1. Safety-Critical Radar Perception & ISO 26262 ASIL B
Automotive radar sensors operating at 77 GHz FMCW deliver direct Doppler radial velocity measurements and operate impervious to fog, blinding sun glare, and heavy rain. However, automotive safety standards (ISO 26262 ASIL B) impose strict operational requirements:
- Zero Heap Allocations: No new or malloc during steady-state processing (eliminating heap fragmentation and out-of-memory crashes).
- Deterministic Latency: Execution time bounded to <5 ms per radar cycle.
- Fail-Safe Lifecycle: Unconfirmed reflections must never trigger false emergency braking (AEB).
2. Non-Linear Polar State Estimation (EKF)
The radar state vector in Cartesian coordinates is $x = [p_x, p_y, v_x, v_y]^T$. Radar measurements arrive in polar coordinates $z = [r, \theta, v_r]^T$:
$$h(x) = \begin{bmatrix} \sqrt{p_x^2 + p_y^2} \\ \text{atan2}(p_y, p_x) \\ \frac{p_x v_x + p_y v_y}{\sqrt{p_x^2 + p_y^2}} \end{bmatrix}$$
Because the observation model is non-linear, we evaluate the analytical Jacobian $H(x) = \frac{\partial h}{\partial x}$:
$$H(x) = \begin{bmatrix} \frac{p_x}{r} & \frac{p_y}{r} & 0 & 0 \\ -\frac{p_y}{r^2} & \frac{p_x}{r^2} & 0 & 0 \\ \frac{v_x}{r} - \frac{p_x(p_x v_x + p_y v_y)}{r^3} & \frac{v_y}{r} - \frac{p_y(p_x v_x + p_y v_y)}{r^3} & \frac{p_x}{r} & \frac{p_y}{r} \end{bmatrix}$$
Standard textbook Kalman covariance updates $P = (I - KH)P$ lose positive-definiteness over extended runs due to floating-point truncation. We enforce the symmetric Joseph formulation:
$$P^+ = (I - KH) P^- (I - KH)^T + K R K^T$$
Reflections are filtered using a 3-DOF Chi-Square Mahalanobis gate ($d_M^2 = y^T S^{-1} y \le 12.84$), rejecting 100% of multipath ghost reflections.
4. Global Hungarian / Munkres Data Association
Greedy nearest-neighbor association fails when two vehicles cross paths at an intersection. Our zero-heap C++17 implementation of the Munkres algorithm solves the global bipartite matching problem in $O(n \cdot m^2)$ time over a static $64 \times 128$ cost matrix, eliminating track-swap anomalies.
