniques have been presented in the past few years (Thoas et al., 000; Wylie & Holtzann, 1996). These approaches identified the BS s that have NLOS coponents in the received range data, and tried to reduce the tie-based NLOS errors by using the NLOS itigation techniques. In (Wylie & Holtzann, 1996), a siple binary hypothesis test was used for the NLOS identification with an understanding that the standard deviation of the NLOS propagation errors is generally uch larger than that of easureent errors in the LOS situation. The understanding ay also be applied to the UWB transission environents. In (Wylie & Holtzann, 1996), prior to the binary hypothesis testing, polynoial fitting was applied to all available easured obile range data collected during a block of tie interval for variance calculation and data soothing. Since the whole block of easured data were needed for the process of polynoial fitting, real-tie positioning ay not be feasible. For itigation of the NLOS errors NLOS (t i ), the existence of non-zero NLOS coponent ay need to be identified first. As shown in Fig., the easured range data are first processed to obtain the soothed data, which can further be used as averaged values at the corresponding tie instants. The standard deviation of the easured range
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 313 data with respect to the soothed values can then be calculated and used in the proceeding LOS/NLOS hypothesis test. Fig.. Identification of LOS/NLOS propagation status By applying the aboveentioned identification schee to wireless location systes, the range (or TOA) easureents related to each base station can be soothed by using the least squares technique in solving the coefficients for fitting the odelled N-th order polynoial function (Wylie & Holtzann, 1996). The standard deviation of the easured range data can be obtained by coputation over a block of K range data r (t i ) periodically: 1 ˆ σ = K i= 1 K ( r ( t ) S ( t )) (3) i i where S (t i ) is the soothed range data, which are obtained fro polynoial fitting. The data soothing can also be conducted by other ethods. In (Le et al., 003), the range data were soothed by utilizing biased Kalan filtering approach. In the case, the soothed range data S (t i ) were obtained fro the output of the biased Kalan filter. The estiated standard deviation obtained in (3) is then copared with a predeterined threshold in the siple hypothesis testing, represented as H : ˆ σ ( k) < γσ LOS case 0 1 H : ˆ σ ( k) γσ NLOS case (4) where σ is the standard deviation of the easureent noise in the LOS environent. The scaling paraeter γ is chosen experientally to reduce the probability of false alar. For the hypothesis testing in (Le et al., 003), a periodical interval checking ethod was used. Periodical LOS/NLOS checking schees, however, have soe drawbacks. First of all, the block size of data saples for variance calculation needs to be chosen experientally. Secondly, the period of using the hypothesis testing result ay not be easily deterined and ust be decided experientally as well. In Fig. 3, the block of C data saples, shown as shaded bars [0, C], are used for status checking. The resulting LOS/NLOS status will be kept unchanged until the tie instant N, when another cycle of status identification begins and the new LOS/NLOS status are used. To choose feasible tie instants C and N would need consideration of ore factors in the transission channels for the positioning systes. In addition to the probles, since the result of the LOS/NLOS hypothesis testing is used as the channel status until the next new periodical checking result is obtained, it is very likely that an NLOS-to-LOS or LOS-to-NLOS transition tie instant is issed or incorrectly detected. The incorrect identification of channel status or the incorrect transition tie ay yield large estiation errors in ranging and localization.
