Noise Estimation Is Not Optimal: How to Use Kalman Filter the Right Way (original) (raw)
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Using Kalman Filter The Right Way: Noise Estimation Is Not Optimal
ArXiv, 2021
Determining the noise parameters of a Kalman Filter (KF) has been researched for decades. The research focuses on estimation of the noise under various conditions, since noise estimation is considered equivalent to errors minimization. However, we show that even a seemingly small violation of KF assumptions can significantly modify the effective noise, breaking the equivalence between the tasks and making noise estimation a highly sub-optimal strategy. In particular, whoever tests a new learning-based algorithm in comparison to a (variant of) KF with standard parameters tuning, essentially conducts an unfair comparison between an optimized algorithm and a non-optimized one. We suggest a method (based on Cholesky decomposition) to apply gradient-based optimization efficiently to the symmetric and positive-definite (SPD) parameters of KF, so that KF can be optimized similarly to common neural networks. The benefits of this method are demonstrated for both Radar tracking and video trac...
A Bayesian Framework for Robust Kalman Filtering Under Uncertain Noise Statistics
In this paper, we propose a Bayesian framework for robust Kalman filtering when noise statistics are unknown. The proposed intrinsically Bayesian robust Kalman filter is robust in the Bayesian sense meaning that it guarantees the best average performance relative to the prior distribution governing unknown noise parameters. The basics of Kalman filtering such as the projection theorem and the innovation process are revisited and extended to their Bayesian counterparts. These enable us to design the intrinsically Bayesian robust Kalman filter in a similar way that one can find the classical Kalman filter for a known model.
Tracking Unmanned Aerial Vehicles Based on the Kalman Filter Considering Uncertainty and Error Aware
Electronics, 2021
Recently, Unmanned Aerial Vehicles (UAVs) have made significant impacts on our daily lives with the advancement of technologies and their applications. Tracking UAVs have become more important because they not only provide location-based services, but are also faced with serious security threats and vulnerabilities. UAVs are smaller in nature, move with high speed, and operate in a low-altitude environment, which makes it conceivable to track UAVs using fixed or mobile radars. Kalman Filter (KF)-based methodologies are widely used for extracting valuable trajectory information from samples composed of noisy information. As UAVs’ trajectories resemble uncertain behavior, the traditional KF-based methodologies have poor tracking accuracy. Recently, the Diffusion-Map-based KF (DMK) was introduced for modeling uncertainties in the environment without prior knowledge. However, the model has poor accuracy when operating in environments with higher noise. In order to achieve better trackin...
The Kalman filter requires knowledge of the noise statistics; however, the noise covariances are generally unknown. Although this problem has a long history, reliable algorithms for their estimation are scant, and necessary and sufficient conditions for identifiability of the covariances are in dispute. We address both of these issues in this paper. We first present the necessary and sufficient condition for unknown noise covariance estimation; these conditions are related to the rank of a matrix involving the auto and cross-covariances of a weighted sum of innovations, where the weights are the coefficients of the the minimal polynomial of the closed-loop system transition matrix of a stable, but not necessarily optimal, Kalman filter. We present an optimization criterion and a novel six-step approach based on a successive approximation, coupled with a gradient algorithm with adaptive step sizes, to estimate the steady-state Kalman filter gain, the unknown noise covariance matrices...
Weak in the NEES?: Auto-Tuning Kalman Filters with Bayesian Optimization
2018 21st International Conference on Information Fusion (FUSION), 2018
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 NEES/NIS costs, Bayesian optimization can efficiently identify multiple local minima and provide uncertainty quantification on its results.
Efficient RADAR Tracking Using Adaptive Kalman Filter
Radar tracking plays a crucial role within the space of early warning and detection system, whose preciseness is closely connected with filtering rule. There are various nonlinear filtering algorithms at the present, owning their explicit characteristics. Through the analyses of linear and nonlinear information filters, we discover that KF is simple to implement and has been wide used. Therefore, we'll simulate and show the performance of the Kalman information filter (KF). One of the issues with the Kalman filter is that they'll not strong against modeling uncertainties. The Kalman filter algorithm is that the optimum filter for a system while not uncertainties. The performance of a Kalman filter is also considerably degraded if the particular system model doesn't match the model on that the Kalman filter was primarily based, therefore required an advance version of Kalman filter , This filter is known as Adaptive Kalman Filter (AKF). Kalman filter (KF) is mostly applicable for linear system i.e. where speed are linear but Radar movements are nonlinear and they cannot easily track with linear system and estimation in Radar system is also not easy, so we can say that Kalman filter is not efficient where delay or uncertainties are present ,So we required a new filter they work efficiently in those condition , we use Adaptive Kalman filter (AKF).
TARGET TRACKING: IMPLEMENTING THE KALMAN FILTER
Target tracking is often complicated by the measurement noise. The noise must be "filtered" out in order to predict the true path of a moving target. In this study of linear filtering, the Kalman filter, a recursive linear filtering model, was used to estimate tracks. Various situations were examined, including maneuvering targets, multiple radars, multiple targets, and collision avoidance. Based on the results, the Kalman filter was successful in smoothing random deviations from the true path of the targets, improving in its ability to predict the path of each target as more measurements from the tracker were processed.
A Kalman-like algorithm with no requirements for noise and initial conditions
2011 IEEE ICASSP, 2011
We address a Kalman-like estimator for solving universally the problems of filtering (p = 0), prediction (p > 0), and smoothing (p < 0) of discrete time-varying state-space models with no requirements for noise and initial conditions. The estimator proposed overperforms the Kalman one when 1) noise covariances and initial conditions are not known exactly, 2) noise constituents are not white sequences, and 3) both the system and measurement noise components need to be filtered out and the deterministic state estimated. Otherwise, the Kalman-like and Kalman filters produce similar errors. A numerical comparison of the Kalman and Kalman-like estimators is provided.