A Kalman filtering approach to the representation of kinematic quantities by the hippocampal-entorhinal complex

Abstract

Several regions of the brain which represent kinematic quantities are grouped under a single state-estimator framework. A theoretic effort is made to predict the activity of each cell population as a function of time using a simple state estimator (the Kalman filter). Three brain regions are considered in detail: the parietal cortex (reaching cells), the hippocampus (place cells and headdirection cells), and the entorhinal cortex (grid cells). For the reaching cell and place cell examples, we compute the perceived probability distributions of objects in the environment as a function of the observations. For the grid cell example, we show that the elastic behavior of the grids observed in experiments arises naturally from the Kalman filter. To our knowledge, the application of a tensor Kalman filter to grid cells is completely novel.

A computational cognitive framework of spatial memory in brains and robots

“…Particle filter-based models of localization on the algorithmic level have been suggested by (Fox and Prescott, 2010;Cheung et al, 2012). Osborn (2010) went beyond self localization, suggesting a Kalman filtering approach to also account for localizing objects in the environment. Recently, Penny et al (2013) argued that if one presupposes the existence of 'observation' and 'dynamic' models 5 , required by Kalman filters, one might as well extend the inference to also use them for model selection ('which environment am I in?…”

Gaussianity and the Kalman Filter: A Simple Yet Complicated Relationship

“…• "Since the Kalman framework requires Gaussian distributions, the model can only be constructed if ... " [2] • "The Kalman filter which is used for integrated navigation requires Gaussian variables ... a multimodal un-symmetric distribution has to be approximated with a Gaussian distribution before being used in the Kalman filter." [3] • "...can be best reconciled with the KF (which requires Gaussian probability distributions) by making the assumption that ... " [4] • " [The] Kalman filter requires Gaussian prior f (x 0 ) ... " [5] • "Notice that each of the distributions can be effectively approximated by a Gaussian. This is a very important result for the operation for many systems, especially the ones based on a Kalman filter since the filter explicitly requires Gaussian distributed noise on measurements for proper operation."…”

Event-based exponential synchronization of complex networks

“…During the past few years, complex networks have become an interesting research topic and appeal to have more attention in different fields from mathematics, biology, engineering sciences (Osborn 2010;Kamel and Xia 2009;Zhang et al 2013e, 2014bWatts and Strogatz 1998;Barabasi and Albert 1999;Zhou et al 2006;Strogatz 2001;Lü and Chen 2005). A complex network is a large set of interconnected nodes, where the nodes and connections can be anything, examples are internet, transportation networks, coupled biological and chemical engineering systems, neural networks in human brains and so on.…”