Joint Channel and Carrier Estimation Using Extended Kalman Filter

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

Given the relevance of sensorless control of surface-mounted permanent magnet synchronous machines (SPMSM) and the challenges of estimating their position and speed with non- sinusoidal back-electromotive force (back-EMF), this work aims to study sensorless methods for medium and high speeds and suggests alternatives to the existing techniques in the literature for this type of machine. Two new approaches are proposed: the first is based on the classic Kalman filter and infers the machines rotor position from the back-EMF estimation in the αβ reference frame; and the second, for rotor speed estimation, consists of a new adaptation law, calculated in the dqx reference frame, for reference model adaptive system (MRAS) estimation. Both proposed methods consider the non-sinusoidal characteristic of the back-EMF and are suitable for any SPMSM. The MRAS-based solution is also appropriate for interior permanent magnet synchronous machines. The vector control of the SPMSM is implemented in the dqx reference frame. The experimental results compared the proposed methods, briefly called KF (proposed) and MRAS dqx, with three others already presented in the literature: extended Kalman filter (called EKF) for direct position and speed estimation; classical Kalman filter for back-EMF estimation ignoring back-EMF dynamics (KF (e = 0)); and classical Kalman filter for back-EMF estimation ignoring back-EMF harmonic components other than the fundamental (KF (sinusoidal)). KF (e = 0), KF (sinusoidal), and KF (proposed) concurrently use the proposed MRAS-based method for speed estimation. The five approaches are compared considering transient (step commands for speed variation and reversal) and steady-state responses (speeds from 20 rad/s to 140 rad/s in steps of 20 rad/s, with and without load torque). The minimum operating speed at no load and the execution time for each method are also checked. All the techniques show similar performance about measured and estimated speed dynamics in transient tests, as well as similar minimum operating speeds. However, only EKF and MRAS dqx execute the reversal command and successfully keep the system stable below the minimum operating speed. As for the steady-state tests, KF (proposed) shows excellent position estimation in the speed range between 20 rad/s and 80 rad/s, which results in low torque ripples. MRAS dqx shows excellent results above 100 rad/s, with the lowest position estimation errors and torque ripple. In terms of computational burden, MRAS dqx has the lowest execution time, and KF (proposed) comes in third, with a time just longer than KF (e = 0). