Adaptive Unscented Kalman Filter for Neuronal State and Parameter Estimation

Abstract

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

Reduced oriens-lacunosum/moleculare (OLM) cell model identifies biophysical current balances forin vivotheta frequency spiking resonance

“…Using our full, multi-compartment OLM cell model as an experimental proxy, we showed that it is possible to directly estimate parameter values from voltage recordings using a noisy input protocol that used multiple current steps. We limited our examination to estimating parameters of maximal conductances of four channel types but this is not a restriction of the RAUKF algorithm itself (Azzalini et al, 2022). Rather, we sought a proof of principle for the approach since we had both full, detailed multi-compartment OLM cell models and reduced single compartment models, the latter’s mathematical model structure that was used with the RAUKF algorithm.…”

“…Since the precise noise profile Q of the state vector X is not well known for a given neuronal model, and its respective discrepancies to the observation, we employed an adaptive method used in previous work in order to update Q as well as the estimate of the observation noise R over time (Azzalini et al, 2022). See SUPPLEMENTARY Material for further details.…”

“…The variables a and b are weights of how much Q and R will be updated proportional to the magnitude of fault detected. The values of a and b were set according to explorations done in previous work when RAUKF was applied to a conductance based model (Azzalini et al, 2022). a >> b was found to be effective and here we use a = 10 and b = 1.…”

“…Using our full, multi-compartment OLM cell model as an experimental proxy, we showed that it is possible to directly estimate parameter values from voltage recordings using a noisy input protocol that used multiple current steps. We limited our examination to estimating parameters of maximal conductances of four channel types but this is not a restriction of the RAUKF algorithm itself (Azzalini et al, 2022).…”

“…From an extensive exploration, we are able to show that a combination of h- and M-channels produce the controlling currents for theta frequency spiking resonance. Inspired by Azzalini et al (2022), we then move on to adjust a robust Kalman Filter (KF) algorithm and use it to estimate parameters of the reduced OLM cell model from membrane potential recordings of the model cells. This indicates that it should be possible to extract parameter values directly from experimental recordings in a real-time fashion.…”