Range-Doppler-Acceleration Estimation for Fast-Moving and Accelerating Targets

TL;DR

This work addresses range-Doppler estimation for fast-moving and accelerating targets by introducing a waveform-independent RD compression framework. It leverages a Cruise-and-Go approximation to linearize delay within each pulse while allowing inter-pulse acceleration, enabling pulse-wise FFT-based processing that compensates for intra-pulse Doppler-time distortion and inter-pulse range/Doppler migration. Key contributions include (i) a generalized RD compression that handles quadratic range, velocity variation, and waveform diversity; (ii) an explicit intra-pulse stretch compensation and inter-pulse acceleration correction; (iii) a unified performance metric predicting SNR loss via the acceleration ratio $\Upsilon = a T_{\mathsf{p}}(T_{\mathsf{p}}+\tau)/\lambda_c$ and practical guidelines for waveform selection. The method enables unbiased, real-time RD estimation in high-dynamics scenarios where conventional methods fail, with clear limitations quantified for large accelerations or long pulses.

Abstract

A central aspect of every pulsed radar signal processor is the targets Range-Doppler estimation within a Coherent Processing Interval. Conventional methods typically rely on simplifying assumptions, such as linear target motion, narrowband operation, or constant velocity, to enable fast computation. However, these assumptions break down in scenarios involving quadratic range-time behavior, high radial velocities or accelerations, or wideband signals, leading to undesired effects such as intra-pulse Doppler shift/stretch and target migration across Range-Doppler cells. This paper presents a generalized waveform-independent Range-Doppler compression approach that compensates for these effects while maintaining minimal Signal-to-Noise-Ratio loss and practical computational efficiency. The performance limits of the proposed method are analyzed and expressed through a unified metric that depends on both scene and system parameters. Comparison with other approaches is presented, showing their estimation bias and performance degradation.

Figures (5)

• Figure 1: Delay induced on transmitted signal by a target with quadratic range-profile. Within one pulse, we illustrate two transmitted samples (beginning and end of the waveform) at times $t_1$,$t_2$, and received at times $t_5,t_6$ respectively. The stretching effect is shown due to the high radial velocity---the received pulse length $\tilde{T}_{\text{tx}}$ is longer than $T_{\text{tx}}$.
• Figure 2: rd maps with and without acceleration compensation. The corresponding parameters are listed in Table \ref{['tab:tab_params_inter']}. The method is compensating for $a_0 = 0$ in the top plot and for the correct $a_0 = 300m\per s\squared$ in the bottom plot.
• Figure 3: Correlation of a simulated noise free target with the proposed method without (blue) and with (red) signal stretch (intra-pulse range migration). The waveform is a chirp and the target and system parameters are given in Table \ref{['tab:tab_params_stretch']}.
• Figure 4: rd maps with lfm (top) and Costas (bottom) waveform for a simulated target. The target and system parameters are given in Table \ref{['tab:tab_params_amb']}.
• Figure 5: snr loss of proposed method in dependence on acceleration ratio. In every case, a target was simulated and processed at the correct $v_0$ and $a_0$ and $r_0$. The resulting power, divided by the theoretical power of a perfect signal compensation, was plotted here, against the acceleration ratio. The parameter combinations used are given in Table \ref{['tab:tab_params_2']}.