Stochastic modelling for vision-based indoor navigation

Abstract

Ubiquitous navigation is becoming highly demanded as Location-Based Service (LBS) becomes increasingly popular. In outdoor environments, Global Navigation Satellite System (GNSS) has been developing rapidly over the past few decades. However, indoor navigation is still in its infancy. Compared with other strategies, vision appears to be one of the most promising indoor navigation technologies. Vision sensors are cheap, self-contained and work well for both indoor and outdoor environments. However, there are several elements affecting the performance of vision-based indoor navigation. The measurements for the navigation are image coordinates of Pseudo Ground Control points (PGCPs). These measurements are processed by least squares method with two types of mathematical models. The functional model has been well documented in the literature. However, the stochastic model still presents various challenges and has not been investigated in enough detail. This research focused on dealing with randomised errors existing in navigation steps. Different stochastic models are built to estimate the covariance matrix for image coordinates of PGCPs. These stochastic models have been tested, indicating a significant improvement in the reliability of the position and orientation of the vision sensor. The major research contributions are in the following three different methods to construct a stochastic model: a. Empirical method In the commonly used stochastic model, the variances of PGCP image coordinates are assumed to be the same. However, as the images from the camera can be affected by different variables such as the light, angle, camera parameters and geometric distribution, this assumption is not always accepted. Based on this fact, the measurements should be assigned with different accuracies. Empirically, the closer to the image centre, the more accurate the PGCP image coordinates are. A realistic stochastic model based on the distance between the image features of PGCPs and image centre was constructed to achieve satisfactory positioning results.

b. MINQUE method Rao (1970) developed the most commonly used method for estimating variance-covariance components, Minimum Norm Quadratic Unbiased Estimation (MINQUE). It was employed to construct the covariance matrices for PGCP image measurements with the condition that redundant measurements were available. Furthermore, a simplified MINQUE procedure was also used to evaluate the accuracy of measurements. In this research, the efficiency of the estimators was tested using simulated and real PGCP data sets in two different structures of variance component models. Group and additive models were discussed using the rigorous MINQUE method and the simplified MINQUE method. c. BQUE method The Best Quadratic Unbiased Estimator (BQUE), another method for estimating variance-covariance components, was introduced to compare the positioning results with MINQUE by the additive model. However, in MINQUE and BQUE procedure, the estimated variance components may be negative. This is not satisfactory in a real environment. The possible reasons could be a) the adjustment and/or the stochastic models are unreasonable or b) there is not enough of redundancy in the least-squares computation for vision-based navigation applications. To deal with these problems, the Best Quadratic Minimum Bias Non-Negative Estimator (BQMBNE) has been designed to obtain non-negative estimates. The six exterior orientation parameters by these methods were analysed.