referring now to fig1 a specific embodiment of a gps receiver system 10 is shown . the system 10 includes an antenna array 12 having plurality of antenna elements 14 , where the components comprising each antenna &# 34 ; leg portion &# 34 ; 15 are substantially identical . in the illustrated embodiment , each antenna element 14 is coupled to a front - end amplifier 16 , the output of which is supplied to a down - converter 18 to convert the signal to an intermediate frequency for processing . each down - converted signal is supplied to weighting circuitry or a &# 34 ; weight &# 34 ; 20 that multiplies the signal by a complex weight value ( having real and imaginary portions ). the outputs of all of the weighting circuits 20 are coupled to a summing circuit 22 , as shown . the term &# 34 ; weight ,&# 34 ; &# 34 ; weight value ,&# 34 ; and &# 34 ; weighting circuit &# 34 ; are used interchangeably . in the illustrated embodiment of fig1 the sum of the signals is then coupled to a power detector circuit 24 and is also supplied to a gps receiver 26 . the output of the power detector circuit 24 is then converted to a digital signal by an analog to digital converter 28 . the digital signal is then processed by an adaptive algorithm ( described hereinafter ) under control of a microprocessor or other suitable computer or processor 30 . alternately , dedicated or discrete hardware circuitry may be used in place of the microprocessor 30 . in the illustrated embodiment of fig1 the microprocessor 30 adjusts the values of the weight values for each antenna element 14 and iteratively processes the digital signal attempting to constantly improve the signal received by the gps receiver 26 . additionally , navigational data , such as data provided by an inertial navigation system ( ins or nav system ) 32 may be utilized by the adaptive algorithm under control of the microprocessor 30 . typically , a wide - band front - end filter is coupled between the antenna 14 and the amplifier 16 . however , its placement may differ from the specific embodiment of fig1 and may not be included in all embodiments . in the illustrated embodiment of fig1 only a single set of weights 20 is required . one weight 20 corresponds to one antenna element 14 . therefore , the single set of weights corresponds to the array 12 of antenna elements 14 , which is optimized for all of the gps satellites . the nav system 32 provides information with respect to the position and / or orientation of the receiver ( the antenna array of the receiver ) which permits the system 10 to solve for the gain of the received gps signal in the direction of each satellite . in the embodiment of fig1 one set of weights 20 in combination with the nav data is used to optimize the average signal to noise ratio ( snr ). accordingly , the gain of the received gps signal is increased . to perform this optimization of the snr in the embodiment of fig1 the total power received by the antenna array 12 is divided by the measurement bandwidth to obtain a &# 34 ; noise floor .&# 34 ; using the positional information provided by the nav system 32 , the gain in the direction of the satellite may be obtained . this value can then be used as the criteria for increasing the snr by adjusting the value of the weights 20 via an adaptive algorithm , such as a &# 34 ; hill climbing &# 34 ; algorithm . therefore , instead of merely reducing the total power received , as is done in known power minimization techniques , the present invention adjusts the weights 20 to maximize the snr , meaning that the signal strength of the received gps signal is boosted , while simultaneously minimizing the jamming signal . because each antenna element 14 is part of the antenna array 12 , each element has a different carrier phase due to its relative position with respect to each satellite . gps receiver systems utilizing an antenna array 12 are useful for nulling the effects of broad band jamming signals . in some situations , multiple jammer signals may be present . to null - out &# 34 ; n &# 34 ; number of different jammer signals , &# 34 ; n + 1 &# 34 ; individual antenna elements 14 are utilized . for example , four antenna elements 14 are used to effectively null - out three jammer signals . the gps signal is &# 34 ; buried &# 34 ; in the background noise . one aspect of the present invention utilizes the fact that the gps signal is extremely weak relative to the strength of the jammer signal . additionally , the jamming signal typically emanates from a different direction than that of the gps signal . often , the gps signal is transmitted from a satellite that is relatively &# 34 ; high &# 34 ; in sky , while the jamming signal is transmitted from a tower or mobile vehicle located on the ground . hence , the signals arrive from different directions . of course , if the jamming signal emanates from an airborne platform and is at the same relative position as that of the satellite , no difference in the angle of arrival between the gps signal and the jammer signal would be seen , and nulling would be very difficult . however , this is a rare occurrence and would only be temporary . as described above , the illustrated embodiment of the system 10 of fig1 utilizes a single set of weights 20 for the entire