Kalman Filter Tuning with Bayesian Optimization

Many state estimation algorithms must be tuned given the state space process and observation models, the process and observation noise parameters must be chosen. Conventional tuning approaches rely on heuristic hand-tuning or gradient-based optimization techniques to minimize a performance cost function. However, the relationship between tuned noise values and estimator performance is highly nonlinear and stochastic. Therefore, the tuning solutions can easily get trapped in local minima, which can lead to poor choices of noise parameters and suboptimal estimator performance. This paper describes how Bayesian Optimization (BO) can overcome these issues. BO poses optimization as a Bayesian search problem for a stochastic ``black box'' cost function, where the goal is to search the solution space to maximize the probability of improving the current best solution. As such, BO offers a principled approach to optimization-based estimator tuning in the presence of local minima and performance stochasticity. While extended Kalman filters (EKFs) are the main focus of this work, BO can be similarly used to tune other related state space filters. The method presented here uses performance metrics derived from normalized innovation squared (NIS) filter residuals obtained via sensor data, which renders knowledge of ground-truth states unnecessary. The robustness, accuracy, and reliability of BO-based tuning is illustrated on practical nonlinear state estimation problems,losed-loop aero-robotic control

Time Dependence in Kalman Filter Tuning

In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error squared and covariance minimization) compute empirical measures of filter performance. The parameters are selected, either manually or by some kind of optimization algorithm, to maximize these measures of performance. However, there are two challenges with this approach. First, in theory, many of these measures do not guarantee a unique solution due to observability issues. Second, in practice, empirically computed statistical quantities can be very noisy due to a finite number of samples. We propose a method to overcome these limitations. Our method has two main parts to it. The first is to ensure that the tuning problem has a single unique solution. We achieve this by simultaneously tuning the filter over multiple different prediction intervals. Although this yields a unique solution, practical issues (such as sampling noise) mean that it cannot be directly applied. Therefore, we use Bayesian Optimization. This technique handles noisy data and the local minima that it introduces. We demonstrate our results in a reference example and demonstrate that we are able to obtain good results. We share the source code for the benefit of the community1

Exploiting semantic and public prior information in MonoSLAM

In this paper, we propose a method to use semantic information to improve the use of map priors in a sparse, feature-based MonoSLAM system. To incorporate the priors, the features in the prior and SLAM maps must be associated with one another. Most existing systems build a map using SLAM and then align it with the prior map. However, this approach assumes that the local map is accurate, and the majority of the features within it can be constrained by the prior. We use the intuition that many prior maps are created to provide semantic information. Therefore, valid associations only exist if the features in the SLAM map arise from the same kind of semantic object as the prior map. Using this intuition, we extend ORB-SLAM2 using an open source pre-trained semantic segmentation network (DeepLabV3+) to incorporate prior information from Open Street Map building footprint data. We show that the amount of drift, before loop closing, is significantly smaller than that for original ORB-SLAM2. Furthermore, we show that when ORB-SLAM2 is used as a prior-aided visual odometry system, the tracking accuracy is equal to or better than the full ORB-SLAM2 system without the need for global mapping or loop closure

Weak in the NEES?: Auto-Tuning Kalman Filters with Bayesian Optimization

ISIF Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model parameters, e.g. Process noise covariance, pre-whitening filter models for non-white noise, etc. Conventional optimization techniques for tuning can get stuck in poor local minima and can be expensive to implement with real sensor data. To address these issues, a new 'black box' Bayesian optimization strategy is developed for automatically tuning Kalman filters. In this approach, performance is characterized by one of two stochastic objective functions: Normalized estimation error squared (NEES) when ground truth state models are available, or the normalized innovation error squared (NIS) when only sensor data is available. By intelligently sampling the parameter space to both learn and exploit a nonparametric Gaussian process surrogate function for the NEESINIS costs, Bayesian optimization can efficiently identify multiple local minima and provide uncertainty quantification on its results

Ataxia-telangiectasia: Linkage analysis in highly inbred Arab and Druze families and differentiation from an ataxia-microcephaly-cataract syndrome

Ataxia-telangiectasia (A-T) is a progressive autosomal recessive disease featuring neurodegeneration, immunodeficiency, chromosomal instability, radiation sensitivity and a highly increased proneness to cancer. A-T is ethnically widespread and genetically heterogeneous, as indicated by the existence of four complementation groups in this disease. Several "A-T-like" genetic diseases share various clinical and cellular characteristics with A-T. By using linkage analysis to study North American and Turkish A-O families, the ATA (A-T, complementation group A) gene has been mapped to chromosome 11q23. A number of Israeli Arab A-T patients coming from large, highly inbred families were assigned to group A In one of these families, an additional autosomal recessive disease was identified, characterized by ataxia, hypotonia, microcephaly and bilateral congenital cataracts. In two patients with this syndrome, normal levels of serum immunoglobulins and alpha-fetoprotein, chromosomal stability in peripheral blood lymphocytes and skin fibroblasts, and normal cellular response to treatments with X-rays and the radiomimetic drug neocarzinostatin indicated that this disease does not share, with A-T, any additional features other than ataxia. These tests also showed that another patient in this family, who is also mentally retarded, is affected with both disorders. This conclusion was further supported by linkage analysis with 11q23 markers. Lod scores between A-O and these markers, cumulated over three large Arab families, were significant and confirmed the localization of the ATA gene to aq23. However, another Druze family unassigned to a specific complementation group, showed several recombinants between A-T and the same markers, leaving the localization of the A-T gene in this family open

Transcriptional changes and the role of ONECUT1 in hPSC pancreatic differentiation

Cell type specification during pancreatic development is tightly controlled by a transcriptional and epigenetic network. The precise role of most transcription factors, however, has been only described in mice. To convey such concepts to human pancreatic development, alternative model systems such as pancreatic in vitro differentiation of human pluripotent stem cells can be employed. Here, we analyzed stage-specific RNA-, ChIP-, and ATAC-sequencing data to dissect transcriptional and regulatory mechanisms during pancreatic development. Transcriptome and open chromatin maps of pancreatic differentiation from human pluripotent stem cells provide a stage-specific pattern of known pancreatic transcription factors and indicate ONECUT1 as a crucial fate regulator in pancreas progenitors. Moreover, our data suggest that ONECUT1 is also involved in preparing pancreatic progenitors for later endocrine specification. The dissection of the transcriptional and regulatory circuitry revealed an important role for ONECUT1 within such network and will serve as resource to study human development and disease

Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics