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Tracking Time-Varying Multipath Channels forActive Sonar Applications

Ashwani Koul, Gustaf Hendeby, Isaac Skog

Abstract

Reliable detection and tracking in active sonar require accurate and efficient learning of the acoustic multipath background environment. Conventionally, background learning is performed after transforming measurements into the range-Doppler domain, a step that is computationally expensive and can obscure phase-coherent structure useful for monitoring and tracking. This paper proposes a framework for learning and tracking the multipath background directly in the raw measurement domain. Starting from a wideband Doppler linearization of the impulse response of a time-varying multipath channel, a state-space model with a heteroscedastic measurement equation is derived. This model enables channel tracking using an extended Kalman filter (EKF), and unknown model parameters are learned from the marginalized likelihood. The statistical adequacy of the proposed models is assessed via a p-value significance test. Finally, this paper integrates the learned channel model into a sequential likelihood-ratio test for target detection. BELLHOP-based simulations show that the proposed model better captures channel dynamics induced by sea-surface fluctuations and transmitter and receiver drift, yielding more reliable detection in time-varying shallow-water environments

Tracking Time-Varying Multipath Channels forActive Sonar Applications

Abstract

Reliable detection and tracking in active sonar require accurate and efficient learning of the acoustic multipath background environment. Conventionally, background learning is performed after transforming measurements into the range-Doppler domain, a step that is computationally expensive and can obscure phase-coherent structure useful for monitoring and tracking. This paper proposes a framework for learning and tracking the multipath background directly in the raw measurement domain. Starting from a wideband Doppler linearization of the impulse response of a time-varying multipath channel, a state-space model with a heteroscedastic measurement equation is derived. This model enables channel tracking using an extended Kalman filter (EKF), and unknown model parameters are learned from the marginalized likelihood. The statistical adequacy of the proposed models is assessed via a p-value significance test. Finally, this paper integrates the learned channel model into a sequential likelihood-ratio test for target detection. BELLHOP-based simulations show that the proposed model better captures channel dynamics induced by sea-surface fluctuations and transmitter and receiver drift, yielding more reliable detection in time-varying shallow-water environments
Paper Structure (17 sections, 43 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 43 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Signal Model
  3. General Continuous Time Channel Model
  4. Wideband Linearized Model
  5. Discrete-Time Linearized Channel Model
  6. Stochastic Multipath Background Model
  7. State-Space Model
  8. Parameter Estimation
  9. Amplitude Tracking
  10. Hyperparameter Learning
  11. Evaluation Methodology
  12. $P$-value Significance Test
  13. Target Detection Performance
  14. Simulation Setup
  15. Results and Discussion
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Illustration of the considered bistatic sonar scenario with a time-varying multipath channel.
  • Figure 2: Simulated CIRs for three scenarios. The trajectories for the stationary and moving target are also shown in (a).
  • Figure 3: Mean time to detection (MTD) versus SNR at $\text{INR}=30$ dB. Solid lines show the mean detection delay over detected trials, and bounds indicate the 10--90 percentile range of detection delays.
  • Figure 4: Probability of detection $P_d$ versus SNR at $\text{INR}=30$ dB. A trial is counted as a missed detection if no alarm is raised by the final ping in the test horizon.
  • Figure 5: Cumulative distribution function (CDF) at an $\text{SNR} =10$ dB. The plateau level equals $P_d$, and the rise rate reflects detection latency.