Emitter Geolocation with Multiple UAVs

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Emitter Geolocation with Multiple UAVs Nickens Okello Melbourne Systems Laboratory Department of Electrical and Electronic Engineering University of Melbourne, Parkville, VIC 3010, Australia [email protected] Abstract - Geolocation of radar and communication emitters based on time difference of arrivals (TDOAs) can be carried out using a network of three or four unmanned aerial vehicles (UAVs) each of which is equipped with an electronic warfare support (ES) sensor, a global positioning system (GPS) receiver, a precision clock and a limited bandwidth communication system. When the leading edge of an electromagnetic pulse is detected by an ES sensor on board a given UAV, the time of arrival and the UAV’s location are transmitted to a fusion centre. The received measurements from all UAVs within the network are then cross-correlated to determine the time difference of arrivals from which emitter location can estimated. This paper presents two sets of emitter location estimation equations. The first set is for 2-D emitter location estimates for a ground based emitter given time of arrival measurements from three netted UAVs. The second set is for an emitter that is locate at an altitude and gives the complete 3-D location estimation equations given measurements from four netted UAVs. Numerical results based on three and four UAVs are presented to validate these equations.

Keywords: TDOA, geolocation, deinterleaving.

1

Introduction

Goeolocation of radio transmitters is an important need in a wide range of areas including search and rescue of planes and ships, location of illegal or interfering emissions, and the location, identification, and targeting of military targets based their radar or communication emissions. Geolocation using satellites has received much attention [1, 2, 3] and its successful use in search and rescue is well known through news reports. This approach is the cheapest method available when the search has to be carried out globally on a continuous basis and there is no prior information on the possible location or type of target. Furthermore is suitable when the emitter is a cooperating (or at least non-evasive) target and the emission has a known format that is designed to aid target identification and status evaluation. Further more it is suitable when ground access of the target location is possible. In military applications, emissions can be evasive or

non-cooperating and may even be specifically designed to be elusive. Secondly, the area of interest is generally limited but inaccessible and the search has to be carried out over a very limited period of time. Under these conditions, geolocation is better carried out using UAVs that are equipped with ES sensors rather than satellites. Furthermore, UAVs can be equipped with appropriate complementary sensors for emitter identification, and fire power to destroy the target if necessary. In Section 2, we present emission signal characteristics and the signal parameters measured by ES sensors. Later in the section we present an overview of deinterleaving, angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA), and how they relate to emitter geolocation and identification. Section 3 is the main body of this paper and contains detailed derivations of geolocation equations for a networks of three and four appropriately equipped UAVs that measure and transmit leading edge time of arrivals (TOAs) to a fusion centre. These derivations are adapted from the problem of geolocation using geostationary satellites first presented in [1]. In [1] however, the derivations for the case involving four satellites is not complete. In this paper, we present complete and accurate derivations involving three and four networked UAVs assuming a threedimensional spherical earth geometry. In Section 4, we discuss the problem of time of arrival measurement association. In Section 5, we present performance results based on a network of three or more UAVs and show that accurate geolocation of ground based emitters is possible.

2

Signal Parameters in Geolocation

The parameters generally measured by the ES system for a pulsed signal include carrier radio frequency (RF), pulse amplitude (PA), pulse width (PW), time of arrival (TOA), and angle of arrival (AOA). In some systems, polarization of the input signal is measured. Furthermore, frequency-modulation-onthe-pulse (FMOP) is another parameter that can be used to identify a particular emitter and also can be used to determine the chirp rate or phase coding of a pulse compression (PC) signal [4].

By definition continuous wave (CW) signals are generally identified as those signals whose pulse lengths exceed several hundred microseconds. TDOA measurements are made with respect to an internal clock on the leading edge of the pulse. Parameters measured on a single intercept are called pulse descriptor words (PDW). The PDW form a set of vectors in the parameter space. By matching vectors from multiple pulses, it is possible to isolate those signals associated with a particular emitter. This process is called deinterleaving [4] Once a signal is isolated, an additional set of signal parameters can be derived. These include: 1. the pulse repetition frequency (PRF) or its pattern (from multiple TOAs), 2. antenna beamwidth from multiple PAs,

significantly change its position in the few milliseconds associated with a PRI. Thus angle of arrival is a relatively stable parameter. Unfortunately, AOA is one of the most difficult parameters to measure. It requires a number of antennas and receivers, all either amplitudeor phase-matched. The signal processing functions of an ES system uses data that is encoded from each intercepted pulse. The data in the form of a vector (Si ) is given by Si = [ AOAi

5. emitter range from multiple AOAs. These derived parameters (sometimes called emitter beam descriptors) are useful in identifying the particular emitters intercepted by the ES system, and the threat they represent.

