Nomenclature F = state transition matrix H = matrix giving the ideal/noiseless connection between measurements and states I = identity matrix k = time index L = noise sensitivity matrix in nonlinear systems N = lag time constant integer P = estimation-error covariance matrix s = arbitrary time step used in inductive proof xk = state at time index k x̂ = state estimate x̂k = a priori state estimat...

This paper deals with the introduction of an approach for the electromagnetic characterization of homogeneous chiral layers. The proposed method is based on the state-space approach and properties of a 4×4 state transition matrix. Based on this, first, the forward problem analysis through the state-space method is reviewed and properties of the state transition matrix of a chiral layer are pres...

A method for the determination of the trajectory of a ballistic missile over a rotating, spherical Earth given only the launch position and impact point has been developed. The iterative solution presented uses a state transition matrix to correct the initial conditions of the ballistic missile state vector based upon deviations from a desired set of final conditions. A six-degree-of-freedom si...

Using Hartree-Fock Su-Sheriffer-Heeger (HF-SSH) model, we have studied the dependence of the energies of the ground (magnetic triplet state) and the first exited (nonmagnetic singlet state) states of the size-2 trigonal zigzag graphene nanoflake (size-2 NF) on the intensity of an external in plane static electric field at zero temperature. We identify a transition from the magnetic triplet stat...

We propose a Dynamic Boolean Network in which a state of a Boolean network and an output label associated with the state are interacting with each other, and a transition matrix keeps changing perpetually. We extrapolate a mutation of a transition matrix as T → Q−1TQ where T is a transition matrix and Q is a matrix representation of a permutation P (where the objects permuted are states of DBN)...

This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t) and conservative matrix Q(t) = [qij(t)] of nonhomogeneous transition rates qij(t), and use it to construct the transition ...

This paper proposes a dynamic preventive maintenance strategy for a multi-state deteriorating production system. A real-time operating state can be derived via the healthy index. A time-dependent state transition probability matrix is used to describe the aging and deteriorating system. The current probability transition matrix and the aging factor are estimated based on historical data. Then o...

In this set of notes the State Transition Matrix for the N -body problem is developed. This matrix is the derivative of the flow generated by the N -body vector field with respect to initial conditions. It, and it’s inverse can be used in concert with the Newton Method in order to find/design orbits which begin at specified states and end in some specific configuration, such as a periodic orbit...