Performance Specified State Estimation With Minimum Risk

Abstract

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.

Outlier accommodation for meter-level positioning: Risk-averse performance-specified state estimation

“…A main new idea of [16], [17] was to change the focus from detecting outliers to find a subset of the measurements that can be consistently produced by the assumed measurement model and satisfying the accuracy specification.…”

“…The outlier detection problem is fundamentally unobservable, when all measurements have the potential to be affected by outliers [16], [17]. Therefore, outlier detection methods such as those reviewed above are built on outlier hypothesis assumptions, resulting in tests to choose the most likely assumption.…”

“…Alternatively, [16] works within an optimization setting to find the largest set of measurements selfconsistent with the assumed model. Finally, [17] works within an optimization setting to choose the set of measurements that achieves a performance specification with minimum risk. The performance specification is phrased in terms of the posterior information matrix.…”

“…The risk is defined by the norm of the covariance normalized residual vector. Reference [17] works in a general theoretical setting, with generic academic examples and no in-depth evaluation has been conducted so far.…”

“…The main contribution of this paper is that for the first time, the risk-averse performance-specified approach of [17] will be applied to and explained for the GNSS state estimation problem, including both the theoretical derivation and experimental results. The experimental results utilize real-world Doppler and differential pseudorange data, considering the risk associated with both sets of measurements.…”