An apparatus includes a sensor module configured for receiving sensed information indicative of a sensed signal. The sensed signal includes a source signal component and a source noise component. The apparatus also includes a reference module configured for reference information indicative of a reference signal. The reference signal also includes a reference noise component. The apparatus also includes a filter module configured as a fixed lag Kalman smoother. The filter module is configured for adaptively filtering the reference signal to generate an estimate of the source noise component. The apparatus also includes a processing module configured for calculating an output signal based on the sensed signal and the estimate of the source noise component. The apparatus also includes an interface module configured for transmitting an indication of the output signal. The filter module is further configured for, based on the output signal, tuning the Kalman smoother.

Method for monitoring a stable convergence behaviour of a Kalman filter (KF), which estimates states and/or parameters of an energy storage system, in particular a battery cell (BZ), wherein a covariance behaviourprovided by the Kalman filter (KF)in terms of at least one state and/or parameter of the energy storage system is compared with a corresponding desired covariance behaviour of the state and/or parameter, wherein the Kalman filter (KF) is automatically deactivated for each state and/or each parameter of the energy storage system, of which the covariance behaviour exceeds the corresponding desired covariance behaviour.

Systems are provided to estimate autoregressive moving average (ARMA) models using maximum likelihood estimation and analytical derivatives, and to use such models for forecasting. The evaluation of the analytical derivatives during estimation of the model parameters may be performed using a state space representation with certain characteristics. An ARMA model estimated using maximum likelihood estimation, analytical derivatives, and the state space representation with certain characteristics can be used to forecast/predict values that are likely to occur in the future, given some set of previously-occurring values.

The invention relates to a global optimal particle filtering method and a global optimal particle filter. The problem of particle filter processing nonlinear and non-Gaussian signals is effectively solved. The main technical means is to use the Lamarck genetic natural law to construct a global optimal particle filter comprising: generating an initial particle set; using Unscented Kalman Filter to perform importance sampling on the initial particle set to obtain sampled particles; performing floating-point number encoding for each of the sampled particles to obtain an encoded particle set; setting an initial population; using the initial population as an original trial population to sequentially perform a Lamarck overwriting operation, a real number decoding operation, and an elite retention operation; using the real-number optimal candidate particle as a prediction sample for a next moment, and obtaining a state estimation value of a system. The invention is applicable to machine learning.

A modified Kalman filter may include one or more neural networks to augment or replace components of the Kalman filter in such a way that the human interpretability of the filter's inner functions is preserved. The neural networks may include a neural network to account for bias in measurement data, a neural network to account for unknown controls in predicting a state of an object, a neural network ensemble that is trained differently based on different sensor data, a neural network for determining the Kalman gain, and/or a set of Kalman filters including various neural networks that determine independent estimated states, which may be fused using Bayesian fusion to determine a final estimated state.

By a tracking device, a tracking method, or a computer-readable non-transitory storage medium storing a tracking program, a state value of a mobile object is estimated to track the mobile object, the observation value of the mobile object observed at an observation time is acquired, a prediction state value is acquired, a true value of the state value at the observation time is estimated by nonlinear filtering.

An apparatus includes a sensor module configured for receiving sensed information indicative of a sensed signal. The sensed signal includes a source signal component and a source noise component. The apparatus also includes a reference module configured for reference information indicative of a reference signal. The reference signal also includes a reference noise component. The apparatus also includes a filter module configured as a fixed lag Kalman smoother. The filter module is configured for adaptively filtering the reference signal to generate an estimate of the source noise component. The apparatus also includes a processing module configured for calculating an output signal based on the sensed signal and the estimate of the source noise component. The apparatus also includes an interface module configured for transmitting an indication of the output signal. The filter module is further configured for, based on the output signal, tuning the Kalman smoother.

An analysis device includes: an estimation unit that obtains a current state variable by state estimation based on a state variable for first sequence data generated by applying a first conversion to observation data, a state space model, and each element included in the first sequence data; an observation unit that generates second sequence data by applying an observation process to the current state variable; an elaboration unit that generates third sequence data by performing an elaboration process of correcting each element included in the second sequence data so that a value of each cell of the estimated observation data does not become a negative value and the number of cells having a value other than 0 included in the estimated observation data is suppressed; and a second conversion unit that generates the estimated observation data by applying a second conversion to the third sequence data.

Provided are an apparatus and method for a statistical memory network. The apparatus includes a stochastic memory, an uncertainty estimator configured to estimate uncertainty information of external input signals from the input signals and provide the uncertainty information of the input signals, a writing controller configured to generate parameters for writing in the stochastic memory using the external input signals and the uncertainty information and generate additional statistics by converting statistics of the external input signals, a writing probability calculator configured to calculate a probability of a writing position of the stochastic memory using the parameters for writing, and a statistic updater configured to update stochastic values composed of an average and a variance of signals in the stochastic memory using the probability of a writing position, the parameters for writing, and the additional statistics.

In one embodiment, a Kalman filter based capacity forecasting method includes acquiring a capacity time sequence of an object to be forecasted; establishing a dynamical model for the capacity time sequence, and extracting a state transition parameter and a process noise parameter of the dynamical model; performing Kalman filter estimation on the capacity time sequence by using the state transition parameter and the process noise parameter to generate at least one state characteristic signal; segmenting the capacity time sequence according to the at least one state characteristic signal, and determining at least one corresponding segmentation point; and forecasting the capacity at future time according to the at least one segmentation point determined in the capacity time sequence. By adopting the technical solutions of the invention, accurate forecasting of the capacity growth is achieved, to facilitate operation and maintenance personnel making a reasonable capacity expansion plan.