Parameter Estimation in System Identification

1. System Identification = Model structure selection or define + Model parameter estimation

2. Parameter estimation is a mapping: Z----> sigma*

3. Essence of Model is its prediction ability.

4. Two criteria:

Scalar norm or function of errors

Data are not related to Predictive error.

pem and lsqcurvefit

they are really sensitive to initial condition and parameter values.

this really haunting on me several days.

Something Help Kalman

Hinfinity Filter is a minmax filter, which minimise worsts estimation. Meanwhile, Kalman minimise average estimation error.

Kalman Smoother is useful, when you want to estimate the state trajectory after obtaining the whole signal serials.

Steady State Kalman filter have constant K and P.

State Space Realization of IIR

cited from [https://ccrma.stanford.edu/~jos/fp/State_Space_Realization.html]

IIR filters have an extensively used matrix representation called state space form (or ``state space realizations''). They are especially convenient for representing filters with multiple inputs andmultiple outputs (MIMO filters). An order digital filter with inputs and outputs can be written in state-space form as follows:

			(F.4)

where is the length state vector at discrete time , is a vector of inputs, and the output vector. is the state transition matrix, and it determines thedynamics of the system (its poles, or resonant modes).