[18] Malmström, J., Robust Navigation with GPS/INS and Adaptive Beamforming, FOI-R--0848âSE, April. 2003. [19] L. Pettersson, âWBBF: A Simulation Tool for.
INS/GPS Integration with Adaptive Beamforming F. Berefelt, B. Boberg, F. Eklöf, J. Malmström, L. Pääjärvi, P. Strömbäck, S.-L. Wirkander Swedish Defence Research Agency (FOI)
BIOGRAPHY
ABSTRACT
F. Berefelt is a Research Officer with the division of Defence Analysis at FOI. His research interests include mathematical analysis and modeling. He holds a B.A. in philosophy from the University of Stockholm and a M.Sc. in mathematical physics from the Royal Institute of Technology in Stockholm.
The Swedish Armed Forces are evolving towards a Network Based Defense (NBD) where accurate position and timing information will be essential. One important capability in NBD is to use, as well as counteract, longrange precision weapons. To simulate and assess the performance of different robust navigation system realizations and countermeasures in various navigation warfare scenarios, a simulation environment is being developed. In this paper we focus on a long-range precision engagement scenario where an aerial platform is navigating towards a stationary target. The proposed navigation system consists of a tightly coupled INS/GPS where measurements are integrated by means of an Extended Kalman Filter (EKF). The INS/GPS is also integrated with an adaptive beamforming antenna array. The target is protected by multiple airborne low-power mini-jammers and a high-power ground based jammer. All jammers are wideband Gaussian noise jammers. Three different beamforming algorithms, Minimum Variance (MV), Linearly Constrained Minimum Variance (LCMV) and Multi-target LCMV (MT-LCMV), from the class of power minimization algorithms are investigated, two of which are direction-constrained. Navigation accuracy in terms of mean position error over the flight path and position error at the end-point is presented for the beamforming algorithms and different antenna array configurations. The system employing the MT-LCMV beamforming algorithm proved to be the most promising, in terms of position error, for navigation warfare scenarios.
B. Boberg is a Research Officer with the division of Systems Technology at FOI. His research interests consist in Navigation, Estimation and Robotics. He holds a M.Sc degree in Applied Physics and E.E. and a D. Eng. degree in Robotics from Linköping Institute of Technology. F. Eklöf is a Research Engineer with the division of Command and Control Systems at FOI. His main research focus is on robust adaptive beamforming for military applications. He holds a M.Sc. degree in Physics from Linköping Institute of Technology. J. Malmström holds a M. Sc. in E.E. from the Royal Institute of Technology in Stockholm. His Master thesis project was done at FOI in the area of robust navigation and adaptive beamforming. L. Pääjärvi is a Research Engineer with the division of Command and Control Systems at FOI. His research interests include robust communication and navigation systems. He holds a M.Sc. degree in E.E. from Luleå University of Technology. P. Strömbäck received his M. Sc. in E.E. from the Royal Institute of Technology in Stockholm. He is currently conducting reasearch in robust navigation at the division of Systems Technology, FOI. S.-L. Wirkander is a Research Officer with the division of Systems Technology at FOI. His research interests consist in Navigation, Estimation and Robotics. He holds a M.Sc degree in E.E from Chalmers University of Technology and a M.E. from Columbia University.
