Convergence analysis of self-tuning Riccati equation for systems with correlation noises

For linear discrete time-invariant stochastic system with correlated noises,and with unknown state transition matrix and unknown noise statistics,substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation,a new self-tuning Riccati equation is presented.A dynamic variance error system analysis(DVESA)method is presented,which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation.Two decision criterions of the stability for the Lyapunov equation are presented.Using the DVESA method and Kalman filtering stability theory,it proves that with probability 1,the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation.The proposed method can be applied to design a new selftuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters.A numerical simulation example shows the effectiveness of the proposed method.

INS stochastic error detection during kinematic tests and impacts on INS/GNSS performance

Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is one method of determining INS stochastic errors.However,it is known that INS errors can vary depending on a vehicle’s motion and environment,and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic.In order to overcome this limitation,this paper proposes the use of Dynamic Allan Variance(DAV).The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV.The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV,applied on a kinematic dataset compared to the AV,applied on a static laboratory dataset.