Mitigation of GPS Multipath Using Polarization and Spatial Diversities

Transcription

1 Mitigation of GPS Multipath Using Polaization and Spatial ivesities Matthew Benneman, Jade Moton Chun Yang Fank van Gaas Miami Univesity Sigtem Technology, Inc. Ohio Univesity BIOGRAPIES Matthew Benneman is a eseach associate in the Electical and Compute Engineeing epatment at Miami Univesity. e eceived a B.S. in Biology fom Canegie-Mellon Univesity and a M.S. in Mathematics fom Viginia Tech. is eseach inteest is in signal detection and paamete estimation.. Jade Moton is an Associate Pofesso of electical engineeing at Miami Univesity. e eseach inteests ae digital signal pocessing, softwae GPS eceives, and ionosphee physics. She holds a Ph in EE fom the Pennsylvania State Univesity.. Chun Yang eceived his title of octeu en Science fom the Univesity de Pais, Fance. Afte two yeas of post-doctoal eseach at the Univesity of Connecticut, he moved on with his industial R& caee. e has been with Sigtem Technology, Inc. since 1993 and has been woking on numeous GPS, integated inetial, and adaptive aay elated pojects.. Fank van Gaas is a Fitz J. and oloes. Russ Pofesso of Electical Engineeing and Pincipal Investigato with the Avionics Engineeing Cente at Ohio Univesity. e is a Past Pesident of the IO (98-99). e eceived the Thulow and Keple awads and is a Fellow of the IO.. Van Gass s eseach inteests cente on all facets of GPS, including aicaft pecision appoach and landing, attitude detemination, and system integation. ABSTRACT This pape pesents a GPS multipath mitigation method using a dual ciculaly polaized antenna aay and a multi-channel eceive. The method is based on the exploitation of both polaization and spatial divesity associated with a GPS signal and its multipath signals available at the eceive input. Conventional GPS antennas ae ight-hand ciculaly polaized (RCP) to suppess multipath contibutions to the input. This polaization-based discimination of multipath signal cannot completely eliminate multipath induced GPS ange measuement eos. We pesent an algoithm that pefoms spatial pocessing on the input fom the left-hand cicula polaized (CP) aay with an inceased elative stength of the multipath signal, theeby poviding impoved multipath angle of aival (AOA) estimation. With the known multipath AOA and diect signal AOA (which can be obtained fom almanac/ephemeis togethe with the antenna attitude o estimated in a sepaate pocess), we can then take advantage of the spatial divesity of the diect signal and multipath by applying null-steeing to the RCP aay input. The pape pesents the algoithm and simulation esults fo a unifom linea aay eceiving one diect signal and one multipath. Ou peliminay studies showed that the multipath AOA estimato poduces negligible eo if the diect signal and multipath AOA ae not close to each othe (moe than 5 degees apat) and that the diect signal is not at low elevation. The esults also suggested that longe time delay between the diect and multipath signal will incease multipath AOA estimation eo but this incease is toleable. Futhemoe, we demonstated that the multipath estimation impoves with inceasing spatial divesity fo multipath and diect GPS signals even if the signal aivals ae close in time. Finally, we demonstated that the multipath mitigation technique does poduce an impoved eceive coelato function which diectly impacts the GPS code ange measuement accuacy. 1. ITROUCTIO Multipath is a majo eo souce in GPS ange measuements [1]. Many techniques have been developed to mitigate multipath eo. These techniques include special consideation in antenna hadwae design [], eceive site selection [6][15], GPS tacking loop design [14][16][17], time- 11

2 fequency domain signal pocessing of GPS code/caie measuements [5][19], multi-channel eceives and/o spatial pocessing techniques [3][8][1][11][1], and the use of multipath polaization popeties [18]. Many of these methods ae only applicable to static applications which equie the eceive emain in one position ove extended time peiod, while othes have difficulties in sepaating the multipath eo fom othe eo souces such as ionospheic delay eos. Spatial pocessing techniques alone ae limited when the multipath and diect signal AOA ae close. Multipath that is close to diect signal in time of aival poses even bigge challenges. In this pape, we pesent a method that uses a dual ciculaly polaized antenna aay and a multi-channel GPS