1. INTRODUCTION The Swedish Armed Forces are evolving towards a Network Based Defense (NBD), [10], where accurate position- and timing information will be essential. High precision military efforts are required and to achieve this, situational awareness is needed. By seamlessly interconnecting communication systems the situational awareness from the commander down to the soldier will be increased. Time synchronization of the constituent
communication systems and position of own units are crucial for the success of NBD. Also required in NBD is the use of long-range precision weapons and the capability to counteract such weapons. Precise position and time can be provided by a GNSS system such as GPS or the coming Galileo system. However, it is well known that GNSS systems are vulnerable to RF interference and this fact becomes even more severe in military scenarios where the receivers are likely to be exposed to jamming. For GNSS systems to function in a harsh environment robustness measures, e.g. inertial aiding and beamforming, must be taken. Today it is common practice to combine INS and GPS, resulting in robust navigation systems. This is treated in [1], [9], [11], and [21], where a number of different filtering techniques are considered. The main drawback with such integration is that in a severe jamming scenario, when the GPS is jammed, the navigation system must entirely rely on the INS. This results in an unlimited position error growth where the error rate is determined by the Inertial Measurement Unit (IMU) performance. In [9] the estimation error growth rate is investigated for different number of Kalman filter states. Due to the unbounded error growth of the INS it is important to get as close to the target as possible before the GPS is jammed. In many cases INS/GPS integrations does not provide sufficient accuracy and additional interference mitigation techniques are necessary. There have been significant efforts in developing interference mitigation techniques for GPS. An overview of potential interference sources and mitigation techniques is given in [15]. Filtering techniques can alleviate many narrowband interference and jamming concerns of GPS. In the case of wideband Gaussian jammers, beamforming is probably the only technique that provides significant immunity [3], [4], and [14]. In [8] and [13] system implementations where the INS/GPS is integrated with adaptive beamforming, to further increase the robustness of the system, are discussed. In [8] a high-fidelity simulation environment under development, resembling the one presented in this paper, is discussed. Their GPS is aided by, but not tightly coupled to, the INS. In [13] two conceptual integration methods of a navigation receiver with adaptive beamforming are discussed, one of which is the integration implemented and tested in this paper. The above two papers report work under progress and so far no performance results of the navigation systems have been given. To simulate and assess the performance of different navigation system realizations and countermeasures in military scenarios, a general simulation environment is being developed, [18]. The simulation model is implemented in a top-down manner to capture the most general trends, i.e., the constituent blocks of the
simulation model have been implemented relatively coarsely and will successively be refined. The refinement process has already started and some parts of the model are more detailed than others. In this work we focus on a long-range precision engagement scenario where an aerial platform is navigating towards a predefined target. The target is protected by multiple airborne low-power jammers, as well as a ground-based high-power jammer. All jammers are wideband Gaussian noise jammers. This scenario is interesting both from an offensive and a defensive perspective. The navigation system chosen for the aerial platform is a tightly coupled INS/GPS system employing an adaptive beamforming antenna array for jamming protection. Results are presented as the following navigation performance measures: number of satellites available to GPS receiver, position error at target, i.e. miss distance, and mean position error over the flight path. The measures are obtained for different antenna array configurations and different types of beamforming algorithms. Other parameters also affecting the results of the simulation, but not varied here, are: number, type, power and position of the jammers, flight path, antenna element type, type of navigation filter, atmospheric disturbances, platform speed, etc. In section 2, Robust Navigation System, a high-level scheme of the system is given. In section 3, Robust Navigation System Model, the simulation environment is described in detail. In section 4, Scenario Description, the investigated scenario is given. Simulation results are presented in section 5 and the pros and cons of the robust navigation system are discussed in section 6. Finally, in section 7 conclusions are presented. 2. ROBUST NAVIGATION SYSTEM This section describes the INS/GPS coupling and the adaptive beamforming antenna array system. The proposed robust navigation system is shown in Figure 1.
Figure 1. Overview of the proposed robust navigation system, consisting of three integrated subsystems: adaptive beamforming, GPS, and navigation filter.
Inputs to the system are signals generated from the scenario. The adaptive beamforming block discriminates between the jammer signals and the GPS signals, based on the available a priori information, and suppresses the jammer signals. The spatially filtered signals are then forwarded to the GPS receiver, which calculates the pseudoranges. The navigation filter uses the GPS pseudoranges and the output from the IMU, containing gyro and accelerometer data, to calculate a navigation solution. INS/GPS coupling In an inertial navigation system (INS), sensed accelerations and angular rates from an IMU are transformed into position, velocity and attitude by solving a set of differential equations. It is a self-contained system in the sense that it does not depend on any externally propagating signals. It is very accurate for short periods of time, but the accumulation of noise and sensor errors makes the navigation error grow without bounds. GPS on the other hand delivers positions with relatively low accuracy but with a bounded error. INS and GPS have complementary properties and are therefore well suited for integration. There are different modes