initsteady: Sets the initial state to the steady state

In MobilePhoneESSnetBigData/destim: R package for mobile devices position estimation

Description

The initial a priori distribution is set to the steady state of the transition matrix.

The Markov Chain is expected to be irreducible and aperiodic. The first because otherwise the devices would not have freedom of movement. The second because some probabilities from one state to itself are expected to be non zero. This implies that there exists one unique steady state.

The steady state is computed by solving the sparse linear system (TM - I)x = 0, where TM is the matrix of transitions I is identity and x the steady state. As it is an homogeneous system, and because of the uniqueness of the steady state, the solution is a one dimensional vector space, and the generator does not have any coordinate equal to zero. Then the last coordinate is set to 1 / number of states, so the sparse linear system becomes inhomogeneous with unique solution. Finally the solution is normalized so that the components of x sum up to 1.

Usage

initsteady(x)

Arguments

x	A HMM object.

Value

The same HMM object of the input with its initial state set to steady state.

See Also

HMM, initparams, minparams

Examples

model <- HMM(2)
model <- addtransition(model, c(1,2))
model <- addtransition(model, c(2,1))
model <- initparams(model)
istates(model)
model <- initsteady(model)
istates(model)
(istates(model) %*% getTM(model))

MobilePhoneESSnetBigData/destim documentation built on Dec. 7, 2020, 7:35 p.m.