eceive to mitigate multipath eo by jointly exploiting both spatial and polaization divesity between a diect GPS and its multipath signals. iect GPS signals ae ight hand cicula polaized (RCP). When a GPS signal is eflected fom a suface, a significant potion of it becomes left hand cicula polaized (CP) when the angle of incidence with the suface fom which it eflects exceeds the Bewste angle. Field studies of multipath in model uban envionments show that detectable multipath signals do have significant incident angles [13], and theeby suppots the geneally accepted notion that multipath poduced by a single eflection tend to be pedominantly CP. This diffeence in the polaization states between the diect and multipath signals can be detected by a RCP antenna, which will act to filte out most of the multipath signal, while allowing the diect signal to pass though. This impovement in the diect to multipath signal gain is the eason why GPS antennas ae typically RCP. Using polaization alone to disciminate against multipath may not be sufficient to eliminate the multipath eo in ange measuements. Spatial divesity is anothe impotant means we can apply to futhe educe multipath contibution. Spatial divesity occus when the diect and multipath signal have diffeent AOAs. The diffeence in the AOAs makes it possible to devise spatial pocessing techniques that will act to educe the gain fom the diection of the multipath signal while inceasing the gain in the diection of the diect GPS signal. It is paticulaly useful fo those cases whee the path length diffeence between the diect and multipath signal is small. These ae pehaps the most difficult cases in multipath mitigation, since the paametic estimation of the diect path delay in such cases becomes ill-conditioned. In such a case, spatial divesity may be the only effective means of mitigating multipath. The main obstacle in employing spatial divesity is that the multipath AOA is not known and vaies fo a mobile platfom. Multipath AOA must be estimated fom the eceive input signal dynamically. The diect signal, which acts as an intefeence souce in this case, deceases the effective signal to intefeence atio fo the multipath signal and theefoe the accuacy of the multipath AOA estimation. One solution to this poblem is to use the CP aay to detect and estimate multipath. The CP antenna acts in the same way the RCP antenna did, except this time instead of educing the multipath elative to the diect signal, it educes the stength of the diect signal elative to the multipath. Thus, the CP potion of the dual ciculaly polaized aay weakens the diect signal, so we can obtain impoved estimates of the multipath AOA. The method pesented in this pape uses the CP channel inputs of a dual polaization antenna aay to estimate multipath AOA. The estimated multipath is then mitigated by applying spatial pocessing techniques to the input signal obtained fom the RCP channels. [7][18] have suggested multipath mitigation using both spatial pocessing and polaization discimination, but no details (methodology, algoithms, o esults) wee given theein. The only a pioi knowledge equied by this method is infomation typically available fom the ephemeis and the eceive tacking loop of the compounded diect and multipath signal. The ephemeis povides the appoximate AOA of the diect signal, while the tacking loop geneates appoximate code phase and caie efeence signal. In this pape, we apply this method to a simple signal model that contains a diect signal, a multipath signal, and andom channel noise. The methodology, howeve, is applicable to inputs that contain seveal multipath signals. The emaining pape is oganized as follows. Section establishes the signal model, mathematical notations, and the assumptions. Section 3 gives a detailed methodology desciption. Section 4 pesents simulation esults and the pefomance evaluation of this method. Section 5 summaizes the method and the findings as well as futue eseach in extending this method to moe geneal scenaios.. SIGA MOE, OTATIOS, A ASSUMPTIOS We conside an M element dual ciculaly polaized linea aay and a M-channel GPS eceive RF font end (see Fig.1). We assume the antenna elements ae isotopic antennas to simplify the mathematics. Factos such as mutual coupling, ealistic antenna element gain pattens and fequency 1