of integration, depending on the degree to which the data processing is fused [11]. In this work, a tightly coupled INS/GPS system has been implemented. This means primarily that GPS pseudoranges are used as inputs to the navigation filter rather than computed GPS positions. This eliminates the Kalman filter in the GPS receiver and the need for an ad hoc process model for the vehicle dynamics, which is less accurate in highly dynamic situations. Various error states related to both the IMU and GPS may be estimated and treated on an equal footing. The great advantage is the optimal utilization of all available information, even when less than four satellites are being tracked. Adaptive Beamforming for GPS Adaptive beamforming is a key technique for suppression of jammer signals or other interfering signals. Beamforming is effective and probably the only method to suppress wideband Gaussian jammers [3], [4], and [14]. A common approach to prevent the degradation due to large bandwidths is to employ tapped-delay-lines (TDL) behind the antenna elements, and perform spatio-temporal processing on the received data [23]. As a rule of thumb, for beamforming a signal can be considered narrowband if the relative bandwidth is less than 1-2%. This is a borderline case for the P-coded signal but for the C/Acoded signal narrowband adaptive beamforming is in general sufficient. In the literature a vast amount of adaptive beamforming algorithms have been presented, see for instance [16] and [22]. The algorithms can be classified into three classes depending on the a priori information they utilize to discriminate between GPS
signal, and jammer and interference signals. The three classes of beamforming algorithms are: reference signal based, blind, and direction based. Direction based algorithms uses information of the direction from which the desired signals, and sometimes the jamming signal, are incident on the antenna array (direction of arrival, DOA) [22]. If the position, attitude of the platform and GPS time are known, the DOA of a satellite signal can easily be calculated. Consequently, when integrating INS/GPS with adaptive beamforming, direction based algorithms seem as a good choice. In this paper two versions of a well-known direction based beamforming algorithm as well as one blind algorithm, all based on power minimization, will be employed. The algorithms have previously been proposed for GPS applications in [24] and are described below. The linearly constrained minimum variance adaptive beamforming algorithm minimizes the output power after beamforming, min w H Rw ,
(1)
w
subject to certain constraints, SH w = c ,
(2)
[3], [6], and [22], where w is the weight vector and R is the covariance matrix, c is a vector containing the constraints and S contains the array response vectors for the directions of the constraints. R contains the covariance between the received data on the different antenna elements. The main purpose of the constraints is to ensure that the GPS signals are not suppressed. The weight vector that minimizes the output power is given by w = R −1S ( S H R −1S ) c . −1
(3)
In the GPS system multiple GPS satellite signals have to be received simultaneously. This may be implemented by setting c in equation (3) to be a vector containing the constraints in the direction towards each satellite. When multiple constraints are used this will be denoted Linearly Constrained Minimum Variance (LCMV). The LCMV algorithm requires the DOA of the GPS signals in order to set the direction constraints. This algorithm has the disadvantage that at least four constraints have to be set to track four satellites. The ability of the algorithm to suppress jammers is reduced with increasing number of constraints. For a two dimensional case the number of jammer signals possible to suppress is N jam = N el - N GPS ,
(4)
where Nel is the number of elements in the antenna array and NGPS is the number of tracked satellites. If the DOA of the GPS signals cannot be determined with sufficient accuracy, or are not available, an alternative approach is necessary. The received power of the GPS
signals are well below the noise level and the jammer signals are assumed to be several times stronger than the GPS signals. Therefore, it is possible to minimize the received power without a direction constraint. To avoid the trivial solution w = 0, a constraint is used to set the gain on a reference element to one [7], δH w = 1 ,
(5)
where δ is the Nx1 vector, δ = [1 0 … 0]T. The weight vector is given by w MV = R −1δ ( δ H R −1δ ) . −1
(6)
This algorithm is also linearly constrained but requires no DOA information of the GPS signals in order to minimize the power. The algorithm will be denoted Minimum Variance (MV), to distinguish it from the direction constrained LCMV described earlier. The disadvantage with the MV algorithm is that a GPS signal may be suppressed if the difference between the angles of arrival of a SOI and a jammer is small. Also, this algorithm will distort the phase of the GPS signal if not compensated for properly. For the same number of antenna elements the MV algorithm can theoretically suppress more jammers than the LCMV algorithm, in the two dimensional case, since only one degree of freedom is used, N jam = N el -1 .
(7)
The two algorithms, LCMV and MV, are implemented as Nel number of analog receiving channels and A/D converters. A digital beamforming unit (beamformer) calculates the weight vector and filters the digitized signal. To avoid that the number of suppressed jammer signals is reduced while creating a main beam towards each GPS satellite, a parallel beamforming strategy where multiple and simultaneous beams are synthesized may be used. In [16] this parallel strategy is denoted multi-target beamforming and only one direction constraint per beamformer is used. When linearly constrained minimum variance is performed using a multi-target strategy it will be denoted Multi-target Linearly Constrained Minimum Variance (MT-LCMV) to distinguish it from the LCMV algorithm which only uses one beamformer and several direction constraints. Multi-target beamforming requires multiple and parallel beamformer units and the digital signals are split before entering the beamformers. The number of beamformers is equal to the number of tracked GPS signals. The proposed receiver structures are general and more detailed descriptions can be found in [12], [13], and [16]. The multi-target beamformer structure is shown in Figure 2.
