We leverage automatic differentiation (AD) and probabilistic programming to develop an end-to-end optimization algorithm for batch triangulation of a large number of unknown objects. Given noisy detections extracted from noisily geo-located street level imagery without depth information, we jointly estimate the number and location of objects of different types, together with parameters for sensor noise characteristics and prior distribution of objects conditioned on side information. The entire algorithm is framed as nested stochastic variational inference. An inner loop solves a soft data association problem via loopy belief propagation; a middle loop performs soft EM clustering using a regularized Newton solver (leveraging an AD framework); an outer loop backpropagates through the inner loops to train global parameters. We place priors over sensor parameters for different traffic object types, and demonstrate improvements with richer priors incorporating knowledge of the environment. We test our algorithm on detections of road signs observed by cars with mounted cameras, though in practice this technique can be used for any geo-tagged images. The detections were extracted by neural image detectors and classifiers, and we independently triangulate each type of sign (e.g. stop, traffic light). We find that our model is more robust to DNN misclassifications than current methods, generalizes across sign types, and can use geometric information to increase precision. Our algorithm outperforms our current production baseline based on k-means clustering. We show that variational inference training allows generalization by learning sign-specific parameters.
Joint tracking and calibration has a long history, @cite_18 . Using bearings-only sensors, @cite_7 developed a unified approach to multi-object triangulation and parameter learning for sensor calibration. @cite_8 developed a joint algorithm for multi-target tracking and sensor bias estimation based on the Probability Hypothesis Density (PHD) filter.
@cite_18 @cite_7 @cite_8
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An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70 compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented. Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object tracking and camera calibration, based on the finite set statistics methodology. In contrast to the mainstream approaches, an alternative parametrization is investigated for triangulation, called disparity space. The approach for feature correspondence is based on the probability hypothesis density (phd) filter, and hence inherits the ability to handle the initialization of new tracks as well as the discrimination between targets and clutter within a Bayesian paradigm. The phd filtering approach then forms the basis of a camera calibration method from static or moving objects. Results are shown on simulated and real data. Tracking systems are based on models, in particular, the target dynamics model and the sensor measurement model. In most practical situations the two models are not known exactly and are typically parametrized by an unknown random vector @math . The paper proposes a Bayesian algorithm based on importance sampling for the estimation of the static parameter @math . The input are measurements collected by the tracking system, with non-cooperative targets present in the surveillance volume during the data acquisition. The algorithm relies on the particle filter implementation of the probability density hypothesis (PHD) filter to evaluate the likelihood of @math . Thus, the calibration algorithm, as a byproduct, also provides a multi-target state estimate. An application of the proposed algorithm to translational sensor bias estimation is presented in detail as an illustration. The resulting sensor-bias estimation method is applicable to asynchronous sensors and does not require prior knowledge of measurement-to-target associations.