Kalman Filter Gain Research Articles

An Interactive Transient Model Correction Active Sonar Target Tracking Method

Active sonar can usually only directly measure the distance and bearing information of underwater targets, and cannot directly obtain target velocity, acceleration and other information. Therefore, the amount of information is relatively small, making it difficult to support the construction of complex motion models. At the same time, the motion state of underwater maneuvering targets is changeable. In response to the problem of detecting and tracking underwater moving targets by active sonar, this paper proposes a target transient model correction (TMC) filtering tracking method. Based on the conventional Kalman filter (KF) estimation, residual covariance is used as a signal quantity. When there is a large change in it, a transient filter with constant gain is adopted to filter the measurement value. The filtered output is used to correct the KF gain matrix and the target motion state model, to avoid the problem of increasing or even diverging KF estimation errors caused by changes in process noise. Using this method can solve the problem of maintaining stability and filtering estimation accuracy of active sonar tracking of underwater maneuvering targets with less computational and engineering costs.

Enhancing Real-Time Kinematic Relative Positioning for Unmanned Aerial Vehicles

Real-time kinematic (RTK) positioning of the global navigation satellite systems (GNSS) is used to provide centimeter-level positioning accuracy. There are several ways to implement RTK but a Kalman filter-based RTK is preferred because of its superior capability to resolve GNSS carrier phase integer ambiguities. However, the positioning performance of the Kalman filter-based RTK is often compromised by various factors when it comes to determining a precise relative position vector between moving unmanned aerial vehicles (UAVs) equipped with low-cost GNSS receivers and antennas, where the locations of both GNSS antennas are not accurately known and change over time. Some of the critical factors that lead to a high rate of incorrect resolutions of carrier phase integer ambiguities are measurement time differences between GNSS receivers, frequent cycle slips with high noise in code and carrier phase measurements, and an improper Kalman filter gain due to a newly risen satellite. In this paper, effective methods to deal with those factors to achieve a seamless Kalman filter-based RTK performance in moving UAVs are presented. Using our extensive 45 flight tests data sets, conducted over a duration of 3 to 12 min, the RTK positioning results showed that the root-mean-square position error (RMSE) decreased by up to 95.13%, with an average of 65.31%, and that the percentage of epochs that passed the ratio test, which is the most common method for validating double differenced carrier phase integer ambiguity resolution, increased by up to 130%, with an average of 23.54%.

Chandrasekhar-type Algorithms with Gain Elimination

Chandrasekhar-type algorithms are associated with the Riccati equation emanating from the Kalman filter in linear systems which describe the relationship between the n-dimensional state and the m-dimensional measurement. The traditional Chandrasekhar-type algorithms use the Kalman filter gain to compute the prediction error covariance. In this paper, two variations of Chandrasekhar-type algorithms eliminating the Kalman filter gain are proposed. The proposed Chandrasekhar-type algorithms with gain elimination may be faster than the traditional Chandrasekhar-type algorithms, depending on the model dimensions.

Improving Kalman filter for cyber physical systems subject to replay attacks: An attack-detection-based compensation strategy

This paper investigates the problem of improving Kalman filtering for a class of multi-layer cyber physical systems (CPS) in the face of multiple consecutive replay attacks. CPS is vulnerable in an open network environment, and the replay attack model is described based on the number and duration of successful message transmissions. For all possible occurrences of replay attacks, a detection and compensation method is obtained with the help of the residual monitoring mechanism and an attack detection function. At the same time, in order to identify the attack has occurred in which, the register is integrated into the system. Furthermore, a novel Kalman filter with a compensation mechanism is designed to estimate the ideal states of CPS subject to replay attacks, and the Kalman filter gain is optimized based on the detection results. Finally, a simulation example is given to verify the effectiveness of the proposed improving Kalman filter.

Seamless MEMS-INS/Geomagnetic Navigation System Based on Deep-Learning Strong Tracking Square-Root Cubature Kalman Filter.

To suppress inertial navigation system drift and improve the seamless navigation capability of microelectromechanical system-inertial navigation systems/geomagnetic navigation systems (MEMS-INS/MNS) in geomagnetically unlocked environments, this paper proposes a hybrid seamless MEMS-INS/MNS strategy combining a strongly tracked square-root cubature Kalman filter with deep self-learning (DSL-STSRCKF). The proposed DSL-STSRCKF method consists of two innovative steps: (i) The relationship between the deep Kalman filter gain and the optimal estimation is established. In this paper, combining the two auxiliary methods of strong tracking filtering and square-root filtering based on singular value decomposition, the heading accuracy error of ST-SRCKF can reach 1.29°, which improves the heading accuracy by 90.10% and 9.20% compared to the traditional single INS and the traditional integrated navigation algorithm and greatly improves the robustness and computational efficiency. (ii) Providing deep self-learning capability for the ST-SRCKF by introducing a nonlinear autoregressive neural network (NARX) with exogenous inputs, which means that the heading accuracy can still reach 1.33° even during the MNS lockout period, and the heading accuracy can be improved by 89.80% compared with the single INS, realizing the continuous high-precision navigation estimation.

An analysis of the translation process of contemporary Chinese literature based on the Kalman filter algorithm

Abstract Exploring the evolution of translation of contemporary Chinese literature better presents Chinese literary charm to foreign readers. This paper starts with the Kalman filter algorithm and introduces its cost function that satisfies the error minimization and the Kalman filter gain. Then the BP neural network is illustrated, its minimization of mean square error is solved using the backpropagation algorithm, and the momentum factor is introduced to update the weight function of the BP neural network. The correlation between the Kalman gain and the filtering error is fitted using BP neural network to optimize the Kalman filtering algorithm, and the algorithm flow chart of the BP-KF algorithm is given. Finally, the BP-KF algorithm is used to analyze the data on the evolution of translation strategies and translation dissemination channels of contemporary Chinese literature on the Internet. From the evolution of the translation strategy, the number of translated works of additive French literature decreased by 5.28% year-on-year from 2016 to 2020, and the number of translated works of annotated French literature increased by nearly 11 times year-on-year from 2016 to 2020. In terms of the evolution of the translation and dissemination channels, the percentage of using the Internet to disseminate literary translation and mediation works reviews increased from 16.29% in 2017 to 41.65% in 2021, an increase of 25.36 percentage points. Based on the BP-KF algorithm, the evolution of translation of contemporary Chinese literature can be effectively analyzed, and the data can visually show the direction of the evolution of literary translation, thus expanding the influence of contemporary Chinese literature.

MIMU Optimal Redundant Structure and Signal Fusion Algorithm Based on a Non-Orthogonal MEMS Inertial Sensor Array.

A micro-inertial measurement unit (MIMU) is usually used to sense the angular rate and acceleration of the flight carrier. In this study, multiple MEMS gyroscopes were used to form a spatial non-orthogonal array to construct a redundant MIMU system, and an optimal Kalman filter (KF) algorithm was established by a steady-state KF gain to combine array signals to improve the MIMU's accuracy. The noise correlation was used to optimize the geometric layout of the non-orthogonal array and reveal the mechanisms of influence of correlation and geometric layout on MIMU's performance improvement. Additionally, two different conical configuration structures of a non-orthogonal array for 4,5,6,8-gyro were designed and analyzed. Finally, a redundant 4-MIMU system was designed to verify the proposed structure and KF algorithm. The results demonstrate that the input signal rate can be accurately estimated and that the gyro's error can also be effectively reduced through fusion of non-orthogonal array. The results for the 4-MIMU system illustrate that the gyro's ARW and RRW noise can be decreased by factors of about 3.5 and 2.5, respectively. In particular, the estimated errors (1σ) on the axes of Xb, Yb and Zb were 4.9, 4.6 and 2.9 times lower than that of the single gyroscope.

NCT:noise-control multi-object tracking

AbstractMulti-Object Tracking (MOT) is an important topic in computer vision. Recent MOT methods based on the anchor-free paradigm trade complicated hierarchical structures for tracking performance. However, existing anchor-free MOT methods ignore the noise in detection, data association, and trajectory reconnection stages, which results in serious problems, such as missing detection of small objects, insufficient motion information, and trajectory drifting. To solve these problems, this paper proposes Noise-Control Tracker (NCT), which focuses on the noise-control design of detection, association, and reconnection. First, a prior depth denoise method is introduced to suppress the fusion feature redundant noise, which can recover the gradient information of the heatmap fusion features. Then, the Smoothing Gain Kalman filter is designed, which combines the Gaussian function with the adaptive observation coefficient matrix to stabilize the mutation noise of Kalman gain. Finally, to address the drift noise issue, the gradient boosting reconnection context mechanism is designed, which realizes adaptive trajectory reconnection to effectively fill the gaps in trajectories. With the assistance of the plug-and-play noise-control method, the experimental results on MOTChallenge 16 &17 datasets indicate that the NCT can achieve better performance than other state-of-the-art trackers.