Figure 2. Block scheme for multi-target LCMV (MT-LCMV). The receiver is implemented as Nel analogue receiving channels and A/D converters and NGPS parallel beamformers.
In Figure 3 a) - c) the antenna pattern differences between the three algorithms, for a 16 element uniform circular array, are shown. Two GPS satellite signals (green and blue line) pass the beamformers undistorted at the same time as a jamming signal (red line) is suppressed. 90 5 120
60
−10 30
150 −25
180
0
210
a)
b)
330
240
300 270
c)
Figure 3. Conceptual beam patterns for a) LCMV, b) MV, and c) MT-LCMV. 16 element uniform circular array.
The performance of minimum variance algorithms is not degraded due to the low power of the received GPS signal [3]. The drawback with these algorithms is the sensitivity to errors such as hardware imperfections, steering vector errors and too few samples for the estimation of the covariance matrix. There are several methods to modify minimum variance algorithms in order to improve robustness, for example: diagonal loading, noise eigenvalue equalization and derivative constraints [2] and [3]. In this paper diagonal loading is used where a diagonal matrix is added to the sample covariance matrix during the beamforming weight calculations. The diagonal load is usually chosen proportional to the smallest eigenvalue of the covariance matrix, e.g. 10λmin , 100λmin etc. This has the effect of making the noise resemble spatially white noise and as a consequence the beam pattern becomes more stable. 3. ROBUST NAVIGATION SYSTEM MODEL In this section the simulation environment is described in detail. The navigation system is divided into three major parts: Navigation filter, GPS and Adaptive beamforming. A flowchart of the simulation environment is presented in Figure 4.
Flight path
Signal environment
Satellite Almanac True directions to satellites and jammers (Azimuths and elevations)
GPS Generate GPS observations
Navigation Filter
Pseudoranges above C/N thresholds
Extended Kalman Filter
Predict satellite directions
ω% = ω + bω + nw
C/N
a% = a + ba + na
Adaptive Beamforming
Pseudoranges C/N above threshold?
Gyro outputs
Accelerometer outputs
IMU
Gyro and accelerometer data ω and a, are extracted from the defined flight profile. These extracted sensor data are the ideal output consistent with the flight profile. To get realistic sensor data ω~ and a~ , errors are added,
Estimate Array Correlation matrix
C/N
Calculate optimal weights
Constraints
Navigation outputs: - Position - Velocity - Attitude - GPS system time
SNR for GPS signals
Calculate SNR
Figure 4. The three sub systems of the simulation environment, the Navigation filter, GPS and Adaptive beamforming.
The user defines the signal environment, i.e., positions and powers of all interfering signals, and chooses a predefined flight profile. It is also necessary to provide a satellite almanac from which satellite positions are calculated. The received power from the GPS satellites is set to –160 dBW, which is the minimum guaranteed power with a 3 dB gain linearly polarized antenna [12]. Navigation filter The data from the IMU (gyros and accelerometers) and the GPS measurements (pseudoranges) are integrated by means of an Extended Kalman Filter (EKF). Figure 5 shows a flowchart of the navigation filter.
,
(8)
where bω and ba are constant biases and nω and na are white Gaussian noise. The values used in the simulations are listed in Table 1, representing the performance of the Litton LN 200 A1 inertial measurement unit. An important issue in the integration is to estimate and compensate for imperfections in the inertial sensors. In this paper, only constant biases are considered. It is assumed that the navigation filter has perfect knowledge of the performance of the inertial sensors, i.e. the Kalman filter parameters that describe the stochastic behavior of the system have their correct values. The Extended Kalman filter gives estimates of a number of states in a state-space system. In these simulations a system model with 16 states is used. Nine states, three each for position, velocity and attitude, originates from the system of error dynamics of the navigation equations, six states contain gyro and accelerometer biases, and one state contains the GPS receiver clock bias. In addition to estimating the states, the filter also provides a covariance matrix that reflects the uncertainty of the state estimates. See [11] for details concerning filter equations, filter parameters and the linearized navigation equations in ECEF coordinates. The update rate of the INS has been set to 10 Hz to limit the simulation time. Table 1. Performance of Inertial Sensors.
