Least Squares Estimation and Cramér–Rao Type Lower Bounds for Relative Sensor Registration Process

Abstract

An important prerequisite for successful multisensor integration is that the data from the reporting sensors are transformed to a common reference frame free of systematic or registration bias errors. If not properly corrected, the registration errors can seriously degrade the global surveillance system performance by increasing tracking errors and even introducing ghost tracks. The relative sensor registration (or grid-locking) process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. In this paper, we consider all registration errors involved in the grid-locking problem, i.e., attitude, measurement, and position biases. A linear least squares (LS) estimator of these bias terms is derived and its statistical performance compared to the hybrid Cramér-Rao lower bound (HCRLB) as a function of sensor locations, sensors number, and accuracy of sensor measurements

Collaborative Sensor Registration without a Priori Association

“…It must be noted that, the azimuth bias and the north angle bias cannot be distinguished in 2-D scenario and have to be merged into a single bias, i.e., dT [2]. The value ranges of dx and dr , so-called parameter space, are denoted as d S x and d S r .…”

“…Since the cooperative targets are selected for sensor registration far from the sensor's location, it means 2 2 P, P,…”

“…Recently, all the registration errors (i.e. measurement, attitude, and location errors) are taken into account in [2]- [3], using linear Least Squares (LS) approach and nonlinear Expectation-Maximization (EM) estimator respectively. However, all of those algorithms assume perfect track-to-track association.…”

“…Now we consider the measurement biases as well as the location biases for 2-D sensor without a priori association. Only the north angle bias, which is an attitude error, is taken into account and combined with the azimuth bias because they are geometrical coupling [2].…”

Step-adaptive approximate least squares

“…Examples of such areas are localization [1,2] and positioning [3], robotics [4] and sensor registration [5], power and battery applications [6,7], biomedical applications [8,9], or image processing [10,11]. For the linear LS problem the following system model is assumed:…”