3D Multi-static SAR System for Terrain Imaging Based on Indirect GPS Signals

Transcription

1 Journal of Global Positioning Systems (00) Vol. 1, No. 1: D Multi-static SA System for errain Imaging Based on Indirect GPS Signals Yonghong Li, Chris izos School of Surveying and Spatial Information System, University of New South Wales, Sydney NSW 05, Australia el: +61() ; Fax: +61() Eugene Donskoi, John Homer, Bian Moarrabi School of Information echnology and Electrical Engineering, University of Queensland, Brisbane QLD 407, Australia eceived: 18 March 00 / Accepted: 16 June 00 Abstract. A 3D multi-static SA imaging system which utilises reflected GPS signals from obects on the Earth's surface is described in this paper. he principle of bistatic radar is used to detect movement of, or changes to, the imaged obect. he indirect GPS signals are processed by a match filter with the aim of improving the spatial resolution of detection. he measure of spatial resolution of this imaging system is derived, and is confirmed by MALAB simulation. Several scenarios are considered, for the visible satellite at a given receiver and obect location. he scenarios for different satellites are: a) static receiver with two targets which move with the same speed; and b) moving receiver with one static target and one moving target. Simulation results show that the spatial resolution of detection depends on the relative positions of the GPS satellites, the imaged obects and the GPS receiver, as well as their respective velocities. Key words: Detection, Imaging, GPS, SA 1 Introduction he Global Positioning System (GPS) is an all-weather, global, satellite-based, round-the-clock Global Navigation Satellite System (GNSS). Measurements on the direct GPS signals have been successfully used in navigation and positioning, while indirect or reflected signals are viewed as a nuisance. However, scattered/reflected GPS signals also can be 'reused' for remote sensing, radar target detection and (reflector) change detection. Examples of remote sensing applications are ocean altimetry, wind speed/direction determination, monitoring of sea ice condition, and for the determination of soil moisture content [1~7]. Analysis of indirect GPS signals has recently attracted a lot of attention because of its potential civilian/military applications. [8~13] established the models for the extraction of sea state and wind speed from ocean reflected GPS signals, and carried out some reflected GPS experiments. A parallel delay mapping GPS receiver on an aircraft was used to confirm the modelling. [14] made ocean altimetry measurements using reflected GPS signals observed from a low-altitude aircraft. he irradiated power of GPS satellites can also be reused for imaging, based only on the analysis of indirect GPS signals. Generalising the bistatic radar concept, this paper describes a multi-static synthetic aperture radar (SA) system consisting of a constellation of visible GPS satellite transmitters, a multi-channel modified GPS receiver and multiple obects. he 'obects' may be one or more moving platforms such as a ship, or a reflective surface that is monitored for its movement. his imaging system has the following useful properties: (a) no dedicated signal transmitter is required; (b) the GPS signal frequency is reused; (c) GPS operates round-theclock and its signals cover the entire Earth's surface; (d) low power consumption; and (e) known GPS signal structure. hat is, the multi-static SA system has the potential to develop high quality, and low cost images, of a localised area.

2 Li: 3D Multi-static SA System for errain Imaging 35 3D Multi-static SA System Model he terrain imaging system provides visual discrimination within the image scene. A common measurement of the ability for spatial discrimination between obects is the spatial resolution. [15] has described the resolution equations for a D configuration in which transmitter traectory, imaged obect, as well as receiver are in the same plane. he bistatic SA principle is traditionally based on the radar positioned on an airborne platform. he transmitter and receiver are on the same moving platform while the imaged obect is static. When the radar moves, the reflected signal from the same imaged obect is processed in order to synthesise an antenna with a synthetic aperture. In this paper, a 3D multi-static SA system, as illustrated in Figure 1, is set up as a terrain imaging system, where transmitter and receiver are located in two separate positions and move with different speeds. here could be one or more imaged obects with different velocity vectors. he visible GPS satellites (r) at the receiver position () act as a series of continuous signal transmission sources. he i-th visible GPS satellite r i moves with velocity. V and V express the V ri velocity vectors of the -th imaged obect O and the GPS receiver respectively. is placed near the obect O. All coordinates of r i, O, and, as well as their velocity vectors, are expressed in the Earth Centred Earth Fixed (ECEF) coordinate system. o frequency modulated (FM) GPS signal. he received indirect GPS signal at receiver will be an approximately linear FM GPS signal. It has been demonstrated that the range resolution of radar is an inverse ratio of the bandwidth of the signal. Hence this makes it possible for the multi-static SA imaging system to get an enough acting range and resolution simultaneously, since the linear frequency modulated GPS signal has the good property of pulse compression. 3 Imaging esolution In such a multi-static SA imaging system, indirect GPS signals that have been reflected from obects are used for their detection using the bistatic radar principle. he spatial resolution is enhanced by the synthetic aperture radar (SA) technique. As shown in Figure 1, suppose the ranges between r i and O and between O and at the beginning of the observation period are represented by and respectively. During the period of measurement, the corresponding ranges are varied with respect to time t and are represented by r i ( ) and ( ) respectively. 1 t r t 1i r 1 i(t) = 1 i + ( V V ) t (1a) r r i O (t) = + ( V ) t (1b) V O Suppose the signal which is transmitted from the GPS satellite is: S = d( t) e[ A exp( w t)] () ri where d(t) is the C/A code (or P code), and w c is the carrier frequency. he received signal at O in complex form is: S O i c [ t α ] K F A exp{ w [ t α ( )]} = d i 1i 1i c 1 1 i t where α 1 i = r1 i / c is the time delay of the signal from the GPS satellite ri to obect O, c is the speed of light, and is the scatter coefficient. is a factor F 1 i which is associated with ( ) and. r1 i t F 1i K 1i (3) Fig. 1 3D Multi-static SA System Model For the terrain imaging application, the bistatic radar principle and the synthetic aperture radar technique are used in the signal processing. If r i, O, and move with constant velocities during the observation period, the signal obtained at the O position will be a linear he Doppler frequency shift caused by the movement of r i and O is: 1 1 f 1 ( ) 1 cos i t Vr + i O t i Vr V i O γ ri λ 1i (if 1 i >> V t ) (4) r i O

