Accurate speed and range estimation from dual hyperbolic frequency modulated signals
Teodoro Aguilera, Fernando J. Álvarez · Signal Processing · 2026
Accurate speed and range estimation is critical in modern radar and sonar systems operating under challenging conditions such as high target velocities, low Signal-to-Noise Ratios (SNRs), and Doppler-induced distortions. Traditional linear frequency-modulated (LFM) signals suffer from range-Doppler coupling and reduced correlation performance when subjected to substantial Doppler shifts. This paper presents a comprehensive analytical and simulation-based study of Dual Hyperbolic Frequency-Modulated (DHFM) signals, which combine upward and downward frequency sweeps to enable simultaneous and decoupled estimation of target speed and range. We derive closed-form expressions for the matched filter response of DHFM waveforms under Doppler scaling and develop explicit formulas for speed and range extraction from the time separation of correlation peaks. Through extensive software simulations of an airborne sonar system, we systematically evaluate the impact of three key parameters: the sweep rate ( k ), Signal-to-Noise Ratio (SNR), and propagation-induced attenuation. Our results demonstrate that speed estimation errors drop below 0.05 m/s for k > 5000 across target speeds of up to 100 m/s, while range estimation remains below 0.2 m accuracy even at SNR levels as low as -15 dB. Distance attenuation analysis under ISO 9613-1 atmospheric absorption models shows that both estimators remain robust up to 200 m range with moderate k values. The findings establish DHFM signals as a superior alternative to conventional LFM waveforms for applications requiring high-accuracy parameter estimation in Doppler-sensitive environments, with particular relevance to airborne and underwater sonar systems.