Gyro
Accelerometer
Bias
4.85·10-6 rad/s
2.94·10-3 m/s2
White noise ( psd )
2.62·10-5 rad/s/Hz1/2
4.90·10-4 m/s2/Hz1/2
GPS
Figure 5. The Navigation filter. Data from the inertial sensors and the GPS measured pseudoranges are integrated by means of an Extended Kalman Filter (EKF).
The EKF uses the navigation equations formulated in earth-centered-earth-fixed (ECEF) coordinates, and the IMU outputs to propagate the solution between the GPS measurements. When GPS measurements are available, the filter gives the optimal trade-off between the noisy measurements and the system model.
The GPS block generates the pseudoranges, which in a receiver are accessible from the code tracking loop. The satellite constellation is generated from a Yuma almanac, from which satellite positions can be calculated for all times. Orbital errors are not taken into account, i.e., the satellite positions are assumed to be true. Since the true position of the receiver is known, the true geometrical distance r can be calculated. Errors are added to the true geometrical distance r to form the pseudorange ρ,
ρ = r + cδ t + v ,
(9)
where δt is the receiver clock bias, c the speed of light and ν is discrete white Gaussian noise. Atmospheric
propagation errors are not considered in the simulations but could easily be added. The variance σν2 of the white noise ν in equation (9) depends on the equivalent carrier to noise power density ratio, denoted [C/N0]eq, i.e., the level to which the unjammed C/N0 is reduced by interference [12], defined in equation (13). This behavior models the influence of the code tracking loop in the GPS receiver, the accuracy of which decreases for low [C/N0]eq. According to [12], the variance σν2 of ν can be written as 2
c 4F d 2 B 4F d σ = [C 1N0 ] / 10 2 (1 − d ) + [C N0 2] / 10 . (10) eq eq R T 10 c 10 2 v
The definitions and values of the constants in equation (10) are listed in Table 2. The resulting 1σ code loop jitter σν is illustrated in Figure 6.
if the receiver has previously acquired the signal,
[C
N 0 ]eq > [C N ]ACQ .
(12)
When [C/N0]eq drops below [C/N]TR the receiver loses lock on the signal and has to reacquire it. The relation between [C/N0]eq, unjammed C/N0 (dB-Hz) and the jammer-to-signal power ratio J/S (dB) is given by 10 ( J / S ) / 10 , (13) [C N 0 ]eq = −10 log10 −( C / N 0 ) / 10 + Q Rc
where the factor Q determines the type of jammer (Q = 2 for a wideband noise jammer) and Rc is the chip rate for the spreading code. C/N0 is the unjammed carrier powerto-noise spectral density ratio. From this point on in the paper the [C/N0]eq will also be denoted C/N0 since it will be clear from the context whether it is the unjammed or equivalent C/N0 that is considered. Table 2. GPS Parameters.
Mask angle
10°
Thermal noise spectral density
-204 dBW/Hz
Chip rate for C/A-code
Rc
Receiver noise figure
Figure 6. The relation between C/N0 and the 1σ code loop jitter σν . The tracking threshold for the carrier tracking loop (28 dBHz) is also shown.
The carrier tracking loop is in general the most sensitive tracking loop to low [C/N0]eq and loses lock first. The lowest [C/N0]eq for which the carrier tracking loop is still able to track the signal is called the tracking threshold. A reasonable tracking threshold for the carrier tracking loop is [C/N]TR = 28 dB-Hz [12]. This threshold is valid for a receiver with pre-detection integration time, Allan deviation and oscillator vibration sensitivity listed in Table 2. During acquisition of the signals, [C/N0]eq needs to be about 5 dB higher than the tracking threshold. The acquisition threshold is therefore set to [C/N]ACQ = 33 dBHz. In this paper no consideration is taken to the acquisition time of the receiver and consequently a pseudorange is measured directly when
[C
N 0 ]eq > [C N ]TR ,
(11)
1.023·106 chips/s 4 dB
Correlator spacing
d
½ chip
DLL discriminator correlator factor
F1
½
DLL discriminator type factor
F2
½
Code loop bandwidth
B
1 Hz
Pre-detection integration time (PIT)
T
20 ms
Allan deviation for oscillator
10-11
Oscillator vibration sensitivity
10-10 s2m-1
Measurement update rate
1 Hz
Adaptive Beamforming The performance of the integrated navigation system is evaluated for four different antenna array geometries: uniform rectangular array (URA) with 3-by-3, 4-by-4 and 5-by-5 elements and a circular antenna array with 7element, six elements arranged around the midpoint element. The antenna array consists of identical isotropic antenna elements, which are spaced ½ wavelength apart. The size of a 4*4 element URA then becomes 3*λ/2 by 3*λ/2. For the L1 band this is approximately 0.3*0.3 m, neglecting the size of the antenna elements. The antenna array is placed on the upper surface of the platform. This results in an increased jamming resistance for signals with a DOA from the lower half sphere (in the antenna frame)
through vehicle shielding. In the indicated scenario it is assumed that the vehicle shielding is 15 dB, [14] and [17]. The incoming signals are generated on each antenna element from the scenario. The GPS and jammer signals are described by their direction, strength and waveform, to which noise is added. The antenna array is described with a model, which may include imperfections in the antenna elements as well as in the receivers. In our simulations the signals are generated digitally in the base band under the assumption of ideal down-conversion and A/D-conversion. The adaptation process is performed on blocks of sampled data where a block of data is used to calculate the correlation matrix, which is then inverted and used to calculate the beamforming weights. The signals are filtered with the weight vector and thereafter the C/N0 for each GPS satellite signal is calculated. In Table 3 the beamforming parameters are given. Table 3. Beamforming parameters.