3 36 Journal of Global Positioning Systems γ ri where is the angle between and, and λ is V ri V o the wavelength of the GPS signal. hen receives the reflected GPS signal from obect O: S [ t α1 i ] K F exp{ woi [ t α ]} w Oi [ ] = d α A (5) where α t) r c and (t) = 1 t ( = / k ai π λ 1i V r i O π λ V O (11) Since the characteristic of the correlation function near the peak of the compressed wave is of interest in this discussion of resolution, let >> τ. So: [ S )] sin c[ k τ / ] π Env i ( f f ( ) ai s c + i. he spatial resolution in directions x and y is: s τ (1) he Doppler frequency shift caused by the relative movement of O and is: f i 1 = π d dt w Oi r c where γ is the angle between V and V. he frequency at is: f o (6) t) = f + f f ( ) (7) i ( c 1i + i t hus, the received signal at is: S [ t α ( t ] K F = d α A i 1 i ) t exp π f i ( t dt 0 1) (8) As the coefficients of items with t can be ignored, (t ) can be considered as an approximately linear FM S i signal. In order to improve the bearing resolution, S i must be compressed. Because the auto-correlating function of a linear FM signal exhibits a narrow pulse property, the output wave will become even more narrow when (t ) is passed through a matching filter. (A S i matching filter is also an optimum filter for signal detection in a white noise environment.) Hence, a matching filter is employed in the received signal processing to improve the system resolution. he output of the matching filter is: s s S ( τ ) = S ( t + τ ) S dt (9) i τ i * where s is the observation time. It can be demonstrated that the normalised envelope E nv[ ] of S i (τ ) is: E nv where s [ S ] = τ ( τ ) exp( k t τ ) dt i s ai i 1 = sin c k ai τ ( s τ ) (10) (t ) Vr x O x + Vx i O x ρ x λ (13a) s V r i O V O + 1i Vr y O y + Vy i O y ρ y λ (13b) s Vr i O V O + 1i he authors have simulated such an imaging system, with the transmitters, receiver, and obects moving at different velocities. 4 Simulations Assume that the observation time is from 00:00:00 4 Sept. 001 to 00:00:0 4 Sept he coordinate of receiver is [ x, y, z ]=[ , , ]m. At this time the distribution of visible GPS satellites is illustrated in Figure. As an example, the signals from satellites # and #4 are used in the obect imaging, and their characteristics are shown in able 1. Suppose there are two targets (O, =1,) in initial locations [ x, yo, z ]=[ , , - O ]m and [,, ]=[ , , - x O ]m respectively. 1 O 1 y O z O ab. 1 Position & Velocity Parameters of Satellite # and #4 During Observation ime GPS Sat. No. # #4 Position ( -5.15, [ xr, yr, zr ] -8.04, 10 6 m ) Velocity ( -4.05, (V rx, V ry, V rz ) -5.41, 10 m/s 30.3 ) (-3.57, 1.33, -1.90) ( 1.07, -3.1, ) Figure 3 shows the simulation results for each scenario in able. Figure 3(a)(b) and (c)(d) show that the resolution ρ is related to the relative velocities of O and. For a static receiver and moving target with speed (0,10,0)m/s, its spatial resolution is the same as that for a static target

