Patent Document ID: 9927806
Application ID: 13733181
Patent Flag: 1

Claim One:
1. A computer implemented method for estimation of a system having state variables representing the state of the system comprising: predicting the estimate of the state variables along with the uncertainties in the state variables; observing a measurement of at least one state variable corrupted with some amount of error; updating the estimates of the state variables using a weighted average, with more weight being given to estimates with higher certainty; and providing an estimator input to update the estimates of the state variables, the estimator input operating to provide asymptotic convergence of the mean estimation error in all of the state variables in the presence of persistent excitation or disturbance that is not asymptotically decaying to zero; wherein the system being estimated is used for time series analysis for signal processing and wherein the system is defined by a process model, and the process model dynamics defining the state variables are unknown and wherein the system is defined by a process model that may be represented as 
 x ( k+ 1)= Ax ( k )+ w ( k )+ω( k ) where k represents, time, x is the state vector comprising the unknown state variables, A represents the system matrix comprising unknown elements, w(k) is unknown persistent excitation, ω(k) is the n dimensional Gaussian white noise process, and wherein the measurement or output may be represented by vector y(k)where 
 y ( k )= Cx ( k )+ν( k ) where C is the unknown output matrix, and ν(k) is the n-dimensional Gaussian white noise process.