Radio altimeters are an important component of modern helicopter on-board systems. These devices currently involve the use of narrowband deterministic signals, that limits their potential technical characteristics. Given the significant breakthrough in the development of wideband and ultra-wideband radio electronics, it is promising to create on-board radio complexes capable of obtaining the necessary information using wideband stochastic signals. At the same time, when developing such complexes, it is important to use optimal synthesis methods for radio systems, which will allow optimal signal processing algorithms and potential accuracy parameters to be obtained. In this work, the algorithm to measure flight altitude for a helicopter or an unmanned aerial vehicle based on the processing of wideband and ultra-wideband pulsed stochastic signals is synthesized for the first time by the maximum-likelihood method. When formulating the problem, the mathematical model of the signal and observation is specified, and their statistical characteristics are investigated. The peculiarity of the synthesis task is the use of a noise pulse transmitter, which implements the function of an underlying surface illuminator, as well as considering the signal structure destruction during its radiation, propagation, and reflection. This signal shape destruction makes it impossible to synthesize a radar with internally coherent processing when working on one receiving antenna. In accordance with the synthesized algorithm, a simulation model of a pulsed radar with a stochastic probing signal has been developed and the results of its modeling are presented.