[Paper Review] Coherent Track Before Detect: Detection via simultaneous trajectory estimation and long time integration

Kimin Kim, Murat Üney+1 more|arXiv (Cornell University)|Sep 1, 2017

Target Tracking and Data Fusion in Sensor Networks23 references3 citations

TL;DR

This paper proposes a coherent track-before-detect framework that simultaneously estimates object trajectories and performs long-time coherent integration across multiple coherent processing intervals (CPIs) in mono-static, bi-static, and multi-static radar configurations. By coherently integrating reflection coefficients while estimating unknown time reference shifts in separated transmitters, the method achieves near-optimal detection performance for low SNR, manoeuvring objects, even when conventional techniques fail.

ABSTRACT

In this work, we consider the detection of manoeuvring small objects with radars. Such objects induce low signal to noise ratio (SNR) reflections in the received signal. We consider both co-located and separated transmitter/receiver pairs, i.e., mono-static and bi-static configurations, respectively, as well as multi-static settings involving both types. We propose coherent track before detect: A detection approach which is capable of coherently integrating these reflections within a coherent processing interval (CPI) in all these configurations and continuing integration for an arbitrarily long time across consecutive CPIs. {We estimate the complex value of the reflection coefficients for integration while simultaneously estimating the object trajectory. Compounded with these computations is the estimation of the unknown time reference shift of the separated transmitters necessary for coherent processing.} Detection is made by using the resulting integration value in a Neyman-Pearson test against a constant false alarm rate threshold. We demonstrate the efficacy of our approach in a simulation example with a very low SNR object which cannot be detected with conventional techniques.

Motivation & Objective

• To address the challenge of detecting low signal-to-noise ratio (SNR) and manoeuvring small objects in radar surveillance.
• To overcome the limitations of conventional pulse integration, which fails to track objects across range-Doppler bins due to trajectory motion.
• To enable coherent integration over arbitrarily long time intervals by simultaneously estimating trajectory and reflection coefficients.
• To resolve the synchronization problem in bi-static and multi-static radar by estimating unknown time reference shifts between remote transmitters and local receivers.
• To achieve detection performance close to the theoretical optimum (clairvoyant integrator) using a Neyman-Pearson test on integrated complex amplitudes.

Proposed method

• The method performs simultaneous trajectory estimation and long-time coherent integration of complex reflection coefficients across multiple CPIs.
• It uses a likelihood-based approach to model the joint distribution of measurements under signal and noise hypotheses, incorporating trajectory and time-reference uncertainty.
• The algorithm estimates the complex reflection coefficient for each CPI while tracking the object's state (position, velocity) via Bayesian inference.
• It accounts for unknown time reference shifts in bi-static systems by jointly estimating the transmitter-receiver time offset during integration.
• Non-coherent integration is performed across different radar channels (mono-static and bi-static) after coherent integration within each CPI.
• A Neyman-Pearson test is applied to the final integrated complex value to detect object presence at a constant false alarm rate (CFAR).

Experimental results

Research questions

• RQ1 Can long-time coherent integration be effectively achieved for manoeuvring targets when conventional methods fail due to low SNR?
• RQ2 How can coherent integration be maintained across multiple CPIs when the target's trajectory moves across range-Doppler resolution cells?
• RQ3 What is the impact of unknown time reference shifts in bi-static radar systems on coherent integration performance?
• RQ4 Can simultaneous trajectory estimation and reflection coefficient integration outperform conventional track-before-detect methods that use only magnitude information?
• RQ5 To what extent can the proposed method approach the performance of a clairvoyant integrator with perfect knowledge of target trajectory and reflection coefficient?

Key findings

• The proposed method achieves detection performance close to the theoretical optimum of a clairvoyant integrator, even for very low SNR targets.
• The method successfully detects a target with an SNR below the detection threshold of conventional matched filtering and non-coherent integration.
• Joint estimation of trajectory and complex reflection coefficient enables coherent integration over arbitrarily long time intervals, overcoming the limitations of fixed-CPI processing.
• The Cramér-Rao bound (CRB) analysis confirms that the estimator achieves near-minimum variance for the complex reflection coefficient, validating its statistical efficiency.
• The algorithm effectively resolves unknown time reference shifts in bi-static configurations, enabling coherent processing without requiring precise transmitter-receiver synchronization.
• Simulation results demonstrate that the method can detect targets that are undetectable using standard track-before-detect or conventional integration techniques.