2.1

Pulse Deinterleaving

Pulse deinterleaving is the process of sorting out pulses intercepted by the ES sensor into individual sets associated with particular emitters. Each intercepted pulse must be compared with all the other intercepted pulses to determine whether they originated from the same radar. Common parameters used to accomplish deinterleaving are: centre frequency (or radio frequency (RF)) and angle of arrival (AOA). Other parameters are PW and difference in time of arrival (TOA) which leads to an estimate of the pulse repetition interval (PRI). For a conventional pulsed radar, the objective is to measure the carrier frequency of the pulse. If the input is a chirp signal, then it is necessary to measure the starting and ending frequencies and the PW from which the chirp rate can be calculated. If the signal is phase coded, then both the carrier frequency and the chirp rate are of interest. With frequency agile signals, the average or centre frequency of the signal and its excursion band are of interest. Frequency is important information used both in sorting and jamming. The accuracy of the frequency measurement determines the resolution that can be achieved in matching various intercepted signals to determine whether they belong to the same emitter. Furthermore, accurately knowing the frequency of the victim radar or communications system allows the jammer to concentrate its energy in the desired frequency range, making the jamming more effective. The AOA is a valuable parameter used in deinterleaving radar signal since an emitter cannot rapidly change its position. Even an airborne radar cannot

P Wi

T OAi

P Ai ]

(1)

for i = 1, ..., n where n pulses are present. The next step is to deinterleave the data to sort pulses into groups belonging to a particular emitter. The most reliable sorting parameters are AOA and frequency. To perform the two dimensional sort using these parameters, the vector Vi is used, where

3. antenna scan rate or type from multiple PAs, 4. mode switching from multiple PWs and TOA, and

fi

Vi = [ AOAi

fi ] , i = 1, ..., n.

(2)

The sorting process then consists of collecting the vectors representing those pulses that match each other within the resolution limit of the sort. Once deinterleaving is accomplished, a number of emitter parameters can be derived from the vector set in (1). The emitter PRI can be determined by comparing successive TOAs. The antenna beamwidth and scan rate can be determined from successive amplitude comparisons. Mode switching can be determined from multiple PWs and range can often be determined from multiple AOAs. In some systems, AOA and frequency are not sufficient to deinterleave emitters. This can occur, for example, with frequency agile emitters. Also for low resolution systems, there may be a number of distinct emitters that fall into overlapping cells due to the coarse cell structure. The resulting ambiguities must then be resolved in an additional step of deinterleaving. This can be accomplished using either an additional primary parameter set such as PW, or a derived parameter such as PRF (or PRI) that has been determined from the first deinterleaving step. The deinterleaving process then becomes a three-dimensional sort that is more powerful than the two-dimensional sort using AOA and frequency.

2.2

Emitter Identification

Emitters are identified by comparing the characteristics derived from the intercept emissions (e.g., frequency, average PRI, PRI type, scan rate, scan type,) with those from known emitters that are stored in an emitter library residing in the ES system computer. However, at times there will be more than one emitter in the library having parameter ranges that include those of the emitter being identified. In these cases, the intercepted emitter’s parameters are compared with those associated with other emitters in the environment to effect the match. For example assume a threat missile is an identification candidate and one of the other emitters is a platform radar associated with a particular threat, and they both fall in the same

AOA bin. The tentative identification is probably correct. If none of the identification candidates for the new emitter can be correlated with any of the other emitters in the environment, then the emitter is given the identification of that particular candidate having the greatest threat potential. There will also be times when an emitter has characteristics that do not match any of those stored in the library of known emitters, thereby making a positive identification impossible. In that case, the emitter is classified as either an unknown lethal or a nonlethal threat based on the emitter’s frequency and scan characteristics.