deployed to protect the strategic point C. In addition, a ground based high-power jammer is situated at the target, see Figure 7. All jammers emit wideband Gaussian noise since this is usually the most stressing type of jammer for an adaptive beamforming antenna array system, [3], [4], [5], and [14]. All jammers are assumed to have isotropic antennas. The effect of other types of jammers may be alleviated by other interference mitigation techniques and are not considered in this paper. The received signal power from the jammers depends on the distance from the source to the receiver. Free space propagation is assumed for the interfering signals; the received power Pr decreases as r-2 where r is the distance from the source [20]. No multipath is assumed since the aerial vehicle has free line of sight to the satellites and the platform is not defined and hence reflections cannot be determined. However, in the simulation environment multipath as well as wideband beamforming are possible to simulate. Parameters related to the scenario are given in Table 4. Table 4. Scenario parameters.
Antenna element spacing
0.09 m
Block size
2048 samples
Airborne jammers
100 mW, wideband Gaussian
Diagonal load
100λmin
Ground-based jammer
10 W, wideband Gaussian
Maximum angular rate
17°/s
4. SCENARIO DESCRIPTION A well-known strategy to degrade navigation performance of platforms aided by a smart antenna is to deploy a socalled cloud of low-power mini-jammers. The objective with this approach is to saturate the antenna array so that its beamforming capability is destroyed [14].
5. SIMULATION RESULTS The purpose of the simulations is to assess the performance of the robust navigation system in the scenario of Figure 7. In the simulations the BPSK modulated L1 civilian GPS signal, with center frequency at 1575.42 MHz and with a bandwidth of 2.046 MHz, is assumed. The results presented in the figures in this section are for a 4x4 URA antenna array. In Figure 8 – Figure 10 the C/N0 is plotted using the beamforming algorithms MV, LCMV and MT-LCMV. In each figure the C/N0 significantly decreases as the platform moves closer to, and finally into, the cloud after approximately 120 seconds. When the C/N0 decreases, the variance of the pseudorange noise grows. Finally, when C/N0 drops below the tracking threshold, [C/N]TR, no pseudorange can be measured. During the simulation a total of nine satellites were visible, but due to jamming only some of them are available during the flight.
Figure 7. Jamming scenario. The vehicle starts at point A and flies along the blue line, through a cloud of jammers, point B, towards the end-point C. The light blue line is the flight profile projected on the ground. The positions of the 12 jammers are marked with red stars.
The scenario chosen for this simulation is shown in Figure 7. An aerial platform is navigating along a predefined flight profile, elevating and accelerating from standing still on the ground to an altitude of 100 m and a velocity of 100 m/s. A cloud of airborne mini-jammers has been
In the figures the black dashed line shows the C/N0 for one single isotropic antenna element and the other colors indicate the C/N0 for each beamforming algorithm. The solid line is the mean value of C/N0 for the satellites and the dotted lines are the C/N0 for each GPS satellite. Also shown are the tracking and acquisition thresholds at 28 and 33 dB-Hz respectively. Figure 8 shows the C/N0 performance of the LCMV algorithm with nine direction constraints. In the beginning
of the flight the C/N0 passes the tracking and acquisition thresholds several times. However, after approximately 50 seconds into the flight the mean C/N0 becomes less than the tracking threshold and after that never recovers above the acquisition threshold again.