314 Kalan Filter Fig. 3. Periodical interval checking for identifying LOS/NLOS status Fig. 4. Periodical interval checking for identifying LOS/NLOS status To avoid the drawbacks, an identification schee using a sliding window can be used in processing the easured range data at the base stations. The function of the sliding window spans fro the data soothing step, the calculation of standard deviation step to the LOS/NLOS identification step. A fixed-length data window of C data saples, shown as the shaded bars [0, C] in Fig. 4, will slide to the right in the tie axis as the new data saple is available for processing. The sliding window schee is considered copatible with the schees using Kalan filtering. 3. Kalan filtering for data processing 3.1 Data soothing for the NLOS hypothesis testing A Kalan filter can be used in estiating the state vector of a obile target fro the observed range data, and therefore soothing the range data. Assue that the state vector of a obile can be represented as (Mendel, 1987) X( k + 1) = ΦX( k) + Γ W( k) (5) where X( k) = [ L( k) L ( k) L ( k)] T is the state vector of the obile target related to the easured data of a base station at the tie t k, W(k) is the driving noise vector with an assued covariance Q = σ w, and the state transition and noise transition atrices can be written as 1 Δt Δt / Φ = 0 1 Δt, and 0 0 1 (6) 0 Γ = 0. Δt (7) The easureent process is represented as Z( k) = HX ( k) + U( k) (8)
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 315 where Z ( k ) is the easured data, easureent atrix H = [1 0 0], and U( k ) is the easureent noise with covariance R = σ u. The iterative operations of the Kalan filter can be suarized as follows: X ( k k 1) = ΦX ( k 1 k 1) (9) T T P( k k 1) = ΦP( k 1 k 1) Φ + ΓQΓ (10) -1 ()=( 1) T T K k P k k H [ HP( k k 1) H + R ()] k (11) X ( k k) = X ( k k 1)+ K( k)[ Z( k)- HX ( k k 1)] (1) P( k k) = P( k k 1) K( k) HP ( k k 1) (13) where K ( k) is the Kalan gain vector and P(k k) is the covariance atrix of X ( k k). By using the Kalan filtering, the standard deviation of the observed range data can be calculated and then used in the LOS/NLOS hypothesis testing. To avoid the drawbacks of using polynoial fitting and periodical interval checking ethods, as discussed in the previous subsection, the sliding window schee for processing the easured range data can be integrated with the biased Kalan filtering and hypothesis testing in the UWB location syste. The standard deviation of data over a sliding block of C TOA (range) easureents r (t i ) at the -th base station can be obtained as k 1 ˆ σ ( k) = ( ( ) ˆ r t L ( t )). (14) i i N i= k ( C 1) In each processing cycle, the standard deviation calculated at base station is then used in the hypothesis testing, as represented in (4). If the LOS TOA propagation status is decided, an unbiased Kalan filter is used to sooth the TOA data at each BS. In the contrast, if the NLOS propagation scenario is detected, a biased Kalan filter is used in itigating the NLOS TOA error. 3. Biased Kalan filtering In a biased Kalan filter, based on the result fro LOS/NLOS hypothesis testing, different values of noise covariance are assigned. Under the LOS situation, unbiased soothing is used for estiating the true TOA. When the NLOS status is detected, the positive NLOS range error in the easured range (or TOA) data can be effectively reduced in the filtering cycle by assigning the diagonal eleents of the noise covariance atrix ˆ σu( k) = ασ, if Z( k) HX( k k 1) > 0 and NLOS detected, = σ, otherwise, where α is an experientally chosen scaling factor. The processed TOA data fro all base stations are then used in obile localization and tracking. (15)
316 Kalan Filter 3.3 Biased Kalan filtering for TDOA location etrics Siilar to the cases in the TOA location ethods, the Biased Kalan filters can also be applied in the TDOA location approaches. Assue that there are M base stations available for easuring the TOA s for locating a obile station. The first base station, BS1 is selected as the reference base station. The difference of ranges of the -th base station and the first base station to the obile station in the location syste can be odelled as ( ) = ( ) 1 ( ) = L ( t ) L ( t ) + n ( t ) + NLOS ( t ) d t r t r t i i i i 1 i d, i d, i =,..., M where n ( t ) is defined as the easureent noise of the range difference, d, i n ( t ) = n ( t ) n ( t ), and NLOS ( t ) is the NLOS error coponent of the range d, i i 1 i d, i difference, NLOS ( t ) = NLOS ( t ) NLOS ( t ). Hence, n ( t ) can be odelled as a d, i i 1 i d, i rando variable, at tie instant t i, with independently identical