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

In high-precision dynamic positioning, it is necessary to ensure the positioning accuracy and reliability of the navigation system, especially for safety–critical applications, such as intelligent vehicle navigation. In the face of a complex observation environment, when the global navigation satellite system (GNSS) uses carrier phase observations for high-precision relative positioning, ambiguity resolution will be affected, and it is difficult to estimate all ambiguities. In addition, when the GNSS signal quality and measurement noise level are difficult to predict in an environment with many occlusions, the received satellite observations are prone to very large errors, resulting in apparent deviations in the positioning solution. However, traditional positioning algorithms assume that the measurement noise is constant, which is unrealistic. This will cause incorrect ambiguity resolution, lead to meter-level positioning errors, reduce the reliability of the system, and increase the integrity risk of the system. We proposed an innovative adaptive Kalman filter based on integer ambiguity validation (IAVAKF) to improve the efficiency of ambiguity resolution (AR) and positioning accuracy. The partial ambiguity resolution (PAR) method is applied to solve the integer ambiguities. Then, the accuracy of the fixed ambiguity is verified by the ambiguity success rate. Taking the ambiguity success rate as a dynamic adjustment factor, the measurement noise matrix and variance–covariance matrix of the state estimation is adaptively adjusted at each time interval in the Kalman filter to provide a smoothing effect for filtering. The optimal Kalman filter gain matrix is obtained to improve positioning accuracy and reliability. As a result, the static and dynamic vehicle experiments show that the positioning accuracy of the proposed IAVAKF is improved by 26% compared with the KF. Through the IAVAKF, a more realistic PL can be obtained and applied to evaluate the integrity of the navigation system in the position domain. It can reduce the false alarm rate by 2.45% and 1.85% in the horizontal and vertical directions, respectively.

A Polar Robust Kalman Filter Algorithm for DVL-Aided SINSs Based on the Ellipsoidal Earth Model.

Autonomous underwater vehicles (AUVs) play an increasingly essential role in the field of polar ocean exploration, and the Doppler velocity log (DVL)-aided strapdown inertial navigation system (SINS) is widely used for it. Due to the rapid convergence of the meridians, traditional inertial navigation mechanisms fail in the polar region. To tackle this problem, a transverse inertial navigation mechanism based on the earth ellipsoidal model is designed in this paper. Influenced by the harsh environment of the polar regions, unknown and time-varying outlier noise appears in the output of DVL, which makes the performance of the standard Kalman filter degrade. To address this issue, a robust Kalman filter algorithm based on Mahalanobis distance is used to adaptively estimate measurement noise covariance; thus, the Kalman filter gain can be modified to weight the measurement. A trial ship experiment and semi-physical simulation experiment were carried out to verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed algorithm can effectively resist the influence of DVL outliers and improve positioning accuracy.

A Blow-Up Function Approach to Global Event-Triggered Prescribed Tracking Output Feedback Control of Nonlinear Systems

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme.

Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.

Design of the high-dimensional SPKF algorithm and application

In the framework of Kalman filtering, the key points is the estimation of the covariance of prediction error which is used to calculate the Kalman filter gain. For the traditional algorithm, e.g. extended Kalman filter, the priori information is obtained on the basis of the Taylor expansion approximation of the nonlinear system. Because the linear propagation approximation of prior information cannot truly reflect the evolution of the probability distribution of the prediction errors in nonlinear systems, however, the traditional method affects the estimation accuracy of the extended Kalman filter. To solve these problems and be easy to apply to high-dimensional nonlinear systems, this paper improves the SPKF algorithm. Firstly, the prediction error propagation model is re-established to eliminate the approximation error of Taylor expansion in the derivation of the probability density function of the prediction error. Then, a Fisher matrix calculation method that is easier for high-dimensional system is obtained by defining the calculation method of Hilbert inner product of vector and matrix function. To illustrate the merits of the novel algorithm, this paper took the oxygen generation system by using electrolytic water in space station as a case study and conducted the state estimation by respectively using the extended Kalman filter, unscented Kalman filter and high-dimensional stochastic projection Kalman filter. The simulation results shown that the new algorithm can obtain higher estimation precision than the traditional algorithm.

