Finite escape means the occurrence of an infinite value in the solution of a time-varyingdifferential equation. Finite escape can occur in the computation of either the Kalman or the Kalman-Bucy filter because the gain is time-varying. When no escape occurs it is analogous to the Heisenberg uncertainty principle [1] in atomic physics. Three noisy examples are given: a single integrator, a double integrator, and a linear oscillator. Finite escape cannot happen in the single integrator or the underdamped linear oscillator, but can happen in the double integrator and undamped linear oscillator. Therefore, finite escape can occur in the estimation of any noisy dynamic system. Except in special situations, it is impossible to achieve certainty in the determination of all state variables using neural nets, machine learning, or artificial intelligence even with an infinite amount of data. Conditions for finite escape to occur are given. Finally, practical solutions for escape are considered for the linear oscillator.

High Frequency (3-30 MHz) radars measure the speed and direction of oceansurface currents in near real time by emitting a vertically polarized electromagnetic signal along the electrically conductive ocean surface. This signal is coherently back-scattered by Bragg resonant ocean waves – travelling radially away or towards the radar with ocean wavelength equal to half of the radar wavelength. More than 400 oceanographic HF radars worldwide use this strong coherent return of energy (Bragg scattering) and its Doppler shift to infer the radial velocity of the surface water and to map the radial currents hourly with 1 to 5 km range resolution. The primary objective of this study is to recognize and isolate the first-order Bragg back-scattered echoes, which are necessary for mapping currents, while excluding second-order echoes that lead to erroneous ocean current estimates. Setting the boundaries of the first order Bragg peaks in the echo Doppler spectra is a very important task. We have observed how present algorithms fail under certain circumstances, e.g. when ocean conditions are influenced by tides or strong off-shore currents and in regions around islands. In order to avoid some of the known shortcomings of conventional methods we have developed a new algorithm to find initial estimates of the boundaries between first and second order echoes by using more advanced null detection methods and normalized radar spectra across multiple ranges. In addition, our approach keeps track of the spatial and temporal history of data and applies Bayesian estimation techniques to the observed radar back-scatter spectra to detect and filter out erroneous observations. Several Bayesian sequential estimation techniques were tested to improve the estimation of the first-order Bragg echo boundaries in the aforementioned challenging scenarios. We begin with simple filters like G-H and Kalman and include more advanced ones like Nearest Neighbor and Probabilistic Data Association filters. Applying these filters to the initial estimates provided by the proposed nullfinding method provides better first-order boundary results than filtering previous conventional estimates. By accepting more valid ocean current radial vectors, yet rejecting second-order spectrum and noise or interference, we improve radial current vector maps.