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Localization is the process of inferring the absolute or relative position of an organism (or prey) from physical cues. The main physical methods are: triangulation by time difference of arrival (TDOA, used in echolocation and binaural hearing), signal strength (RSSI, used in electrolocation) and position accumulation by odometry (velocity integration).

TDOA converts time differences t between separate sensors into hyperbolic curves of possible position. The intersection of two or more hyperbolas locates the emitter. The human binaural auditory system uses interaural t (ITD, resolution ~10 s) and interaural level differences (ILD) to localize sounds with accuracy of ~12° in the horizontal plane.

The Kalman filter is the optimal estimator for linear systems with Gaussian noise. It combines the dynamic model prediction (F·x) with the sensory measurement correction (K·(z-H·x)), weighting each source by its uncertainty. Many biological neural systems implement computations analogous to the Kalman filter to integrate vestibular, visual, and proprioceptive signals.

The Cramér-Rao bound establishes the lower limit of the variance of the best possible estimator. For time delay estimation (TDOA), ²_pos c²/(4²·SNR·B²): larger B bandwidth and larger SNR improve localization. Dolphins and bats use broadband pulses precisely to maximize I_F and the accuracy of their echolocation.

Probabilistic occupancy maps (occupancy grids) accumulate sensory evidence over time to construct spatial representations of the environment. Each cell accumulates the probability of being occupied through sequential Bayesian updates. This approach is robust to noise and occlusions, and is the basis of autonomous navigation in robotics and probably in mammals with active exploration.

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