3 esponses, as well as possible antenna phase cente shift and channel biases among othes ae not taken into consideation hee. Most of these eo tems can be calibated out o estimated jointly, which we will addess in sepaate papes. caie efeence signal which will be used in the algoithm descibed in the following section. 3. METOOOGY A AGORITM Ou algoithm is based on the following 3-step algoithm: 1) etect the multipath signal in the CP input by coelating the CP channel signal with the tacking loop efeence signal. ) Estimate the multipath AOA fom Step 1. 3) Use the estimated multipath AOA and known diect signal AOA to pefom null-steeing on the RCP aay signal. S MP S In the emainde of this section, we discuss each of these steps in detail. Fig. 1 Schematics of the analysis scenaio We assume an input signal contains one diect GPS signal, a multipath signal, and andom white channel noise. We also assume that the GPS eceive RF font end outputs digitized baseband sample steams which can be conveted to complex signals containing I and Q channel samples pio to spatial pocessing. The RCP and CP channel signals at the k th sample (fo k=1, ) as: XR ( k ) = υ ( k ) S + κ R υmp ( k) + εr ( k ) (1) X( k ) = κ υ ( k) S + υmp ( k) + ε ( k ) In equation (1), the subscipts and R denote quantities associated with the RCP and CP channel inputs, while the subscipts MP and denote quantities associated with the multipath and diect signals, espectively. The S vectos efe to the steeing vectos of the souces; while the quantity υ epesents the time dependent potion of the signal (i.e. caie signal times the CA code). κ is a facto epesenting signal loss due to antenna polaization mismatch and eflection. Without loss of geneality and fo the sake of simplicity in analysis, we will use κ R = κ =.3 thoughout the pape. The andom channel signals, given by the quantities ε, will be modeled as independent and identically distibuted complex white Gaussian noise (CWG) that have unity vaiance and ae uncoelated both spatially and tempoally. We assume that the GPS eceive is aleady tacking the compounded input signal and that the eceive has knowledge of ephemeis, and theefoe, the appoximate diect signal AOA. The eceive tacking loop also povides the pompt code and 1) etecting the Multipath Signal in the CP Input. The CP signal has moe gain fo the multipath component than fo the diect signal. Ou goal is to manipulate them to estimate the multipath AOA. Since both the diect GPS signal and its multipath ae fa below the noise floo, signal detection will be pefomed fist. This can be achieved by coelating the aay signal, channel wise, with the known tacking loop pompt code and caie efeence. We denote the compounded signal tacking loop efeence sequence as ˆ (k). The coelated output, which we will denote by Y, can be easily expessed as: X ( k) ˆ* ( k ) = k = 1 Y () whee * epesents the complex conjugate opeation, and is numbe of samples used in the coelation opeation. Substituting the CP channel signal model in (1) into (), we can ewite Y as: Y = κ ρs + ρmp + η (3) whee * υ ( k ) ( k ) k MP ˆ = 1 ρ MP = * υ ( k ) ( k ) k ˆ = 1 ρ = * ( m, k ) ˆ ( k ) k 1 η ( m ) ε = = ( m = 1,..., M ) The inceased signal stength in Y can now be used to estimate multipath AOA. We would like to point out hee that using unit modulus efeence signal implies that η is a complex 13

4 nomal andom vecto with zeo mean and covaiance 1 Σ = IM (whee I M = M M identity matix). ) Multipath AOA Estimation. The main quantity used in estimating the multipath AOA is a beamfoming weight which has the following fom: P Sˆ MP = (4) Sˆ MPP Sˆ MP whee the supescipt denotes the complex conjugate of a vecto and hats on all vecto quantities denote estimates, not unit vectos. P is the pojection matix onto the subspace othogonal to S and ŜMP is an estimate fo the multipath steeing vecto. As long as Sˆ MP S, ŵ is well-defined. The method fo estimating the multipath AOA is based on the following poposition: = AgMax w Y E M w Χ / S Sˆ MP { } iff = and S We pesent the poof below: Poof: The backwads implication is a well-known esult that can be found elsewhee in the liteatue [4], so we pove just the fowads implication. et us assume the fom of Y given in equation (3) and the hypothesis of this poposition is tue. Since by constuction, ŵ is othogonal to S fo all allowed multipath steeing vecto estimates, it follows that: Y = ρmp + η (5) Futhemoe, because the matix P is both idempotent and emitian, it is easy to veify that ŵ is a unit vecto. This allows us to conclude that the noise tem educes to a