GeezerVison

This PR adds new functionality for supporting analysis and simulation of stochastic systems, based on a class that I taught at Caltech:

• Adds two new functions supporting random signals: white_noise, which creates a white noise vector in continuous or discrete time, and correlation, which calculates the correlation function (or [cross-] correlation matrix), R(tau).

• Adds a new function create_estimator_iosystem that matches the style of create_statefbk_iosystem (I/O system enhancements #710) and creates an I/O system implementing an estimator (including covariance update).

• Adds the ability to specify initial conditions for input_output_response as a list of values, so that for estimators that keep track of covariance you can set the initial conditions as [X0, P0]. In addition, if you specify a fewer number of initial conditions than the number of states, the remaining states will be initialized to zero (with a warning if the last initial condition is not zero). This allows the initial conditions to be given as [X0, 0].

• Adds the ability to specify inputs for input_output_response as a list of variables. Each element in the list will be treated as a portion of the input and broadcast (if necessary) to match the time vector. This allows input for a system with noise as [U, V] and inputs for a system with zero noise as [U, np.zero(n)] (where U is an input signal and np.zero(n) gets broadcast to match the time vector).

• Added some new Jupyter notebooks demonstrate the use of these functions:

  • stochresp.ipynb: illustrates the implementation of random processes and stochastic response.

  • pvtol-outputfbk.ipynb: illustrates the implementation of an extended Kalman filter and the use of the estimated state for LQR feedback of a vectored thrust aircraft model.

  • kincar-fusion.ipynb: works through estimation of the state of a car changing lanes with two different sensors available: one with good longitudinal accuracy and the other with good lateral accuracy.