2.3

f1 f2

∆t =

d sin θ c

(3)

where d is the distance between the antennas, c is the speed of light, θ is the AOA. Hence, the resulting AOA is θ = sin−1

c∆t . d

c cos θ∆t. d

(6) (7)

∆f = f1 − f2 =

1 (r22 − r21 − r12 + r11 ). λT

(8)

This equation defines a surface in three-dimensional space on which the transmitter must lie. If the transmitter lies on the surface of the earth, the intersection of the two surfaces defines a curve on the earth on which the emitter lies. If a second measurement of FDOA is made or if another type of measurement like TDOA or AOA can be obtained, two curves can be obtained and the intersection of the two curves provides an estimate of the transmitter location. The use of both TDOA and FDOA generally provides greater precision than either used alone. FDOA is appropriate for stationary emitters, while TDOA can be used for either fixed or mobile emitters.

(4)

The sensitivity to time difference measurement noise can be determined by differentiating (4),viz, ∆θ =

r11 − r12 λT r21 − r22 = f0 − λT = f0 −

where rij is the distance of receiver i from the transmitter at time tj , T = t2 − t1 , and λ is the wavelength. The FDOA is defined by

Time Difference of Arrival

Time difference of arrival (TDOA) is another method of measuring AOA. It uses the configuration of the interferometer but with the time difference between the signals in the two antennas measured instead of the phase difference. It has the advantage that the time is invariant with frequency. It is also applicable when a reasonable baseline is involved. The TDOA between the signal in the two antennas is given by

2.4

A complementary method that can be used to determine emitter location uses the difference in Doppler shift which results when two platforms are closing on the emitter with different radial velocities. The frequencies at the two platforms are

(5)

Passive geolocation techniques

The passive geolocation of ground emitters from airborne or space platforms is an important function useful for weapons targeting and situational awareness. The basic technique for geolocation of an emitter involves measuring AOA from multiple locations and triangulating to determine its location. Two methods that have proven to be capable of providing highly accurate estimates of emitter location are TDOA and frequency difference of arrival (FDOA), also called differential Doppler techniques. A single TDOA measurement from two airborne platforms provides a hyperbolic curve containing the emitter location that is formed by the intersection of a cone with the surface of the earth. A second measurement between a third airborne platform and either of the first two provide similar type hyperbolic lines, the intersection of which provides the emitter location. This method requires a precise knowledge of the distance between the airborne platforms and a precision system clock to synchronise TDOA measurements. GPS can be used to accurately locate the platforms, while a cesium clock is generally used to provide high time precision.

3

TDOA UAVs

Geolocation

with

TDOA measures the difference in arrival times of a signal at two separate locations. When there are more than two receivers, we have several TDOA measurements. In the problem of emitter geolocation using UAVs, only a limited number of receivers or platforms are available. A minimum of three UAVs are required when the transmitter is known to be on the surface of the earth and four if the altitude of the transmitter is not known. Figure 1 show a scanning radar emitter E to be geolocated using a network of up to four UAVs each of which is equipped with an ES sensor. Let Ui , i = 1, 2, 3, 4 be the UAVs and let Di+1,i , i = 1, 2, 3, be the TDOA measured between Ui+1 and Ui . If c is the signal propagation speed, then ri+1,i = cDi+1,i = ri+1 − ri , i = 1, . . . , 3

(9)

where ri denotes the distance between the transmitter and the ith UAV. Let Ui be at a known position (xi , yi , zi ), i = 1, 2, 3, 4 and the transmitter unknown coordinates be (x, y, z), then ri2 = (xi − x)2 + (yi − y)2 + (zi − z)2

(10)

for i = 1, . . . , 4. Equations (9) and (10) yield three unknowns with the three unknowns being the three coordinates of the emitter position. Solving for the emitter

position is not easy because the equations involved are nonlinear. An iterative solution by linearization using Taylor series expansion is one way but this requires a proper initial position estimate close to the true solution and convergence is not guaranteed. North

