Performance Specified State Estimation With Minimum Risk

Measurements that significantly deviate from those predicted by the model or from the normal pattern of sensed data are considered as outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The traditional Neyman-Pearson Kalman filter approach is to ignore all residuals greater than a designer specified threshold. The criticism of such techniques is that they allow missed detections to pass through undetected thereby corrupting both the state estimate and covariance. This causes the state estimation gain and all subsequent outlier decisions to be based on an invalid model. In sensor rich applications, where large numbers of sensor measurements are available, all the sensor data may not be needed to achieve the system accuracy specification. Global navigation satellite systems (GNSS) is one such sensor rich application since various satellite systems are available, each of which supplies more than the minimal number of satellites needed to estimate the system state. Using more data than is required to meet the specification exposes the state estimate to unneeded risk of outlier inclusion. This paper formulates and solves the state estimation problem from the perspective of minimizing risk while achieving a performance specification.

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