# Problem definition

Parameter estimation problems typically have two phases: *estimation* and *configuration*:

> estimation > / \ (physical system) (model) \ / < configuration <

Typically the physical system is modelled, and parameter estimation techniques apply inputs to the physical system and use its measured output to derive/estimate the model parameters [CRE08].

If the *physical system* is a multi-neuron chip and the model is a set of equations, or a SW program, we can use the same Dynamic Parameter Estimation (DPE) techniques to *estimate* the model parameters based on the chip's bias settings used.

If on the other hand we have a set of equation or model parameters, and we want to *configure* the chip to reproduce the model dynamics, we have to use a different solution.

### General aspects

- Physical time
- In our hybrid analog/digital VLSI systems "time represents itself". That is, time is not discretized (no global clock), circuits perform in
*physical time*, and signals are transmitted using asynchronous communication protocols.

- In our hybrid analog/digital VLSI systems "time represents itself". That is, time is not discretized (no global clock), circuits perform in
- Real-time
- Typically, we'll need to find configuration settings so that our chips and systems perform in
*real-time*. Note that this does not necessarily mean that the time constants of the neurons and synapses have to match the ones of real/biological systems. - A real-time behaving system will need to be configured so that the system can process sensory signals and produce (motor) outputs with delays that are not perceivable by the users that the system interacts with.

- Typically, we'll need to find configuration settings so that our chips and systems perform in
- Matching time-constants
- Processing signals with given dynamics requires appropriate time-constants. Increasing time constants above the minimum required does not improve the system performance (and leads to inefficient use of resources).
- In absence of a specific task with specific dynamics, we choose to use biologically realistic time constants, so that the physical system can on principle emulate human-relevant behaviours

### Multi-neuron chip parameter estimation/bias configuration

Multi-neuron chips typically comprise sets of VLSI neurons and synapses with fixed and/or configurable network topologies. Parameters affect properties of synapses, neurons, and networks. The general procedure for estimating optimal bias configurations is pretty straightforward. The specific procedures/modules for configuring synapse and neuron parameters are more tricky, and discussed in this page.

[CRE08] | Creveling et al. 2008, "State and parameter estimation in nonlinear systems as an optimal tracking problem", http://www.sciencedirect.com/science/article/B6TVM-4RH94RX-2/2/e087d04483f706ca711aa3c9aba883f7 |