Image reconstruction algorithm of electromagnetic tomography based on fractional Kalman filter

Aiming at the problem of low quality of image reconstruction of electromagnetic tomography (EMT), in this paper, an image reconstruction algorithm of EMT based on fractional Kalman filter (FKF) is proposed. Firstly, the principle of EMT and the principle of state equation of FKF are expound respectively. FKF is often used in the state estimation of nonlinear systems. There is a nonlinear relationship between the object field distribution and the sensor signal in the EMT. Therefore, according to this feature, FKF is applied to the image reconstruction algorithm of EMT. The image reconstruction process of EMT is regarded as the state estimation process of FKF, the normalized measurement voltage is taken as the observation value, and the sensitivity matrix is taken as the measurement matrix. To establish the nonlinear state estimation equation of the FKF and a priori estimation error covariance equation in the EMT, the gray value of image obtained by LBP is used as the initial value of the state estimation, a prior estimation state vector and a priori estimation error covariance matrix are obtained by prediction update, the Kalman filter gain and the posterior estimation error covariance matrix are obtained by the correction feedback process. After repeated iterations, the final state vector, i.e. reconstructed image of EMT is obtained. Finally, simulation experiments are carried out for seven different flow patterns. The results show that the image error and correlation coefficients of the reconstructed image of this algorithm are better than traditional algorithms such as LBP, Landweber, Kalman filter, and have better anti-noise effect than Kalman filter. Therefore, the image reconstruction algorithm of FKF is a new method and means to study the image reconstruction of EMT.

Distributed Kalman Filters With Random Sensor Activation and Noisy Channels

This paper studies distributed Kalman filtering problems for sensor networks with random sensor activation and noisy channels. Each sensor measures the target state with a random activation and receives state estimates of its neighbor nodes. Communication noises are considered in communication links between sensors and their neighbor nodes. Considering cross-covariance matrices between sensors, an optimal distributed Kalman filter (ODKF) with a given recursive structure is proposed for each sensor, which depends on the knowledge whether a sensor itself is activated to measure the target state or not and whose filter gains and covariance matrices depend on random activation rate of the sensor. In the ODKF algorithm, optimal Kalman filter gain for each sensor and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. To reduce computational cost, a suboptimal distributed Kalman filter (SDKF) is also presented by considering a locally minimum upper bound of the filtering error covariance matrix, where the calculation of cross-covariance matrices among sensor nodes is avoided. The stability and steady-state property of the proposed ODKF and SDKF algorithms are explored. Finally, the proposed methods are also extended to the nonlinear scenarios. Simulation examples show the effectiveness of the proposed algorithms.

Robustness and sensitivity metrics-based tuning of the augmented Kalman filter for single-channel speech enhancement

The inaccurate estimates of the speech and noise linear prediction coefficients (LPCs) introduce bias in augmented Kalman filter (AKF) gain, which impacts the quality and intelligibility of enhanced speech. Although current tuning methods offset the bias in AKF gain, particularly in colored noise conditions, they do not adequately address nonstationary noise conditions. This paper introduces a new tuning algorithm of the AKF gain for speech enhancement in real-life noise conditions. Due to this purpose, a speech presence probability (SPP) method first estimates the noise power spectral density (PSD) from each noisy speech frame to compute the noise LPC parameters. A whitening filter is constructed with the noise LPCs to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. The AKF is then constructed with the estimated speech and noise LPC parameters. To achieve better noise reduction, the robustness metric is employed to dynamically offset the bias in AKF gain during speech absence of the noisy speech to that of the sensitivity metric during speech presence. The speech activity is obtained through adopting the speech and noise production model parameters. It is shown that the reduced-biased AKF gain achieved by the proposed tuning algorithm addresses speech enhancement in real-life noise conditions. Objective and subjective scores on the NOIZEUS corpus demonstrate that the proposed method produces enhanced speech with higher quality and intelligibility than the competing methods in real-life noise conditions for a wide range of signal-to-noise ratio (SNR) levels.

