Dynamic Multipath Estimation by Sequential Monte Carlo Methods

Transcription

1 Dynamic Multipath Estimation by Sequential Monte Carlo Methods M. Lentmaier, B. Krach, P. Robertson, and T. Thiasiriphet German Aerospace Center (DLR) Slide 1

2 Outline Multipath problem and signal model Maximum-likelihood delay estimation Efficient likelihood computation Limitations of ML estimation Sequential Bayesian estimation Incorporation of channel characteristics Particle Filter implementation Simulation results Comparison with conventional DLL (narrow correlator) Slide 2

3 The Effect of Multipath Multipath: superposition of received signals with different amplitude and delay delayed path offset Offset in Loop-S curve: DLL estimate gets biased error due to multipath Signal with multipath at the receiver: Slide 3

4 Maximum Likelihood Estimation Discrete Signal Model: Likelihood function: τ 1 τ 1 τ 2 -τ 1 Slide 4

5 Efficient Likelihood Computation Bank of Correlators Signal-matched correlators: Likelihood Computation Data size reduction: Estimation within subspace Correlator outputs are sufficient statistics for delay estimation Fourier Interpolation: Continuous time-shifts possible Independent of sampling rate Correlator Outputs: Slide 5

6 Limitations of ML Estimation Urban channel measurement: Measurement vector: Parameters assumed constant during observation time ML estimator requires adjustments: Short coherent integration time measurements very noisy Longer integration time parameter changes violate assumptions Dependence of consecutive time instances not modeled adequately Slide 6

7 Sequential Bayesian Estimation Slide 7

8 Movement Model: Characterization of the Channel State vector: State transition process: (Markov model) τ k-1 τ k τ k+1 α k-1 α k α k+1 Slide 8

9 Movement Model with Path Activity Tracking State vector: Markovian multipath activity model: path activity 1 - p onoff 1 - p offon p onoff on off p offon Slide 9

10 Sampling Importance Resampling Particle Filter Start Maximum A Posteriori Initialization New Measurement Importance Sampling Resampling Minimum Mean Square Error w i k = p( z k x i k ) Weight Updating Output Estimation More Observation? End Slide 10

11 Posterior Distribution a posterior density of Direct path a posterior density of second path a posterior density of Direct path a posterior density of second path Delay [m] Delay [m] Represented by particles: Contains all uncertainty about range: perfect for sensor data fusion (also non-gaussian and multi modal PDFs) Slide 11

12 Simulation Results: Static Multipath RMSE [m] N m,k =2 N m,k =1 implicit estimation of N m,k Channel example: Static multipath Relative amplitude: 0.5 C/N 0 : 45 db-hz GPS C/A signal Relative Delay [m] 0.8 The model implicitly represents number of paths: Relative Delay [m] Slide 12

13 Simulation Results: Dynamic Multipath Delay x Speed of light [m] Channel example: Up to N m =3 paths Relative amplitude: 0.5 C/N 0 : 45 db-hz GPS C/A signal 0 Error [m] Time [s] Time [s] DLL with 0.1 chip spacing RMSE: 3.49 m Particle Filter with N s =20000 RMSE: 0.77 m Slide 13

14 Directions of Future Work Improved movement models Adaption to measured channels Complexity/performance tradeoffs Bayesian estimator in the position domain Complexity/performance tradeoffs Utilization of posterior PDFs Integrity Carrier phase positioning Combination with other sensors Slide 14