joint probability density function with n ( t ) N(0, σ ). d, i To perfor range difference estiation in the TDOA data processing, the Kalan filtering schee discussed above can be applied in the cases here. Three cases with different LOS/NLOS cobinations are considered for deterining the biased easureent noise covariance R = in the syste. σˆu Case 1: BS is an NLOS BS, and BS 1 is an LOS BS. We have ( ) Z k + 1 HX ( k + 1 k) > 0 Case : BS 1 is an NLOS BS, and BS is an LOS BS. We have ( ) Z k + 1 HX ( k + 1 k) < 0 Case 3: Both BS and BS 1 are NLOS BS s. When the three different cases are not et, both BS and BS 1 are considered LOS BS s. Fro the results of case deterination, the value of ˆu σ can be assigned by using the following rules: ασ, Case 1 or Case, c ˆ σ = σ, Case 3, (17) u Λ σ, otherwise, where α is experientally chosen scaling factors, c is the speed of light, Λ is the cluster arrival rate and σ is the standard deviation of AWGN easureent noise. If an all-los scenario exists, the range difference estiation is constructed by an unbiased Kalan filter; otherwise, the range difference is estiated by using a biased Kalan filter. 4. Range estiation with odified biased Kalan filtering 4.1 Probles in NLOS identification using Kalan filter and sliding window In data soothing, the cobination of Kalan filtering and sliding window schee has been considered a possible solution to the shortcoings caused by using polynoial fitting (16)
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 317 or periodical interval checking. Probles reain when trying to identify the NLOS-to-LOS channel status transition. In Fig. 5, it can be seen that the range data soothed by the Kalan filter decrease slower than expected. The phenoenon ay cause a tie period with identification errors in the proceeding hypothesis test. During the falling edge of transition, earlier values of the soothed range data ay yield standard deviations which will be larger than the threshold in the hypothesis test, as represented in (4). Instead of using the outputs of Kalan filter as the soothed range data, a odified schee is considered for directly generating range estiates. The forulation will be discussed in Section 4.3. Fig. 5. Slow falling transition of range data soothed by Kalan filter during the NLOS-to- LOS change of channel status 4. Proble in NLOS itigation using biased Kalan filter The bias adjusting rule in (15) was used in the hope that the positive NLOS propagation errors be itigated effectively by increasing the estiated noise standard deviation. The positive NLOS range bias can be reduced by assigning the diagonal eleents of noise covariance atrix. However, a resultant side effect is that exceeding negative adjustents ay occur in the beginning part of the NLOS status, as shown in Fig. 6. Generally speaking, if an NLOS status is detected and the innovation fro the easured data is positive, the easured data ay be treated as affected by noise with larger variance and the adjusting rule will achieve the objective of NLOS itigation in the iteration. In the contrast, if the innovation fro the easured data is negative, a possible LOS status would be assued. The assuption ay becoe incorrect in the next iteration, when the channel is actually in NLOS status. The error would yield an even ore negative adjustent in the estiated range value. To tackle the undesirable effect, a new bias adjusting rule is required.
318 Kalan Filter Fig. 6. Exceeding negative adjustents in the beginning part of the NLOS status, 4.3 Functional cobination of NLOS identification and itigation A novel range estiation schee with a odified biased Kalan filter for NLOS range itigation and LOS/NLOS identification is presented and shown in Fig. 7. The odified biased Kalan filter is used to process the range (or TOA) easureent according to the feedback identification result fro the processed data in the previous iteration of Kalan filtering. Before coputing the Kalan gain in (11), the easureent noise covariance σ u or the range prediction covariance P ( 1) 1,1 k k ust be adjusted by the following adjusting rules. For NLOS case and Zk ( ) HX ( k k 1) > 0, let ˆ k function u For NLOS case and Zk ( ) HX ( k k 1) < 0, let σ = ˆ σ ( 1) + (innovation) ; (18) ˆ σ ( k) = σ, and (19) u For LOS case, let P ( k k 1) = P ( k k 1) + function(innovation) ; (0) 1,1 1,1 ˆ σ u( k) = σ, (1) where ˆ σ ( k 1) is the standard deviation obtained by the sliding window in the previous iteration. By adjusting noise covariance in (18) and (19), the positive NLOS range error can
