Pseudo State Measurements Applied to Recursive Nonlinear Filtering

Abstract : Pseudo state measurements are constructed to make the measurement (geometry) model linear in the state. In the past, linear measurements have often proved to give better state estimates than nonlinear measurements. They are nonlinear functions of the actual measurement model bias parameters and are constructed to be linear functions of the state variables or to vanish in the absence of model or measurement error. Some examples of constructing pseudo state measurements are given in the paper. Recursive filter equations are derived using the pseudo state measurements and including colored (Markov) measurement noise and unestimated state and measurement model parameters. The filter estimates minimize the usual weighted least squares cost function with correlated state and pseudo state measurements. The filter is linear by construction. Higher order partial derivatives, if retained, would appear only in the computation of error variance and covariance matrices.