4 Li: 3D Multi-static SA System for errain Imaging 37 with receiver moving with velocity (0,-10,0)m/s. he greater the relative speed, the higher the resolution. As indicated in Figure 3(a)(c) and (b)(d), ρ is also a function of the position of ri with respect to and O. GPS Sat. No. (V x, V y, V z ) m/s Fig. Distribution of Satellites During Observation ime (V O1x, V O1y, V O1z ) m/s ab. Scenarios in the Simulation (V Ox, V Oy, V Oz ) m/s obect 1 obect ρ o1x (m) ρ o1y (m) ρ ox (m) ρ oy (m) (0,0,0) (0,10,0) (0,10,0) (0,-10,0) (0,0,0) (0,7,0) (0,0,0) (0,10,0) (0,10,0) (0,-10,0) (0,0,0) (0,7,0) Fig. 3: Simulation esult

5 38 Journal of Global Positioning Systems Fig. 3 Simulation esult (Continuous)

6 Li: 3D Multi-static SA System for errain Imaging 39 5 Concluding emarks his paper describes a 3D multi-static SA imaging system using the reflected GPS signals. he bistatic radar principle is used to detect movement of, or changes to, the imaged obect. he indirect GPS signals are processed by a match filter with the aim of improving the spatial resolution of detection. he measure of spatial resolution of this imaging system is derived, and is confirmed via simulation studies. he simulation results show that the indirect GPS signals can be used for certain remote sensing applications. In such multi-static SA imaging system the detection based only on the reflected GPS signal can be made for moving obects and a moving receiver. he spatial resolution is a function of the mutual positions and velocities of the satellites, imaged obects, and receiver. he 3-D multi-static SA model also has potential benefits in sea surface imaging and target detection. eferences Armatys M., et al (000), Exploiting GPS as a New Oceanographic emote Sensing ool, National echnical Meeting of the U.S. Institute of Navigation, Anaheim, California, 6-8 January, Komathy A., et al (001), Developments in Using GPS for Oceanographic emote Sensing: etrieval of Ocean Surface Wind Speed and Wind Direction, National echnical Meeting of the U.S. Institute of Navigation, Long Beach, California, -4 January. Martin-Neira M., et al(001), he PAIS Concept: An Experimental Demonstration of Sea Surface Altimetry using GPS eflected Signals, IEEE rans. on Geosci. & emote Sensing, 39(1), Garrison J.L, et al (00), Wind Speed Measurement Using Forward Scattered GPS Signals, IEEE rans. on Geosci. & emote Sensing, 40(1), Zavorotny V.U. & A.G. Voronovich (000), Scattering of GPS Signals from the Ocean with Wind emote Sensing Application, IEEE rans. on Geosci. & emote Sensing, 38(), Komathy A., et al (000), owards GPS Surface eflection emote Sensing of Sea Ice Conditions, Sixth Int. Conf. on emote Sensing for Marine & Coastal Environments, II: Masters D., et al (000), GPS Signal Scattering from Land for Moisture Content Determination, Proceedings of IEEE International Geoscience. & emote Sensing Symposium, vol.7: Garrison J.L. & S.J. Katzberg (1997), Detection of Ocean eflected GPS Signals: heory and Experiment, IEEE Southeastcon Blacksburg'97 Engineering New New Century, USA, 1-14 April, Zavorotny Z.U., et al (000), Extraction of Sea State and Wind Speed from eflected GPS Signals: Modeling and Aircraft Measurements, IEEE Int. Geosci. & emote Sensing Symposium, 4: Komathy A., et al (1998), GPS Signal Scattering from Sea Surface: Comparison Between Experimental Data and heoretical Model, Fifth Int. Conf. on emote Sensing for Marine & Coastal Environments, 1: Komathy A., et al (000), GPS Signal Scattering from Sea Surface: Wind Speed etrieval Using Experimental Data and heoretical Model, emote Sensing of Environment, 73, Lin B., et al (1998), he elationship Between the GPS Signals eflected from Sea Surface and the Surface Winds: Modeling esults and Comparisons with Aircraft Measurements, J. of Geophysical esearch - Oceans, 104(C9), Elfouhaily. & C. Zuffada (000), On Deriving Near-Surface Wind Vector Information from GPS Ocean eflections: Simulation and Measurements, IEEE Int. Geosci. & emote Sensing Symposium, 7: Lowe S.., et al (000), An Ocean-Altimetry Measurement Using eflected GPS Signals Observed from a Low- Altitude Aircraft, IEEE Int. Geosci. & emote Sensing Symposium, 5: Willis N.(1991), Bistatic adar, Artech house Inc., Norwood.