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 319 be significantly reduced. The inclusion of (0) is essential in copensating the range prediction covariance P 1,1 ( k k 1). The biased ter avoids inaccurate estiation of the range rate L ( k) fro the NLOS itigation. Measured TOA fro Sensor TOA estiated by odified biased Kalan filter Estiated TOA Standard deviation calculation with sliding window and LOS/NLOS test Estiated TOA LOS/NLOS test result and Standard deviation Fig. 7. Range (TOA) itigation and LOS/NLOS identification In the range estiation schee, easured TOA data are first processed by a odified biased Kalan filter. Based on the LOS/NLOS status and the standard deviation feedback fro the previous processed data, the odified biased Kalan filter generates an estiated TOA for the current processed data. Under the NLOS situation, the easured TOA s are soothed by using biased filters, and the positive NLOS errors are itigated. The standard deviation fro the feedback path is regarded as a reference representing the degree of NLOS errors. Under the LOS situation, unbiased soothing is used for estiating the true TOA value. Fig. 8. Results of using the range estiation schee with a odified biased Kalan filter
30 Kalan Filter In the second functional block in Fig. 7, the standard deviation of the estiated TOA is calculated. With a sliding window, the standard deviation of the last C estiated TOA s is calculated. The obtained standard deviation is passed through an LOS/NLOS hypothesis testing to deterine the status of propagation. The resultant LOS/NLOS status and the standard deviation are then used as feedback to the odified biased Kalan filter for data processing in the next cycle. The design objective is that the transition between LOS and NLOS conditions can be detected iediately and the NLOS effects can be effectively itigated in order to obtain a sequence of estiated TOA s, which are close to the corresponding true range between the obile and a base station. Fig. 8 shows the results of applying the novel range estiation schee with a odified biased Kalan filter for NLOS range itigation and LOS/NLOS identification For a location syste with ultiple base stations, the processed TOA data fro all participating base stations are then used in positioning and tracking. Forulated TDOA data are also possible if TDOA location syste is desired. 5. Hybrid TDOA/AOA indoor positioning and tracking 5.1 Extended Kalan filter for TDOA/AOA positioning Both tie-based and angle-based categories have their own advantages and liitations, it is therefore reasonable to consider hybrid ethods to integrate the erits of using the two types of etrics. In (Cong & Zhuang, 001), a hybrid TDOA/AOA location schee was presented for wideband code division ultiple access (WCDMA) systes. The schee uses TDOA inforation fro all base stations (BS s) and the AOA inforation at the serving base station to perfor obile location estiation. In other obile location ethods, biased versions of the Kalan filter were used in itigating the NLOS range error. With the rule-deterined coefficient for the easureent noise covariance atrix, good location estiation results would be obtained (Le et al., 003; Thoas et al., 000). In (Najar & Vidal, 003), Kalan filtering algorith with NLOS bias estiation was proposed for UMTS obile positioning. The estiation of range bias provided perforance iproveent of location tracking in NLOS environents. To eet the deand of high location accuracy in indoor positioning applications, the UWB syste is considered due to the fine tie resolution. The fine resolution of UWB signals provides potentially accurate ranging for indoor location counications, where dense ultipath and NLOS errors are the ajor challenge to the quality of indoor positioning applications. To iprove the accuracy of positioning, ethods for eliinating or itigating the effects of NLOS errors and ultipath in the UWB environents need to be applied before the TDOA/AOA location technique is used. For designing suitable NLOS identification and itigation algoriths for the UWB systes, paraeters of the standard UWB channel odels provided by the IEEE 80.15.3a standards task group are used in the studies and siulations. In contrast to the schee in (Cong & Zhuang, 001), all good AOA data along with TDOA inforation fro all BA s are considered in locating the MS position. The AOA and TDOA inforation are processed centrally by the extended Kalan filter (EKF) for MS positioning and tracking. The architecture of location estiator is illustrated in Fig. 9. For attaining effective NLOS itigation and obtaining ore accurate TOA estiates, the functional blocks in each branch ay be replace by the schee shown in Fig. 7.
