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Mataveid 6.0
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DanielMartensson committed Apr 25, 2020
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Mataveid contains realization identification and polynomal algorithms. They can be quite hard to understand, so I highly recommend to read papers in the "reports" folder about the realization identification algorithms if you want to understand how they work.

### OKID - Observer Kalman Filter Identification
OKID is an algoritm that creates the impulse makrov parameter response from data for identify a state space model and also a kalman filter gain matrix. Use this if you got regular data from a dynamical system. This algorithm can handle both SISO and MISO. OKID have it's orgin from Hubble Telescope at NASA. This algorithm was invented 1993.
OKID is an algoritm that creates the impulse makrov parameter response from data for identify a state space model and also a kalman filter gain matrix. Use this if you got regular data from a dynamical system. This algorithm can handle both SISO and MISO. OKID have it's orgin from Hubble Telescope at NASA. This algorithm was invented 1991.

Use this algorithm if you got regular data from a open loop system.

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![a](https://raw.githubusercontent.com/DanielMartensson/Mataveid/master/pictures/OKID_Result.png)

### RLS - Recursive Least Squares
RLS is an algorithm that creates a state space model from regular data. Here you can select if you want to estimate an ARX model or an ARMAX model, depending on the number of zeros in the polynomal "nze". Select number of error-zeros-polynomal "nze" to 1, and you will get a ARX model or select "nze" equal to model poles "np", you will get an ARMAX model that also includes a kalman gain matrix K. I recommending that. This algorithm can handle data with high noise, but you will only get a SISO model from it. This algorithm was invented 1821, but it was until 1950 when it got its attention in adaptive control.
RLS is an algorithm that creates a state space model from regular data. Here you can select if you want to estimate an ARX model or an ARMAX model, depending on the number of zeros in the polynomal "nze". Select number of error-zeros-polynomal "nze" to 1, and you will get a ARX model or select "nze" equal to model poles "np", you will get an ARMAX model that also includes a kalman gain matrix K. I recommending that. This algorithm can handle data with high noise, but you will only get a SISO model from it. This algorithm was invented 1821 by Gauss, but it was until 1950 when it got its attention in adaptive control.

Use this algorithm if you have regular data from a open loop system and you want to apply that algorithm into embedded system that have low RAM and low flash memory. RLS is very suitable for system that have a lack of memory.

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![a](https://raw.githubusercontent.com/DanielMartensson/Mataveid/master/pictures/SSFD_Result.png)

### OCID - Observer Controller Identification
This is an extention from OKID. The idea is the same, but OCID creates a LQR contol law as well. This algorithm works only for closed loop data. It have its orgin from NASA around 1994 when NASA wanted to identify a observer, model and a LQR control law from closed loop data that comes from an actively controlled aircraft wing in a wind tunnel at NASA Langley Research Center. This algorithm works for both SISO and MIMO models.
This is an extention from OKID. The idea is the same, but OCID creates a LQR contol law as well. This algorithm works only for closed loop data. It have its orgin from NASA around 1992 when NASA wanted to identify a observer, model and a LQR control law from closed loop data that comes from an actively controlled aircraft wing in a wind tunnel at NASA Langley Research Center. This algorithm works for both SISO and MIMO models.

Use this algorithm if you want to extract a LQR control law, kalman observer and model from a running dynamical system. Or if your open loop system is unstable and it requries some kind of feedback to stabilize it. Then OCID is the perfect choice.

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