A. Dong, N. Garcia, A.M. Haimovich

Transcription

1 A. Dong, N. Garcia, A.M. Haimovich

2 2 Goal: Localization (geolocation) of unknown RF emitters in multipath environments Challenges: Conventional methods such as TDOA based on line-of-sight (LOS) Non-line-of-sight (NLOS) paths Blocked LOS paths (e.g. indoor source) Applications: Defense applications Location based services E9

3 3 Goal Estimate emitters locations Sensor assumptions Network of distributed sensors with fixed, known locations Sensors have ideal communication with a fusion center Sensors are time synchronized Source assumptions Emitter waveforms are unknown Fusion center PSD is known Channel assumptions Time-invariant unknown multipath channel No prior information on the multipath channel

4 4 Sensor Step Step 2 Estimate TDOA s Multilateration Sensor 2 Multilateration Indirect localization Direct Positioning Determination (DPD) [Weiss 2004] 000 Sensor 3 Downconverted baseband signals 0 Direct localization

5 5 TDOA, DPD fail in multipath channels can not apply the principle that the shortest delay difference = LOS TDOA Very scarce literature on localizing emitters over multipath channels. sensor2 sensor sensor sensor2 TDOA t 0 t 0 < TDOA

6 6 Signal at n-th sensor t Q Q ( ) ( ( )) ( m) ( m) z = α τ + β τ + n t sq n pq sq N sensors, Q emitters s q = source e signals LOS α = p q β τ NLOS = ( m) ( m) = = ( t ) wn ( t ) n q n q = q = m = complex gain LOS source location path complex gain NLOS path multipath time delay M M t t w t LOS NLOS

7 7 Signal model for n-th sensor (frequency domain) Q ( m j2πτ f ) n ( pq ) ( m) j2πfτ z f = s f e + β s f e + w f n ( ) α ( ) q q= q= m= LOS NLOS Covariance matrix H ( f) = E ( f) ( f) R z z Model of vectorized covariance matrix γ γ S ( ) ( ) Q M q ( ) ( ) ( f) = vec R ( f) ( m j2πτ f ) n ( pq ) ( m) j2πfτ f = x S f e + y S f e + w f n q q q= q= m= q ( f) Q LOS NLOS = known power spectral density Covariance matrix depends on unknown parameters γ ; ( m) ( m) θ = x,,,, τ pq M y Q M ( ) n n ( f θ) ( ) ( )

8 8 MLE of unknown parameters from covariance matrix is too difficult Simpler alternative: approximate cov mat with sample cov mat Compute the sample covariance matrix Vectorize R = γ = J H zz j j J j = vec ( R ) Solve optimization to find C min θ ( ( )) H γ γ θ C γ γ ( θ) ( ) is the covariance matrix of the residue ( )( ) H γ γ γ γ C = E R R J θ ( )

9 9 Even applying COMET leads to very complex problem Measurements Unknown parameters related to LOS paths Unknown parameters related to NLOS paths min x, pq M ( m), τ ( m y ) C /2 ( ( ) ( ) γ γ ( x,,,, τ )) m m pq M y 2 Large pool of unknown parameters Impractical complexity

10 0. A small number of sources Q to be localized 2. A large number of possible locations for the sources G >> Q θ θ 2 Possible emitter locations Emitter θ G Φ LOS g + noooo Φ NLOS m GN x Q<<G Measurements N x Transfer matrix Locations Measurements N x GN NLOS Highly underdetermined system Unique solution under sparsity assumption Efficient algorithms active area of research

11 Emitters are sparse LOS originate from common location NLOS is local to the sensors Mixed norm optimization to control LOS vs. NLOS assignments min x g, y m G M v xg + 2 ym g= m= subject to G /2 LOS γ = Φ x + Φ g= g C g ( γ γ) ε M m= 2 2 NLOS m y m

12 2 Design challenge Explain received data with correct mixture of LOS and NLOS min x g G v x + M y g, 2 m y m g= m= Source is missed when LOS is explained as NLOS False alarm occurs when NLOS is explained as LOS Theorem Given measurements collected by L sensors and L < L, if L L < v < L L, then the optimization problem will seek a feasible solution that explains a source with no less than L LOS components Significance L LOS components are not explained as NLOS (prevent missed source) Fewer than L NLOS components are not explained as LOS (prevent false alarm)

13 3 0 MHz emitter (30 m ranging resolution) Multipath channel RMS delay spread is 500 ns (exponential profile, Poisson arrivals) Search area: 200 x 200 m 5 sensor and emitter 000 samples/sensor Channel impulse response

14 4 Correct recovery if error smaller than 0 m Unknown signal

15 5 Correct recovery if error smaller than 0 30 m

16 6 Error normalized to 30m SNR = 30 db per sample (000 samples and 5 sensors)

17 7 SNR = 30 0 db per sample

18 8 A novel approach for localizing unknown emitters over multipath channels Solution developed directly from observations Solution relies on sparsity of emitters and of multipath Solution is blind with respect to transmitted signals and channel Mixed norm optimization exploits properties of LOS vs. NLOS