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 31 Fig. 9. Hybrid TDOA/AOA positioning and tracking In Fig. 9, the NLOS error itigation consists of two parts: the NLOS TOA error itigation and the AOA inforation selection. If the LOS TOA propagation scenario is decided, an unbiased Kalan filter is used to sooth the TOA data at each BS. In the contrast, if the NLOS propagation scenario is detected, a biased Kalan filter or odified biased Kalan filter is used in itigating the NLOS TOA errors. The positive NLOS range bias can be reduced by assigning the diagonal eleents of noise covariance atrix. The processed TOA data fro all base stations are then used in forulating the TDOA data, which can be further used for obile positioning and tracking. The AOA inforation fro all base stations are processed by the AOA selection to avoid introducing large NLOS bearing error into the position tracking stage. Only AOA data fro LOS base stations are selected for further processing. In other words, any NLOS AOA data will be discarded. The forulated TDOA data and the selected AOA data are processed by the extended Kalan filter for the MS location estiation. The state vector of a obile station is defined as ( k) S( k k 1) = Φ S( k 1 k 1)+ W ( k 1) () T where S =[ x( k) y( k) x ( k) y ( k)] is the state vector at tie instant k. The covariance atrix of the driving noise vector W ( k ) is and the state transition atrix is 0 0 0 0 0 0 0 0 Q =, (3) 0 0 σ u 0 0 0 0 σ u 1 0 T 0 0 1 0 T Φ = 0 0 1 0. (4) 0 0 0 1
3 Kalan Filter In the case where the LOS status exists between the obile station and all base stations, the TDOA/AOA easureent process can be represented as Z( k) = f ( S( k)) + U ( k), (5) where Z ( k ) is the easured data vector, f ( S ( k )) is a nonlinear transforation, and U ( k ) is the easureent noise. The covariance atrix of U ( k ) is R T Hσ H 0 = 0 σ I AOA (M 1) (M 1) in which the TDOA forulation can be written as, (6) and H 1 1 0 0 1 0 1 0 = 1 0 0 1 (M 1) M, (7) σ σr 0 0 0 σr 0 =, (8) 0 0 σ R MM where σ R is the variance of the range related to the output of the unbiased or biased Kalan filter. The AOA variance σ is related to the selected LOS AOA data. The AOA diension of the atrix I, is the deterined nuber of LOS base stations fro the AOA selection. As shown in Fig. 10, the results fro the LOS/NLOS hypothesis are used in selecting the LOS AOA etrics. When the NLOS situation occurs, the covariance atrices of the processed TDOA and AOA data are different fro those in the LOS situation. The diension of the atrix in easureent process for the NLOS situations will be decreased, and deterined by the su of the nuber of TDOA and the nuber of LOS AOA data. 5. Siulations results and discussions The perforance of the hybrid TDOA/AOA positioning technique for indoor UWB systes is studied by conducting coputer siulations. We assue that three base stations are used in the location syste. The coordinates are BS1: (0, 0), BS: (5, 8.66), and BS3: (10, 0), respectively. The NLOS range error is assued to be an exponential distribution, which is defined in the standard indoor UWB channel odel (Foerster, 003; Molisch, et al., 003). A ultipath cluster arrival rate 0.0667*10 9 for CM3 is used for the case where the distance
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 33 Fig. 10. Hybrid TDOA/AOA positioning and tracking with AOA selection between any BS and the MS is within the range fro 4 to 10 eters. The NLOS bearing is assued to be uniforly distributed fro π to π. It is assued that an MS travels fro location (7, 4.5) to (4, 0.5) with a constant velocity, 0.5/s, as illustrated in Fig. 11. The observed tie length is 10s, and the saple spacing is 5s. Two LOS/NLOS propagation scenarios are investigated. In the first scenario, the LOS propagation between the MS and BS3 turns NLOS at t = s, and reains NLOS until t = 10s. The siulation results in Fig. 1 shows that the hybrid TDOA/AOA positioning schee with the AOA selection function perfors well in ters of root ean square location errors. Without the AOA selection, the NLOS bearing error ay lead to severe degradation of position accuracy. Fig. 11. A siulation exaple with three BS s and one obile target