single scala, e, which has the distibution CWG(,1/). This gives us the final expession: Y = ρmp S MP + e (6) Taking the expected value of the squaed nom, we find: 1 E ˆ w Y = ρ MP + (7) Fom which we see that Y E is maximized iff w ˆ S MP is maximized. If we conside the quantity w ˆ S MP, we note that it can be ewitten as: ˆ P = P (8) P ˆ P Since the facto P S MP is a fixed quantity, we see that w ˆ S MP is maximized when the backeted quantity on the RS of equation (8) is maximized. It is known [9] that unde the conditions stated in this poof that the tem inside the backet is an inne poduct, and hence, it satisfies the Cauchy-Schwaz inequality, which in ou case, can be witten in the fom: ˆ P 1 (9) P ˆ P This quantity is maximized when equality holds in the above elationship. But fom the Cauchy- Schwaz inequality, it is known that equality holds iff the estimated and tue multipath steeing vectos ae elated by a scala. Since the steeing vectos ae paametically defined as phase factos, this equies the two steeing vectos to be elated by a constant phase facto. QE The significance of this esult is that we now have a simple way to estimate the multipath AOA. If we pefom a gid seach ove the one dimensional space of possible multipath AOA values, constuct the steeing vecto fo each AOA, and then using the steeing vecto to constuct the weight ŵ accoding to (4), we can compute the value of the quantity Y w ˆ fo each multipath AOA. The pevious theoem tells us that the choice of the AOA with the lagest value of w ˆ Y will yield the tue multipath AOA. Figue shows a simulation esult fom a gid seach fo a five element UA. The solid cuve shows the esult of the gid seach when the input signal contains no noise. The maximum value of Y w ˆ occus exactly at the tue multipath AOA (within the gid esolution of.1 ). The black cuve 14

5 is geneated using the same signal except now andom channel noise is added. In this case, the (pecoelation) multipath SR is -8 db, and we see that the location of the maximum peak has an offset of about.6 o fom the tue AOA. Although the distibution of the AOA values emains unde investigation, we can pove that the estimato fo the maximum peak height is asymptotically unbiased and consistent. w Y Spectum o oise Spectum With oise Tue MP Oi = 33. Est MP Oi (w/o noise) = 33. Est MP Oi (w/ noise) = Tial MP AOA Fig.. Simulation esults demonstating the effectiveness of the multipath AOA estimato. It is impotant to point out hee that the gid seach involved in this method is not computationally intensive fo two easons. Fist, the seach is pefomed on post-coelation vectos whose size is limited by the aay dimension. Second, the multipath AOA estimation is intended fo the pupose of nullsteeing. As shown by the analysis in [4], the powe leakage due to an eo in the multipath AOA estimation is on the same ode as the poduct of the powe atio of multipath to diect signal and the squae of the AOA eo (in adians). This can be a seious poblem if we ae dealing with high powe intefeences. oweve, since the multipath signal is typically much weake than the diect signal, a coase gid seach of 1 gives an AOA estimation eo that will not significantly affect ou final null-steeing esult. It can be shown fo a linea aay of M elements, a gid seach with a esolution of Δ equies 7 M/ Δ multiplications fo the entie seach opeation, which is a easonable numbe in tems of computational cost. 3) ull-steeing on the RCP Channel Signal Using the Multipath AOA Using the multipath AOA estimation obtained with the CP aay input, we can fom the estimated multipath steeing vecto. Using this estimated multipath steeing vecto and known diect signal steeing vecto, we can now constuct the optimal null-steeing weight fo the RCP aay input: R = P MP S (1) whee PMP is the pojection matix onto the subspace othogonal to S MP. The final output signal that has the educed multipath contibution is: yr( k) = R XR ( k) (11) yr( k) = υ( k)( SPMPS ) + SPMPηR ( k) We pesent ou peliminay simulation esults on the above algoithm pefomance in the next section. 