Distributed Filtering for Sensor Networks with Fading Measurements and Compensations for Transmission Delays and Losses

This paper studies a distributed filtering problem for sensor networks, where sensor nodes may suffer from their own fading measurements and random delayed and lost state estimates of their neighbor nodes. A distributed filter is presented based on statistical characteristics of fading measurements of sensors, where an optimal Kalman filter gain for each sensor node and different optimal consensus filter gains for state estimates of neighbor nodes are solved to minimize locally an upper bound of filtering error covariance matrix under given parameters. The proposed filter has reduced computational cost since calculation of cross-covariance matrices between sensors is avoided. Predictors of delayed and lost estimates of neighbor nodes are used for compensations to improve estimation accuracy. To further minimize the upper bound of covariance matrix, optimal parameters are solved, which are nonlinearly coupled with optimal gains. Their approximate numerical solutions can be obtained by nonlinear optimization methods. The boundedness of covariance matrix of the proposed filter is analyzed. As a special case, a distributed filter with constant delays can be obtained, which has the steady-state property. To further reduce online computational cost, two conservative distributed filters are also presented under the steady-state parameters obtained by using the upper bound of delays.

Kalman filtering under unknown inputs and norm constraints

Due to its potential applications in robotics and navigation, recent years have witnessed some progress in Kalman filter (KF) with norm constraints on the state. A noticeable discovery of the existing literature is that the KF gain has an analytical expression, and the brute-force normalization (i.e., estimation without considering the norm constraints, followed by a normalization operation) is optimal in the mean-square sense. Although there are some extensions of the former works to situations with uncertainties, existing results are only limited to cases where models/bounds or statistical properties of the disturbances are known. The paper considers the design of KF for systems subject to norm constraints on the state and unknown inputs, whose models or statistical properties are not assumed to be available. Both cases with and without direct feedthrough will be discussed. For systems without direct feedthrough, we show that the KF gain can be derived explicitly and the brute-force normalization is optimal in the mean-square sense, thereby generalizing the above-mentioned works on norm-constrained KF. However, for the case with direct feedthrough, the KF gain does not seem to admit an analytical solution, as to be shown via a counterexample.

Distributed Kalman filtering for sensor networks with random sensor activation, delays, and packet dropouts

ABSTRACT This paper studies a distributed Kalman filtering problem for sensor networks, where sensor nodes may suffer from measuring the target state with a random activation nature and random delayed and lost state estimates of neighbour nodes due to unreliability of communication links. A distributed Kalman filter (DKF) is proposed, where predictor compensations for delayed and lost estimates of neighbour nodes and different consensus filter gains for state estimates of different neighbour nodes are used to improve estimation accuracy. Optimal filter gains with optimal parameters are designed to obtain a local minimum upper bound of filtering error covariance matrix, where optimal filter gains include an optimal Kalman filter gain for each sensor node and optimal multi-consensus filter gains for state estimates of its neighbour nodes. Our proposed DKF has a low computational cost because the calculation of cross-covariance matrices between estimates of sensor nodes is avoided. Besides, the boundedness of the proposed DKF is analysed. Finally, an example of a target tracking system in sensor networks demonstrates effectiveness of the proposed DKF.

Robustness and Sensitivity Tuning of the Kalman Filter for Speech Enhancement

Inaccurate estimates of the linear prediction coefficient (LPC) and noise variance introduce bias in Kalman filter (KF) gain and degrade speech enhancement performance. The existing methods propose a tuning of the biased Kalman gain, particularly in stationary noise conditions. This paper introduces a tuning of the KF gain for speech enhancement in real-life noise conditions. First, we estimate noise from each noisy speech frame using a speech presence probability (SPP) method to compute the noise variance. Then, we construct a whitening filter (with its coefficients computed from the estimated noise) to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. We then construct the KF with the estimated parameters, where the robustness metric offsets the bias in KF gain during speech absence of noisy speech to that of the sensitivity metric during speech presence to achieve better noise reduction. The noise variance and the speech model parameters are adopted as a speech activity detector. The reduced-biased Kalman gain enables the KF to minimize the noise effect significantly, yielding the enhanced speech. Objective and subjective scores on the NOIZEUS corpus demonstrate that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than some benchmark methods.