34 Kalan Filter Fig. 1. Perforance of positioning with and without AOA selection (Scenario 1: one NLOS BS is assued) In the second scenario, the propagation between the MS and two BS s (BS and BS3) turn NLOS at t = s, and reains NLOS until t = 10s. In the situation, the data available to the extended Kalan filter will change fro three AOA s and two TDOA s to one selected AOA and two TDOAs. The siulation results are shown in Fig. 13. It can be seen that the position errors are a bit larger in this case. The increased errors are ainly due to the larger residual errors at the NLOS TOA itigation stage and the processing of fewer available AOA data in the adjustable TDOA/AOA-based extended Kalan filter for positioning. Fig. 13. Perforance of positioning with and without AOA selection (Scenario : Two NLOS BS s are assued)
Kalan Filtering for NLOS Mitigation and Target Tracking in Indoor Wireless Environent 35 6. Conclusion We present the applications of Kalan filter and extended Kalan filter on data soothing, NLOS identification, NLOS itigation and obile target tracking in the UWB indoor wireless environents. To iprove the accuracy of tie-based UWB ranging, data soothing with Kalan filtering for the NLOS hypothesis testing has been discussed. For the function of NLOS itigation, biased Kalan filtering is investigated. To tackle the undesirable detection probles of using data soothing and biased Kalan filtering in range estiation, a novel odified biased Kalan filtering schee is presented. In the odified biased Kalan filtering schee, functional cobination of NLOS identification and NLOS itigation is discussed. To investigate obile target positioning and tracking in the NLOS indoor environents, with a focus on the network-based location syste, where ultiple base stations are involved in the location estiation, a hybrid TDOA/AOA location syste forulated with extended Kalan filters is proposed. Siulation results show the Kalan filter-based schee is capable of effectively itigating the NLOS errors and therefore iproving the accuracy of target positioning and tracking. Further efforts of NLOS itigation will lead to iproved estiation of signal arrival tie and ore accurate obile target positioning and tracking. The integration of ultiple Kalan filters and statistical data fusion schees ay also provide a proising solution to the eerging tracking applications using ultiple obile robots and wireless sensor networks in indoor wireless environents. 7. References Cong, L. & Zhuang W. (001). Non-Line-of-Sight Error Mitigation in TDOA Mobile Location, Proceedings of IEEE Global Telecounications Conference, Vol. 1, pp. 680-684, San Antonio, TX. USA, Nov. 001. Foerster, J. Editor. (003). Channel Modeling Sub-coittee Report Final. Docuent IEEE P80.15-0/490r1-SG3a, IEEE. Le B. L.; Ahed K. & Tsuji H. (003). Mobile Location Estiator with NLOS Mitigation using Kalan Filtering. Proceedings of IEEE Wireless Counications and Networking Conference, Vol. 3, pp. 16-0, March 003. Mendel, J. M. (1987). Lessons in Digital Estiation Theory, Prentice-Hall, Inc., ISBN: 0-534- 06660-7, Upper Saddle River, NJ, USA. Molisch, A. F.; Foerster, J. R. & Pendergrass, M. (003). Channel Models for Ultrawideband Personal Area Networks. IEEE Wireless Counications, Vol. 10, No. 6, Deceber 003, 14-1, ISSN: 1536-184. Najar M. & Vidal J. (003). Kalan Tracking for Mobile Location in NLOS Situations. Proceedings of The 14th IEEE International Syposiu on Personal, Indoor and Mobile Radio Counication, Vol. 3, pp. 03-07, Sept. 003. Pahlavan, K.; Krishnaurthy P. & Beneat, J. (1998) Wideband Radio Channel Modeling for Indoor Geolocation Applications. IEEE Counications Magazine, Vol. 36, No. 4, April 1998, 60 65. Saleh, A. & Valenzuela, R. (1987). A Statistical Model for Indoor Multipath Propagation. IEEE Journal on Selected Areas in Counications, Vol. SAC-5, No., Feb. 1987, 18 137, ISSN: 0733-8716.
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