4. SIMUATIO RESUTS The main facto affecting the pefomance of the method pesented in Section 3 is the accuacy of the multipath AOA estimation. Theefoe, ou pincipal aim in this section will be to use simulations to evaluate the pefomance of the algoithm to estimate the multipath AOAs. We can bette undestand how the vaious signal paametes will affect the esults fom ou estimations by analyzing the quantity Y E used in the gid seach to estimate the multipath AOA. Fom equation (7), we notice that fo a fixed numbe of data points, Y E is effectively the poduct of two factos. The fist facto, ρ MP is a diect measue of the multipath post-coelated signal s stength (elative to the noise). If we use the fact that the coelation fo multipath signals close in time to the diect signal is a tent-function, then we can wite this facto as: δn ρ MP = PMP 1 (1) Δn whee P MP is the multipath signal s (input) powe, δn is the CA code offset between the multipath and efeence signal, and Δn is the numbe of data points in 1.5 chip lengths (which in ou system, tuns out to be 7). The second facto, w ˆ S MP, is a diect measue of how close the multipath and diect souce steeing vectos ae. To deive the elationship that shows this, we note that simila to the inne poduct defined in the pevious poof, we can also define the following diection cosine: S S cos γ = = (13) ( S )( ) M MP SS If we now conside the quantity of inteest, we find it can be expessed in tems of this diection cosine as follows: 15

6 P = = S P (14) P MP The pojection matix can be expessed as: 1 P IM M S S = (15) Substituting fo P into equation (14) 1 = M S (16.a) M and use of equation (13) gives us: w ˆ = M M cos γ (16.b) S MP efining sinγ as 1 cos γ, it thus follows that: w ˆ = M sin γ (16.c) S MP Combining both factos now, we see that the pincipal quantity of inteest can be expessed totally in tems of the signal paametes on which it depends as: δ ˆ n E w Y M P = MP 1 sin γ (17) Δn This esult gives a simple expession that shows how the polaization divesity (which hee is given by the net multipath powe obtainable fom the aay, M P MP ), the time divesity (given by the squae of the tent function), and the spatial divesity (given by the sin γ tem) affect the quantity fom which the multipath AOA is estimated. We conducted a seies of simulations to analyze the impact of these factos on the multipath AOA estimato. These simulations wee caied out with a 5 element UA. The SR of the diect and multipath signals ae -18dB and -3dB, espectively. The eceive RF font end sampling fequency is 5 Mz and msec data (1 GPS data bit) o 1K samples ae used in analysis. A vaiable in the simulations is the CA code offset between the diect and multipath signal. Given the sampling fequency, thee ae 7 samples in 1.5 CA code chip lengths (which is typically the ange in the time delay whee the effects of multipath ae most significant). We allow the CA code offset to vay fom to 3 samples. Fo ease of analysis, we will only investigate the scenaio in which the path length diffeence between the diect signal and multipath signal is independent of thei AOAs. With this consideation, we can compute the phase diffeence between the two signals using the path length diffeence. All simulations ae pefomed using 5 Monte-Calo uns. Because we shall efe to the angles of aival of the diect and multipath signals thoughout this analysis, we shall intoduce the notation fo these quantities as θ and θ MP, espectively. As equation (17) pedicts, we will see that the two majo factos affecting the quality of the multipath AOA estimates will be the time delay between the efeence and multipath signal and the elative oientations of the diect and multipath steeing vectos. In ou fist simulation, we let the time delay between the diect signal and multipath to be. We choose 3 diffeent diect signal AOAs at 1, 4, and 7 elative to the aay axis, espectively. We computed the accuacy of thei multipath AOA estimation fo all θ MP in the to 9 o ange (in incements). Fig. 3 plots the multipath AOA estimation eo as a function of θ MP. One immediately can see that the multipath AOA estimation eo is lagest when θ MP and θ ae close to each othe. Also notice that when θ is 4 and 7, even the lagest multipath AOA estimation has only small deviations on the ode of the gid seach esolution (of 1 ) fom the tue AOA. In the case whee θ =1, howeve, the deviation is ponounced when the diect signal and multipath AOA ae close. This demonstates that multipath AOA estimation is moe eo pone fo low elevation incidence. Avg AOA - Tue AOA iect AOA= Tue MP AOA (degs) Fig.3 Simulate multipath AOA estimation eo as a function of tue multipath AOA fo thee diffeent diect signal AOAs. A second obsevation we see fom Figue 3 is that the multipath AOA estimation eo inceases as θ MP appoaches zeo. This esult is an atifact of the gid seach method. As θ MP appoaches zeo, the gid seach function about θ MP flattens out as shown in figue 4. To validate this agument, we plot the gid functions fo a multipath souce with a fixed AOA of 5 o, fo thee diffeent θ values of o, 5 o, and 8 o, espectively. Figue 4 shows that fo all thee θ values, the multipath AOA estimato is flat in the vicinity of the tue multipath AOA (at 5 o ). otice that the flatness is indeed affected by θ : as it

