Microwave Imaging of Airborne Targets

Transcription

1 IMA, October 2005 Microwave Imaging of Airborne Targets Brett Borden Physics Department, Naval Postgraduate School, Monterey, CA USA Telephone: ; Fax: ;

2 Methods for airborne target ID Target ID: match a target signature to a template in a template library. Non-imaging methods. Existing methods: Identify Friend/Foe (IFF) transponder; Jet Engine Modulation (JEM); Radar operator experience. Methods in (limited) development: Polarization-based classifiers; Target resonances; Target skin-induced modulation. The imaging methods are, essentially, HRR and ISAR.

3 Overview Background: Radar data; Radar imaging; Standard methods. Current research: Model errors; Image artifacts; Ad hoc mitigation schemes. Research opportunities

4 Radar parameters: range and speed Distance estimates Short time-domain pulses Pulse return time-delay t Velocity estimates Short frequency-domain pulses Doppler frequency shift ω D Range: R = ct/2 Range-rate: v R = cω D /2ω 0

5 Radar detection in noise Scattered field energy falls off as R 4 Thermal noise in receiver can swamp measured field E meas (t) = E scatt (t) + n(t) Scattered field power ~ Watts is not uncommon Expand the measured field as Ẽ(t) = i where C i = E meas (t )φ i (t )dt C i φ i (t) and φ i are chosen by maximum likelihood: max φ i model space p n The Ci become the radar data ( ) E meas Ẽ

6 Correlation reception p n (n) Gaussian φ i (t 0 ) = E scatt;i (t 0 ): But what is E scatt;i (t 0 )? Isotropic point scatterer target at (t i, ω D) E scatt;i (t ) = E inc (t t i ) e iω D(t t i ). Radar data are output from the correlation receiver: data(t i, ω D ) = E meas (t ) Einc(t t i ) e iω D(t t i ) dt.

7 Measurement scheme data N M = E meas (t ) E 1,1 (t ) E 1,2 (t )... E 1,M (t ) E 2,1 (t ) E 2,2 (t )... E 2,M (t ) E N,1 (t )E N,2 (t )...E N,M (t ) dt. E i,j (t ) E inc (t t i ) e iν j(t t i ) Blip dimensions are determined by the Ambiguity Function.

8 Scintillation Radar systems were developed to exploit the early model: targets are isotropic points. Model evolution: Decreasing radar wavelengths increasing sensitivity to sub-scatterers; Scintillation is caused by sub-scatterer interference.

9 Correlation with more complete scattering models High frequency scattering. Accurate numerical calculations require: Typical size: thousands to millions of unknowns; Typical times: hours to days. Very active area of research. May be unnecessary for target identification. Ad hoc simplifications. Ignore infrequent scattering events. Reduce number of unknowns to minimal set. Canonical set of scatterer types. Sub-scatterers do not interact.

10 The usual (simplified) target model Present-day model: Scattered field is usually estimated by asymptotic methods; Target is usually represented as collection of scattering centers; Multiple scattering is usually ignored. (More) general model: scattered signal obeys E scatt (t) = ρ(t, ω D) E inc (t t ) e iω D (t t ) dt dω D. Scattering center density function: generally depends on target/radar relative position

11 Radar ambiguity data(t, ω D ) ρ(t, ω D) A(t t, ω D ω D) dt dω D. Radar ambiguity function: A(t, ω) E inc(t t/2) E inc (t + t/2) e iωt dt. Forms a point spread function. Would like to use A(t, ω D ) = δ(t)δ(ω D ) but can t: t and ω are conjugate Fourier variables. Radar uncertainty principle.

12 The radar imaging equation Notation change for rigid bodies: t R, ω D v = dr/dt radar data(r, v) ρ(r, v ) A(R R, v v ) dr dv. Range-Doppler imaging. ρ(r,v) is target scatterer strength at range R and cross-range v. ρ(r,v) is assumed to be independent of θ. Fine resolution in v requires long dwell use fine resolution in R.

13 The range profile High range resolution imaging (HRR) uses A(R,v) δ(r) data(r) ρ(r, v ) dv. Range-only (wide band) version of radar imaging equation. Measured dependence on v (cross-range) requires multiple pulses.

14 Example 1-D image The Range Profile Peaks define 1-D target signature. Strength and location characterize the target (for each target orientation ). Typically, < 10 peaks used for target ID. Can be measured very quickly. Easy to implement. But, no cross-range information.

15 ID by template matching Measured range profile P (R) compared to template τ(r). Templates stored in template library. Templates generally parameterized by target type and target aspect. Comparisons usually performed by correlation. Typical result of match is target type and target orientation. Complications: Varying target configurations (stores); Broadside profiles contain little information; Ducts and cavities (and other model errors); Scintillation very large libraries.