antenna array 12 . for each antenna element 14 , processing the signal in accordance with the weight 20 causes the phase and / or amplitude of the received signal to be modified in an attempt to &# 34 ; steer &# 34 ; a null in the direction of the jamming signal to reduce its received signal strength , while simultaneously increasing the gain of the received signal in the direction of the gps satellite . referring now to fig2 there is illustrated an example of an implementation of the above - described process for an analog gps system . the illustrated specific example is generally referred to as a &# 34 ; hill - climbing &# 34 ; method . however , other methods in addition to &# 34 ; hill - climbing &# 34 ; methods may be used ( including but not limited to such known techniques as matrix inversion , which may be used in digital gps systems ). the process begins , as shown at a step 100 . first , an initial set of weight values is selected as a starting point , as shown at a step 102 . for example , a weight of &# 34 ; 1 &# 34 ; may be selected which provides no phase shift and no modification in amplitude . of course , any weight may be used as an initial starting point . as shown in a step 104 , a power level p coming out of the antenna array is measured . this is the measured power contributed by each antenna element as it is modified by whatever weight value is implemented . the output of each antenna element is summed and routed to power detecting circuitry , as is shown in fig1 . the power level term p in the illustrated example is preferably divided by the measurement bandwidth bw , for example , a 20 mhz bandwidth . thus , p / bw provides the &# 34 ; noise floor &# 34 ; term referred to as n 0 measured in watts per hertz . this represents a background noise level and includes the transmitted satellite signals in addition to any jammer signals which may be present . the following equation governs : using the information with respect to the satellite locations and the orientation of the receiving platform supplied by the nav system , in addition to knowing the value of the weights , the gain g of the antenna array as a whole , in the direction of each satellite is obtained , as shown in a step 106 . accordingly , the gain g of the antenna array as a whole is obtained , as is known in the art using conventional methods . next , an estimate of the received satellite signal power sp at the input of the antenna array is calculated , as shown in a step 108 . the gps satellites are known to provide a worst - case signal power level of about - 163 dbw on the surface of the earth . however , this level may increase depending upon the elevation of the satellite relative to the receiver ( antenna array ). depending upon the elevation angle of the satellite , which is known via the nav system and almanac data , the satellite signal power sp is estimated . the value of sp may , for example , may range from about - 163 dbw to - 150 dbw . equation 2 : snr α c / n 0 , where c is the signal power at the output of the antenna array . given equation 2 above , and using the estimated satellite power sp , the signal to noise ratio ( snr ) corresponding to each satellite is obtained , where ( snr ) α ( c / n 0 ) and c α ( g * sp ), as shown in a step 110 . the terms are proportional to each other , related by bandwidth . this value is calculated for each satellite because the value of gain g corresponds to a specific satellite . the term &# 34 ; snr &# 34 ; is used interchangeably with the term &# 34 ; c / n 0 &# 34 ; although the two terms are not necessarily equal to each other , but rather , proportional to each other . and solving for the value of snr yields equation 4 below : next , as shown in a step 111 , the average snr is calculated by summing the calculated snr values for each satellite and dividing the total by the number of satellites . in a step 112 , the average snr is compared to the previous average snr value found , assuming that the above process has been iteratively repeated . of course , in the first iteration of the above - described steps , no prior average snr value will exist . the goal is to adjust the weights to obtain the highest value of the average snr . the weights are adjusted according to a predetermined pattern to obtain the best possible value of the average snr . if the present adjustment to the weight value causes an improvement in the average snr value relative to the previous weight values , then adjustment of the weight value continues in that direction according to the predetermined pattern , as shown in a step 118 . if the present adjustment to the weight value causes an degradation in the average snr value relative to the previous weight value , then adjustment of the weight proceeds in the opposite direction with the same weight , as shown in a step 120 . alternately , rather than proceeding in the opposite direction as shown in the step 120 , the next weight may be selected for adjustment . this process is repeated so that all weight values are optimized . the process branches back to the step 104 so that the steps 104 through 120 are continuously repeated to obtain the best possible average snr values . the processes shown in the steps 118 and 120 where the weight adjustment &# 34 ; scheme &# 34 ; is adjusted may be implemented , for example , by using a coarse step adjustment followed by a fine step adjustment . in this approach , adjustment of the weight is initially performed using a coarse step size to obtain the best possible snr measurement of all of the possible coarse steps available . once the best coarse step is obtained , fine tuning may be performed using small step sizes within the coarse step . this prevents &# 34 ; falling &# 34 ; into a localized minimum or maximum . referring now to fig3 - 12 the histograms show comparisons of the signal to noise ratio ( c / n 0 ) for a specific satellite geometry that includes for example , four satellites and two jammers . with respect to calculating the data points comprising the histograms , the following assumptions have been made : 4 . the sum of the thermal noise and the antenna noise at each element is equal to - 202 dbw / hz . 5 . the signal strength of the gps received signal is - 163 dbw . 8 . the satellites and the jammers are placed randomly over a +/- 86 ° angle in azimuth and elevation . 9 . the antenna array is perfectly calibrated and the estimates of received signals are perfectly accurate . referring now to fig3 - 5 , the histograms show the difference between the signal to noise ratio ( snr ) achieved using a known power minimization algorithm compared to the snr achieved using the present beam forming approach described above . the top frame of each of the figures are obtained on a satellite by satellite basis , while the bottom frame of each of the figures is obtained based on the average of the four satellites in each geometry . as shown , the present beam forming approach is significantly superior to the known power minimization or simple null steering techniques . referring now to fig6 - 8 , the histograms shown in the figures illustrate the advantages of the present beam forming technique ( using multiple antenna elements ) and power minimization or null steering techniques ( using multiple antenna elements ), compared to a single element antenna obtained on a per satellite basis . of course , the amount of benefit obtained depends on the amount of jamming that is present . this is to be expected because the strength of the present spatial nulling technique is based on steering nulls in the direction of the jammer signals , rather than nulling thermal noise . when jamming signal levels are low , use of known power minimization techniques are detrimental to the signal to noise ratio , and such techniques should not be used . in contrast , the present beam forming technique provides an improvement over the full range of jamming signal strengths . referring now to fig9 - 11 , the histograms show the improvement in the average signal to noise ratio over a single element antenna for the beam forming and for known power minimization techniques . as shown in the figures , known power minimization techniques disadvantageously permit the signal to noise ratio to drop to a level lower than it would normally be when using a single element antenna . this occurs when jamming levels are low . as shown in the histograms , the present beam forming technique does not permit this anomaly to occur . note that fig3 - 11 involve matrix inversion techniques for both power minimization and beam forming techniques . referring now to fig1 , the histograms show the difference in signal to noise ratio levels between a matrix inversion approach and a hill climbing approach . the top frame of the figure represents a per satellite approach while the bottom frame of the figure represents an average of four satellites in each geometry . referring now to fig1 , the histogram illustrates the improvement in signal to noise ratio using the matrix inversion technique and the hill climbing technique over a single element antenna , on a per satellite basis . referring now to fig1 , the histogram shows the improvement in signal to noise ratio using the matrix inversion technique and the hill climbing technique over a single element antenna based on the average of the four satellites in each geometry . as shown in the above figures , use of the hill climbing technique in the present inventive method typically attains results within three to five decibels of an optimal level . occasionally , the hill climbing technique may be come &# 34 ; stuck &# 34 ; at a local maximum . however , in practice , the hill climbing technique does not terminate , and changing conditions would obviate this problem by overcoming the local maximum condition . specific embodiments of a method and apparatus for reducing jamming using beam forming with navigational data according to the present invention have been described for the purpose of illustrating the manner in which the invention may be made and used . it should be understood that implementation of other variations and modifications of the invention and its various aspects will be apparent to those skilled in the art , and that the invention is not limited by the specific embodiments described . it is therefore contemplated to cover by the present invention any and all modifications , variations , or equivalents that fall within the true spirit and scope of the basic underlying principles disclosed and claimed herein .