7 incease, the extent ove which the peak is flat deceases. Peak eight x 1-3 Tue Multipath AOA at 5 iect AOA = iect AOA = 5 iect AOA = Tial MP AOA (degs) Fig.4 Multipath AOA estimato as a function of tue multipath AOA fo thee diffeent θ values. The standad deviation of the multipath AOA eo follows a simila tend. The top panel of Figue 5 shows that except fo the case when the diect and multipath AOAs ae both vey small, the standad deviation is acceptably low fo all multipath AOA estimation if θ - θ MP > 5. The lowe panel of Figue 5 is geneated to illustate the oigin of the standad deviation. Fo each of the thee diect signal AOAs, we plot sin γ as a function of the θ MP, whee γ is angle between the diect and multipath steeing vectos. As we showed peviously, the tem sin γ captues all of the multipath and diect signal AOA dependence in the multipath AOA estimato. When the multipath AOA is close to that of the diect souce, sin γ monotonically goes to zeo as θ MP θ. σ sin (γ) 3 1 Standad eviation of MP AOA Tue MP AOA 1.5 Poximity S and S MP ealy ealy iect AOA = 1 iect AOA = 4 iect AOA = Tue MP AOA Fig. 5 Multipath AOA estimation standad deviation as a function of tue multipath AOA fo thee diffeent θ values. As a consequence, when null-steeing is applied to the diect souce, an inceasingly lage potion of the multipath is also emoved. This effectively educes the multipath signal stength, which, in tun, leads to a lage standad deviation in the multipath AOA estimation. The above simulation esults imply that when two signals that ae eplicas of each othe and when they occu close in both time and space, it is difficult to selectively emove just one of them o estimate a specific signal s paametes. This should not come as a supise. If a multipath and its diect countepat have a lage time delay, the multipath AOA estimation will have lage eo. This is because mismatch between the efeence and the multipath signal will be moe seve, leading to a loss in the effective postcoelation multipath signal stength. Figue 6 compaes the eo and standad deviation fo two scenaios whee the multipath and diect signal time delay is half a code chip and espectively. The esults indicate that as long as θ - θ MP > 5, the multipath AOA estimation is acceptable. Bias σ Affect of CA Code Offset on Bias θ =1 δn= θ =1 δ n=3 θ =4 δn = θ =4 δn =3 θ =7 δn = theta =7 δn = Tue MP AOA 3 1 Affect of CA Code Offset on Standad eviation Tue MP AOA Fig. 6 Multipath AOA estimation eo and standad deviation dependency on the delay time between diect and multipath signal. A final simulation is pefomed to validate the effectiveness of the multipath mitigation algoithm by examining the diect signal coelato output which diectly impacts the ange measuement accuacy. Figue 7 is a schematic of the diect signal and multipath used in the simulation. The diect signal elevation is 75 o while the multipath AOA is 1 o. The time delay between the two signals is.4 17

8 sample intevals. Figue 8 shows two coelato outputs. The black cuve is geneated using the oiginal input while the ed cuve is poduced using the output afte applying the multipath mitigation algoithm pesented in this pape. The effect of multipath mitigation on the RCP antenna input is evident. SR = -18 db 5º ( φ, θ ) ( 3,5) ( φ, θ M M) ( 113,8) SR = - db 183 m 1º = γ = 94 = 18 m 33 m delay = 145 m δ n =.4 Fig. 7 Schematic of a simulation scenaio Coelation Befoe Afte δ n Fig. 8 Compaison of coelato output befoe and afte multipath emoval 5. COCUSIOS A FUTURE WORKS This pape pesented a GPS multipath mitigation method that utilizes a dual cicula polaized antenna aay and a multichannel GPS eceive. The CP aay input was used to detect and estimate the multipath signal AOA. Using the estimated multipath AOA and known diect signal AOA, nullsteeing was applied to the RCP aay input to minimize multipath contibution. This method theefoe takes full advantage of both spatial and polaization divesity of the diect signal and multipath signal. The