ω φ

U4 U1 U2

r1

r4 U3

r2 r3

θ

From  x1  x2 x3

(12) and (13)     2 2 y 1 z1 x K1 + rE − r2,1 + 2r2,1 r2 − r22 1 2 . y 2 z2   y  =  K2 + rE − r22 2 2 2 2 y 3 z3 z K3 + rE − r3,2 − 2r3,2 r2 − r2

By inverting the matrix formed by the UAV positions, we can express the transmitter coordinates in terms of r2 , i.e.,     2  x Ax Bx Cx r2  y  =  Ay By Cy   r2  (14) z Az Bz Cz 1 where the elements of the coefficient matrix are known. Substituting this result into (10) with i = 2 produces a 4th-order equation in r2 which can then be solved. Inserting the positive r2 values into (14) gives at most four possible transmitter positions. The proper solution is obtained from knowing in which quadrant the transmitter lies. For the case of four emitters, we observe from equation (9) that r3,2 + r2,1 − r3,1 r4,3 + r3,1 − r4,1

Ε Figure 1: Emitter geolocation using a network of up to four UAVs that are equipped with ES sensors.

r4,2 + r2,1 − r4,1 r4,3 + r3,2 − r4,2

= =

0 0

(15) (16)

= =

0 0.

(17) (18)

Using the relation ri,j = ri − rj , we have r3,2 r2,1 r3,1 = r3,2 r12 + r2,1 r32 − r3,1 r22 .

UAV 1

UAV 2

UAV 3

Substituting equation (10) into (19) and using (18), we can express (19) as a linear equation in (x, y, z), viz,

Communication Link: multicast using tcp/udp/ip toolbox Association and Signal Processing

r3,2 r2,1 r3,1 = l1 + m1 x + u1 y + v1 z Emitter Location Estimates

UAV 4

o Beamwidth: 2

u1 v1 Direction of wave front

= r3,2 K1 + r2,1 K3 − r3,1 K2 = −2(r3,2 x1 + r2,1 x3 − r3,1 x2 ) = −2(r3,2 y1 + r2,1 y3 − r3,1 y2 ) = −2(r3,2 z1 + r2,1 z3 − r3,1 z2 ).

(21) (22) (23) (24)

Similarly, r4,3 r3,1 r4,1

Figure 2: Wave front of a narrow beam rippling through an area containing four networked UAVs. For an alternative solution we first consider the case of three receivers. Let rE be the radius of the earth. Since the transmitter is on the surface of the earth, (11)

Let Ki = x2i + yi2 + zi2 . Equation (10) can be rewritten as 2 2xi x + 2yi y + 2zi z = Ki + rE − ri2 , i = 1, 2, 3. (12)

From (9), we have 2 2 ri+1 = ri2 + 2ri+1,i ri + ri+1,i , i = 1, 2.

(20)

where l1 m1

2 rE = x2 + y 2 + z 2 .

(19)

(13)

r4,2 r2,1 r4,1 r4,3 r3,2 r4,2

= r4,3 r12 + r3,1 r42 − r4,1 r32

= l 2 + m2 x + u 2 y + v 2 z = r4,2 r12 + r2,1 r42 − r4,1 r22 = l 3 + m3 x + u 3 y + v 3 z r4,3 r22

r3,2 r42

(25) (26)

r4,2 r32

= + − = l 4 + m4 x + u 4 y + v 4 z

(27)

where li , mi , ui , vi , i = 2, 3, 4 are defined analogous to those in equations (21)-(24). While it may appear that there are four linear equations, they are however dependent because by using equations (15)-(18), we find that (20)+(25)-(26)=(27). In addition r4,1 (20)+r2,1 (25)= r3,1 (26). Thus there are only two independent equations. Now x and y can be determined in terms of z from (20) and (25), viz, · ¸· ¸ · ¸ m1 u 1 x r3,2 r2,1 r3,1 − l1 − v1 z = m2 u 2 y r4,3 r3,1 r4,1 − l2 − v2 z

or

Alternatively, it is also possible to show that · ¸ · ¸ x p0 + p1 z = y q0 + q1 z

(28)

where p0

=

p1

=

q0

=

q1

=

d

=

u2 u1 (r3,2 r2,1 r3,1 − l1 ) − (r4,3 r3,1 r4,1 − l2 ) d d 1 − (u2 v1 − u1 v2 ) d m2 m1 − (r3,2 r2,1 r3,1 − l1 ) + (r4,3 r3,1 r4,1 − l2 ) d d 1 (m2 v1 − m1 v2 ) d m1 u 2 − m 2 u 1 .