Figure 10. C/N0 for the MT-LCMV algorithm and a 4x4 URA (blue line). C/N0 for one isotropic antenna element (black dashed line).
Figure 8. C/N0 for the LCMV algorithm with 9 direction constraints and a 4x4 URA (orange line). C/N0 for one isotropic antenna element (black dashed line).
The MT-LCMV algorithm yields the highest C/N0, which results in the smallest code loop jitter, approximately 2 meters according to Figure 6. In Figure 11 the number of available satellites for the MV, LCMV and MT-LCMV algorithms is shown.
The performance of the LCMV algorithm is bad because there are less available degrees of freedom for jammer suppression than there are jammers in the scenario, equation (4).
Figure 11. Number of satellites available over time. The antenna array geometry is a 4x4 URA. Total of nine GPS satellites are available during the simulation. Figure 9. C/N0 for the MV algorithm and a 4x4 URA (green line). C/N0 for one isotropic antenna element (black dashed line).
In Figure 9 the C/N0 for the MV algorithm is shown. As can be seen the C/N0 performance of the MV algorithm is better than for the LCMV algorithm. The mean C/N0 (solid green line) stays above the tracking threshold until the platform is inside the jammer cloud. In Figure 10 the C/N0 for the MT-LCMV is given.
Using the LCMV algorithm the satellites are only available for short periods of time and after approximately 50 seconds, tracking of any GPS satellite is impossible. For the MT-LCMV and MV beamformers the availability of the satellites is comparable but for three of the satellites the MT-LCMV algorithm performs better. Over the entire flight the MT-LCMV and MV algorithms always have at least four satellites available. Even inside the jammer cloud the MT-LCMV and MV algorithms makes
measurements from four to six GPS satellites available, see Figure 11. Figure 12 shows how the position error, i.e. the distance between the estimated positions and the true positions, vary over time for the different algorithms.
Table 5. Mean position error over the flight path for different antenna arrays and beamforming algorithms. The errors presented are mean values from 30 Monte Carlo simulations.
Number of antenna elements BF algorithm
7
3x3
4x4
5x5
MV
1.67
1.15
1.03
0.95
MT-LCMV
1.24
1.09
0.96
0.93
–
21.53
12.07
1.16
LCMV
Table 6. End-point position error for different antenna arrays and beamforming algorithms. The errors presented are the mean values of 30 Monte Carlo Simulations.
Number of antenna elements BF algorithm
Figure 12. Position errors for the beamforming algorithms using a 4x4 URA.
From Figure 12 it can be seen that the navigation performance using the MT-LCMV and MV beamformers are more or less equal, even though the C/N0 was significantly higher for MT-LCMV than for MV. However, in the final stage of the flight the MT-LCMV algorithm gives a slightly smaller position error than the MV algorithm. When the LCMV algorithm loses lock on all satellites, after approximately 50 seconds, the drift of the INS can clearly be seen, Figure 12. If an isotropic single element antenna would be used, no satellites would be available at any time. For an INS/GPS system without adaptive beamforming in the given scenario, all GPS satellites are jammed and the navigation system can only use the INS. For a system using only INS, i.e., the IMU biases are not estimated and compensated for, this would result in a position error of approximately 70 meters, at the end of the simulation. For a scenario with the same nominal trajectory, but without jammers, the end-point position error is about one meter when employing the INS/GPS integrated system and no beamforming. This clearly shows the benefits of employing INS/GPS and adaptive beamforming. Performance results for other combinations of algorithms and antenna arrays, in terms of mean position error and end-point position errors, are presented in Table 5 and Table 6, respectively. It should be noted that the errors presented are for a reduced error budget, i.e. ionospheric, tropospheric and multipath errors etc. are not included and the errors are only due to receiver thermal noise, GPS receiver clock offset and jamming, cf. equation (9).
