The synthesis of the observer (27) is reduced  to determining the observer gain coefficients [G.sub.i] by minimization of the error vector of the recovery of the state vector
x(t) of the initial system (25) and maximization of the same norm of the error vector along the plant uncertainty vector [eta](t) and the vector of external signal influences [omega](t), which also corresponds to the worst case disturbance.
where: x is a PS state vector
; z is a vector of measurements; h(x) is a vector of functions (also nonlinear), representing dependence of measured quantities from the state vector
x; R is a diagonal matrix of measurement covariances.
The EKF process (4) and output (5) models are driven by the nonlinear, differentiable vector functions, f( x ) and g( x ), where [x.sub.k+1] is the unknown system state vector
at time index k+1, [y.sub.k] depicts the observation or output vector, [u.sub.k] is the control vector and the random variables [w.sub.k] and [v.sub.k] (6) represent the process and measurement additive, zero-mean noise samples.
This paper considers a solution to the problem of development of the effective accommodation system for faults caused by errors in the sensor, which measure the position of output shaft of gear and by changing the value of viscous friction coefficient in electric servo actuators of the UMs described by mathematical model including differential equations with nonlinearity and variable parameters and not fully known state vector
In this paper, an outline of the state vector
, state prediction f(x), and observation functions h(x) for each measurement update is discussed.
where [x.sub.j](t) = [[[x.sub.j1](t), [x.sub.j2](t), ..., [x.sub.jn](t)].sup.T] is the state vector
of system (2).
In attitude estimation, the quaternion can be used as the state vector
. The accelerometer-magnetometer combination can be used for measurement model.
In this paper, the receding horizon UFIR (RHUFIR) filters using only known means of state vector
components at starting points of sliding windows are suggested.
In Figure 2, these are state vectors
(t + 1) and (t).
The traditional KNN algorithm includes five procedures: data acquisition and input, state vector
construction, pattern library establishment, K value calibration, and prediction based on weighted average functions.
where [m.sup.b] is the state vector
before update and the superscript b refers to background; B is the covariance matrix of [m.sup.b]; [d.sup.obs] is the observed responses; d = f(m) is the dynamic vector composed of simulated responses obtained by running a reservoir simulator f for the state vector
m; and R is the covariance matrix of observation error.