Equations (15) to (28) were first derived in [1] for the problem of emitter geolocation using TDOA measurements from geostationary satelites. However in [1] the authors did not proceed to the final solution. In the remainder of this section, we complete the derivation for the emitter location estimate given TDOA measurements from a network of four UAVs. Substituting (28) into (10) for any one i, we obtain ri2 = az 2 + bi z + ci

(29)

where a = p21 + q12 + 1 h i bi = −2 (xi − p0 )p1 + (yi − q0 )q1 + zi

ci

=

(xi − p0 )2 + (yi − q0 )2 + zi2 .

The left-hand side of equation (29) is the square of a positive real number and so the second order quadratic on the right-hand-side should be a perfect square. Hence, r √ bi ci a z2 + z + ri = a a √ bi = a(z + ) (30) 2a Since coefficients a, bi , and ci are dependent on noise contaminated measurements, a perfect square is not going to be possible and so equation (30) can only be an approximation. We therefore make the assumption that if the measurement set used to generate the coefficients are from a common wavefront, then the approxp imation is deemed sufficient if b2i − 4aci /bi < 10−3 . Now multiplying both sides of equation (10) by r2 + r1 , we obtain r2,1 (r2 + r1 )

= r22 − r12

(31)

Now substituting for r1 and r2 given that b2 ≈ 4aci , √ h b1 + b2 i = r2,1 a 2z + 2a

(b2 − b1 )z +

b22 − b21 4a

or z=−

(b1 + b2 ) . 4a

(32)

z=−

√ √ c2 + c1 √ 2 a

(33)

A positive (negative) sign for the value of z means that the possible emitter location lies within the northern (southern) hemisphere. Any value of z that lies in the wrong hemisphere should therefore be rejected.

4

Measurement Association

We note that for a scanning radar the beam is narrow and will envelope all three UAVs over a small interval of time given by the intersection of the time intervals when the beam is over the individual UAVs. Thus, while each UAV can generate many measurements, only those measurements corresponding to the intersection of the time intervals are relevant to the geolocation estimation problem. We assume that as the beam sweeps over the UAVs, each UAV collects time-of-arrival measurements and after detecting the end of the sweep, it transmits all these measurements including its GPS location to each of the other UAVs, or to a common processing centre. Thus all UAVs will have identical measurements after the last UAV has detected the end of the sweep. Figure 3 shows the relationship between the time intervals within which the UAVs fall within the radar beam and the pulses that contribute to their measurements.

UAV 1 UAV 2

UAV 3

Time

PW = 1.2 µ s

UAV 1

Time

T = 2000µ s

UAV 2 UAV 3

Figure 3: Measurement contributing pulses during a sweep over the UAVs. The size of the region bounding the loitering UAVs is limited by the need to keep them within the beamwidth of the scanning beam, but within this region, the UAVs should be kept as far apart as possible to maximize the accuracy of the geolocation estimates. For a ground based radar emitter, and assuming the

5

Numerical Results

In the simulation results presented in this section, a scanning radar was used to simulate an emitter located on the surface of the earth. In particular the radar parameters that were considered to be relevant to the detectability of the beam and therefore needed to be specified were: horizontal beamwidth, vertical beamwidth, antenna speed of rotation, pulse repetition frequency and range.

−19

−19.5

UAV Base

−20 Latitude [deg.]

UAVs fly at a constant altitude along a circular trajectory centred directly above the UAV base, the maximum TDOA possible, τmax is the time a wave front takes to traverse the diameter of this circle. Thus in carrying out measurement association, we look for groups of three measurements, one from each UAV, whose TDOAs are less than τmax . For a radar transmitter whose maximum unambiguous range is 96nm, τmax (≡ 4km)