7
3x3
4x4
5x5
MV
8.61
1.48
1.21
1.07
MT-LCMV
2.08
1.69
1.16
1.03
–
69.70
44.14
1.21
LCMV
From Table 5 it can be seen that the MT-LCMV algorithm provides the best navigation performance in terms of mean position error over the flight path, for all antenna array geometries. Furthermore the MT-LCMV algorithm, in all cases but one, gives the smallest position error at the end-point, see Table 6. In Figure 9 and Figure 10 it was shown that the MTLCMV algorithm provided a better C/N0 than the MV algorithm and hence better GPS measurements are expected. However, in Table 6, for large antenna arrays (relative to the number of jammers, i.e., the 4x4 5x5 arrays) the end-point performance of the MT-LCMV and MV algorithms are comparable. For a 3x3 array, the MV algorithm actually gives a smaller end-point position error than the MT-LCMV algorithm. It can be concluded that when the array has sufficient degrees of freedom the performance of the MT-LCMV and MV algorithms is comparable. Either of the algorithms can provide the best position and in this case the end-point position error is not a good measure of the relative performance of the algorithms. For a small number of antenna elements compared to the number of jammers e.g. the 7-element array in Table 6, the MT-LCMV beamformer yields the smallest position error at the end-point. In combination with a tightly coupled INS/GPS the MT-LCMV algorithm works well even when the number of antenna elements is smaller than the number of jammers. This indicates that the MTLCMV beamformer, in combination with a tightly coupled INS/GPS, may provide the best robustness of the three investigated algorithms in navigation warfare
scenarios where many more jammers than antenna elements are likely to be present. The MV algorithm can be used to minimize the power even though the directions to the signals are unknown. This is an advantage compared to the multi-target algorithm. However, the MV algorithm has a disadvantage in that the signal, after beamforming, is phase shifted depending on the direction of arrival of the received signal, Figure 13. 200 150
Phase shift (deg)
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Figure 13. Phase shift for the MV algorithm where the green lines represents the GPS satellite signals and the red lines the jammer signals.
If the phase is distorted and has abrupt shifts there is a risk that the carrier-tracking loop in the GPS receiver loses lock. However, it is possible to compensate for the phase shift the MV algorithm introduces. Due to the real valued direction constraints, the multi-target LCMV algorithm preserves the phase of the original signal assuming that the constraints are set correctly. 6. DISCUSSION For long-range precision engagement scenarios the use of robust navigation systems is of outmost importance. The required robustness of the system is scenario dependent and can in many cases be provided by INS/GPS/Beamforming integration. In this paper a simulation environment of a robust navigation system has been presented. The system consists of a tightly coupled INS/GPS and beamforming antenna array, which share information in an integrated manner. The system was evaluated in a jamming scenario where an aerial vehicle flies along a predefined flight path, through a cloud of jammers and towards a target protected by a ground-based jammer. For the protection of a vital location the scenario may give valuable insight in how jammers must be placed for sufficient probability of succeeding in misguiding the aerial platform.
When integrating an adaptive beamforming antenna array with a tightly coupled INS/GPS system, directionconstrained beamforming is a good choice. As long as the drift of the INS is not excessively large it can provide sufficiently accurate satellite directions as a priori information to the beamformer. However, when the GPS is jammed the drift of the INS will cause the performance of the direction estimates, supplied to the beamformer, to deteriorate. When this happens it is important that the platform is as close to the target as possible since INSonly navigation in this case will be initiated. The results indicate that for a large number of jammers compared to the number of available degrees of freedom, i.e., number of antenna elements, the MT-LCMV algorithm performs the best and will take the platform closer to the target than any of the other two beamforming algorithms. From Table 6 it can be seen that also the MV algorithm may perform well even when the number of elements is less than the number of jammers (3x3 rectangular array and 12 jammers). This may be a result of the jammer constellation. Depending on the angular spread of the incident jammer signals a single null may suppress two jammers, e.g., a sharp null is formed in the direction of one jammer and another jammer signal is incident on the flank of the null and is also suppressed to some extent. In contrary to the MT-LCMV approach, where one constraint is used per beamformer, the LCMV algorithm have to set several direction constraints. In our simulations nine constraints are set, one towards each satellite. This is in general not a good idea since all degrees of freedom are spent on maintaining the direction constraints and the jamming suppression capability is low. A better idea would be to set four or five directional constraints since only four satellites are needed to obtain a position fix. 7. CONCLUSIONS Three beamforming algorithms and four different antenna array geometries, integrated with a tightly coupled INS/GPS, were tested. The system employing the MTLCMV beamforming algorithm proved to be the most promising, in terms of position error, for navigation warfare scenarios. The MV algorithm, which requires no direction-constraints, is also a promising algorithm if the phase-shift can be compensated for. An extension of the simulation environment, with a higher degree of modeling of the subsystems, will provide useful guidelines for designing an integrated system designated for specific scenarios.
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