Diagnosis and mitigation of state space model biases

State space models are used widely to process data in navigation and kinematic (dynamic) positioning. The quality of these models has a direct impact on the positioning results and thus the assessment of possible biases in the models is of significant importance. Using the principle of least squares, this paper derives a diagnosis and mitigation procedure for dealing with the state space and the observation biases in state space models based on the evaluation of the least squares residuals (filter residuals). The relationship between the test statistic of an observation and its redundancy number is established for the cases of independent or approximately independent observations. The successful performance of bias mitigation using the proposed procedure is demonstrated with simulated kinematic data in one dimensional space and real kinematic pseudorange data (C/A code) from the Global Positioning System (GPS). It is shown that the proposed procedure can successfully mitigate the state space or observation biases when both the redundancy of the models and its distribution on a biased state space variable or an observation are large enough.