Target Tracking: Statistics of Successive Successful Target Detection in Automotive Radar Networks

TL;DR

The paper defines tracking probability as the probability that an ego automotive radar detects a target in at least $\nu$ consecutive slots within a block of $T$ slots, linking this metric to QoS requirements through a block ALOHA MAC. Using stochastic geometry, it derives the conditional detection probability $P_d$ under network realization $\Phi$, then obtains the CCDF of the tracking length $L$ via de Moivre's theorem and computes moments $\zeta(l)$ to characterize the average tracking performance. A QoS-aware frame-design framework optimizes the MAC parameter $\delta$ and the block structure by maximizing $(1-(1-\delta)^N)P_t$, revealing that the MAC setting that maximizes detection may not maximize tracking. The results show how frame length, beamwidth, street/vehicle density, shadowing, and use-case QoS requirements influence tracking, and demonstrate the feasibility of a centralized, network-assisted parameter configuration for adaptive radar sensing in urban vehicular networks.

Abstract

We introduce a novel metric for stochastic geometry based analysis of automotive radar networks called target {\it tracking probability}. Unlike the well-investigated detection probability (often termed as the success or coverage probability in stochastic geometry), the tracking probability characterizes the event of successive successful target detection with a sequence of radar pulses. From a theoretical standpoint, this work adds to the rich repertoire of statistical metrics in stochastic geometry-based wireless network analysis. To optimize the target tracking probability in high interference scenarios, we study a block medium access control (MAC) protocol for the automotive radars to share a common channel and recommend the optimal MAC parameter for a given vehicle and street density. Importantly, we show that the optimal MAC parameter that maximizes the detection probability may not be the one that maximizes the tracking probability. Our research reveals how the tracking event can be naturally mapped to the quality of service (QoS) requirements of latency and reliability for different vehicular technology use-cases. This can enable use-case specific adaptive selection of radar parameters for optimal target tracking.

Figures (14)

• Figure 1: Illustration of the interfering ranges in an intersecting street in $L_0$.
• Figure 2: Illustration of the frame design and the MAC protocol from the perspective of the ego-radar.
• Figure 3: Comparison of detection and tracking performance with respect to the ALOHA parameter. Here $\lambda = 5e-2$ m$^{-1}$, $T = 20$ slots, $\nu = 6$, and $\lambda_L = 5e-4$ m$^{-1}$.
• Figure 4: Impact of shadowing on the trends of the tracking probability with respect to $\nu$.
• Figure 5: Impact of the system parameters on the tracking probability with respect to $\nu$. Here $R = 10$ m.

Theorems & Definitions (15)

• Definition 1
• lemma 1
• Definition 2: Successful target detection
• Definition 3: Successful target tracking
• lemma 2
• Remark 1
• Remark 2
• Remark 3
• Theorem 1
• lemma 3