Track-Before-Detect Algorithm Based on Dynamic Programming

In radar signal processing, Track-Before-Detect (TBD) represents an advanced target detection technique, particularly effective in low signal-to-noise ratio environments. Dynamic Programming (DP), as one of the core algorithms for TBD, significantly enhances weak target detection capabilities through joint processing of multi-frame data. The implementation typically involves constructing a state transition matrix and recursively computing cumulative likelihood ratios across frames.

Probability of Detection (Pd) and Constant False Alarm Rate (CFAR) serve as fundamental evaluation metrics for TBD algorithms. The dynamic programming TBD balances these metrics through the following mechanism: First, the algorithm constructs a state transition grid from multi-frame observation data, using dynamic programming recursion to calculate cumulative likelihood ratios. Second, during each state update step, a CFAR threshold is introduced to eliminate false alarm paths caused by noise while retaining potential target trajectories. This approach enables the detection probability to increase with the number of accumulated frames, while adaptively controlling the false alarm rate through threshold adjustments. Code implementation often involves creating a DP score matrix where each cell stores the maximum cumulative score reaching that state, with threshold pruning applied at each iteration.

Key optimization aspects include: 1) The state transition model must align with target motion characteristics, which in practice requires defining appropriate state variables (e.g., position, velocity) and transition probabilities; 2) Threshold design must balance sensitivity and stability, often implemented through adaptive CFAR techniques like cell-averaging or order-statistics CFAR. In practical applications, Monte Carlo simulations are commonly employed to determine optimal parameter combinations, achieving maximum detection probability under low false-alarm constraints. Algorithm tuning typically involves sweeping parameters such as process noise covariance and detection thresholds while evaluating receiver operating characteristics (ROC) curves.