16 Synthetic apertures Synthetic Aperture Radar (SAR): Target fixed; Antenna moves; Radar always points at the target (spotlight-mode). Inverse SAR (ISAR): Antenna fixed; Target rotates. Range profiles are now parameterized by target aspect angle θ: data(r, θ j ) R cos θ j +v sin θ j =R ρ(r, v )dl

17 The back-projection algorithm Range profiles collected at many different aspects Combined using backprojection Same scheme as used for x-ray tomography

18 Example 2-D aircraft image The ISAR image Two-dimensional image by backprojection. Cross-range information, but: Unknown dθ/dt image scaling issues; Lengthy data acquisition times; Difficult to implement (motion compensation).

19 DoD Relevance State-of-the-art radars (deployed or about to be deployed on airborne platforms) Some polarization functionality Multi-spectral (radar bands) Digital waveform selectivity Very large bandwidths (~ GHz) ISAR capable (near real-time) HRR capable (real-time) Goal is independent, all-weather, Non-Cooperative Target Classification/Recognition/Assessment

20 Problems with the model Underlying assumptions. Shape of the pulse is fundamentally unchanged: Sub-scatterers are noninteracting: E scatt (t) = E scatt (t) = E inc (t t ) e iω D(t t ) ρ(t, ω D) E inc (t t ) e iω D (t t ) dt dω D But: Scattering strength depends on wavelength; Scatterers can (and do) interact; Model mismatch image artifacts.

21 Point scatterers Point scatterer model Frequency-domain: ρ(r, v) = N n=1 a n δ(r R n )δ(v v n ). F{δ(R R n )}(k R ) = e ik RR n Actual behavior (k R = 2º/ ): Rayleigh scattering: r; Resonant scattering: r; Optical scattering: ø r.

22 Artifacts: isotropic points ρ(r, v) = N a n δ(r R n )δ(v v n ). n=1 Effectively isotropic if a n a n (θ) over the aperture θ. No problem for HRR profiles. Persistence a problem for ISAR. Effectively a point if scattering center is well-localized and position is independent of θ. Misbehaved scattering centers: Edges, flat and gently curved plates (rare and often ignored); Ducts and cavities (important special case); In images, these features are under-resolved and smudged.

23 Artifacts: multiple scattering Nonlinearity maybe more than one blip per scattering center.

24 Artifacts: structural dispersion Structural dispersion (from the waveguide model): F{ρ disp }(ω) D n (ω, θ) exp ( it ) ω 2 ωco 2. Ducts and cavities. Common to most aircraft. Observable at most aspects. Very strong returns. Displaced from expected (R = ct/2) position. Can occlude other scattering centers.

25 Artifacts: examples 10 GHz center frequency 5 sliding aperture 30 elevation

26 Expert systems Weak, point-scatterer model is mostly correct. Experienced observers can tell the difference. Structural dispersion (usually). Non-point scatterers (sometimes). Multiple scattering (rarely, though often invoked). This intuition should be coded in software. How? (AI, ANN, Genetic algorithms, etc.) Common justification: Traditional approaches haven t worked.

27 Point scatterer fixes: location Local amplitude unmodified: F{ρ(R, v)}(k R, k v ) = N n=1 a n F{δ(R R n )δ(v v n )}(k R, k v ). Approximate parametric models: replace F{δ(R)}(k R ). F{δ(R R n )}(k R ) = e ik RR n exp( ik R ϕ n (R)). (And similarly for F{δ(v v n )}(k v ).)

28 Point scatterer fixes: strength Fourier transform of the point scatterer model: F{ρ(R, v)}(k R, k v )= Advanced parametric models: a n a n (ω,θ). Frequency dependence: a n (ω,θ) (iω) α n, where α n {0,±½,±1}. Aspect dependence: a n (ω,θ) exp(β n θ). = N F{a n δ(r R n )δ(v v n )}(k R, k v ) n=1 N a n e ik RR n e ik vv n. n=1 Polarization dependence: a n [ã 11;n, ã 12;n, ã 22;n ] T

29 Structural dispersion F{ρ disp }(ω) a n (ω, θ) exp ( it ) ω 2 ωco 2 Time/frequency approaches. T/F behavior is dispersion-sensitive. Basis for filtering scheme. Expert system pattern matching. Large bandwidth required. Complex model fitting. More complete scattering models. Bessel function-like in time domain. Shooting and bouncing rays. More computationally expensive scattering models.

30 Multiple scattering Expert systems... Live with it (incorporate multiple scattering events into template library). Very detailed scattering model fitting.

31 Other issues Highly maneuvering targets. 3-D target motion. Imaging of multiple targets. Substructures for target identification?

32 Research Opportunities Multiple scattering effects Ground-bounce Re-entrant structures Urban environments Multistatic configurations Sparse data collection arrays Coherent correlation Passive (ambient) radar Foliage and ground penetrating radar imaging Signal design Superresolution

33 Some final comments Big issues are: Complex-valued data (imaging); Scattering model improvement (artifact mitigation); Real-time algorithms. Enabling technologies: Improved computational resources; Signal design; Improved system performance (digital radar).

34 IMA, October 2005 Microwave Imaging of Airborne Targets Brett Borden Physics Department, Naval Postgraduate School, Monterey, CA USA Telephone: ; Fax: ;