Solving the Nonlinear Problems of Estimation for Navigation Data Processing Using Continuous-Time Particle Filter

Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems

“…where 𝜉 k ∈ N (𝜉, 0, 2𝜎 2 𝜉 𝛼 k Δt ), x 0 ∈ N (x 0 , x0 , 𝜎 2 x 0 ), T k is a known sequence (temperature). In (38), parameter 𝛼 k characterises the gyroscope drift stability with time, and parameter 𝛽 k determines the effect of the temperature on it. Both parameters are unknown and supposed to be determined during testing.…”

“…Both parameters are unknown and supposed to be determined during testing. We assume that the measured values of the gyroscope drift are determined as a sum of the sequence (38) and a discrete white noise…”

“…Now, similarly to the preceding example, we synthesise the polynomial filter to estimate the state vector (39) based on the measurements (38) and compare it with the EKF and the particle filter.…”

“…It should be noted that nonlinearities in state and measurement equations are often represented by polynomials. From this point of view, polynomial filtering methods have been quite successfully used to solve estimation problems [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In particular, in [24,31], the authors consider problems whose specific feature is nonlinearity of measurements, whereas the equations of the shaping filter that describe the estimated sequence are linear.…”