pape povided mathematical poofs fo the method and detailed algoithms. Simulations wee pefomed to evaluate the effectiveness of the method fo the simple scenaio involving one diect signal, one multipath, and andom channel noises. A unifom linea aay with ideal and isotopic antenna elements wee assumed in the analysis and simulation. The esults showed that the multipath AOA estimato poduces negligible eo and standad deviation if θ - θ MP > 5 and that the diect signal AOA is not nea o. The esults also showed that longe time delay between the diect and multipath signal inceases multipath AOA estimation eo but this incease is toleable. Finally, we demonstated that the multipath mitigation technique does poduce impoved eceive coelato function which diectly impacts the GPS code ange measuement accuacy. Thee ae a numbe of issues that ae wothy of continued studies. Fist, although the simulation is pefomed fo an UA with idealized antenna element and a simple signal model containing only one diect signal and multipath, the basic idea should apply to aay and multiple multipath signals in input. Second, we have deived an optimized beam foming weight that minimizes multipath contibution to the RCP input and povides an altenative means to the null-steeing appoach used in this pape. The advantage of this optimization appoach is that it eliminates the need fo the gid seach opeation we pesented in this pape. We plan to cay out moe in-depth study on the pefomance of the optimization method. Thid, the impact of mutual coupling and othe mismatching factos on the pefomance of the method needs to be investigated. ACKOWEGEMET: This poject is funded by AFOSR gant # FA REFERECES: [1] Baasch, M., Multipath effects, in Global Positioning System: Theoy and Applications, edited by Pakingson B. W. and Spilke J. J. J., AIAA Publishe, vol. 1, Chp.14, pp , [] Counselman, C. C., Aay antennas fo GPS, Poc. IEEE PAS, pp , Palm Spings, CO, Ap [3] Fante R.. and J. J. Vaccao, Evaluation and eduction of multipath-induced bias on GPS time-of-aival, IEEE Tans. Aeo. Elec. Sys., vol.39, pp , 3. [4] Fiedlande B. and B. Poat. Pefomance analysis of a null-steeing algoithm, IEEE Tans. Acoustics, Speech and Signal Pocessing, Vol. 37, o. 4, pp , [5] Geenspan, R., A. g, J. Pzyjemski, and J. Veale, Accuacy of elative positioning by intefeomety with econstucted caie GPS: expeimental esults, Poc. 3 d Int. Geodetic Sym. Satellite opple Positionining, pp , as Cuces, M, Feb

9 [6] achapelle, G., W. Falkenbeg,. eufeldt, and P. Keilland, Maine GPS using code and caie in a multipath envionment, Poc. IO- GPS, pp , Coloado Sping, CO., Sept [7] Manandha,., R. Shibasaki, P. omak, GPS signal analysis using CP/RCP antenna and softwae GPS eceive, Poc. IO-GSS, ong Beach, CA, Sept. 4. [8] Moelke,., Multipath antennas fo advanced GSS multipath mitigation and multipath diection finding, Poc. IO-GPS, pp , Kansas City, KS, Sept [9] Otgea, J.M., Matix Theoy: a Second Couse The Univesity Seies in Mathematics, Plenum Pess, Y and ondon, [1] Raquet, J. and G. achapelle, etemination and eduction of GPS efeence station multipath using multiple eceives, Poc. IO-GPS, pp , Kansas City, KS, Sept [11] Ray, J. K., Use of multiple antennas to mitigate caie phse multipath in efeence stations, Poc. IO-GPS, pp , ashville, T, Sept [1] Seco, G. and J. Fenadez-Rubio, Aay signal pocessing techniques fo pseudoange and caie phase measuement, Poc. nd Euopean Symp. GSS, pp. -3, vol.ix-p-1, [13] Steingass, A. and ehne, A., avigation in multipath envionments fo sububan applications, Poc. IO GSS, Ft. Woth, TX, Sept. 7. [14] Townsent, B. and P. Fenton, A pactical appoach to the eduction of pseudoange multipath eos in a 1 GPS eceive, Poc. IO-GPS, pp , Salt ake City, UT, Sept [15] Tanquilla, J. and J. Ca, GPS multipath field obsevations at land and wate sites, avigation, vol.37, pp , [16] Van ieendonck, A. J., P. Fenton, and T. Fod, Theoy and pefomance of naow coelato technology in GPS eceive, avigation, vol.39, pp , 199. [17] Van ee, R., Multipath and Multi-tansmitte Intefeence in Spead-Spectum Communication and avigation Systems, elft Univesity Pess, elft, the ethelands, [18] Yang, C. and A. Pote, GPS multipath estimation and mitigation via polaization sensing divesity : paallel iteative coss cancellation, Poc. IO-GSS, ong Beach, CA, pp , 5, Sept. 5, [19] Zhang, Y. and C. Batone, Multipath mitigation in the fequency domain, Poc. IEEE PAS, pp , Monteey, CA, Apil 4. 19