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An Adaptive Divided Difference filter has been proposed for joint estimation of parameter and states of nonlinear systems in situations with unknown process noise statistics. The proposed filter, which is based on the innovation sequence, ensures improved estimation performance adapting the unknown process noise covariance. The performance of the filter is assessed with a benchmark nonlinear problem. Simulation results demonstrate that the performance of the proposed filter is superior compared to a non adaptive Divided Difference filter when the process noise covariance is unknown.

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one‐step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off‐line harmonics estimation problem with real data.

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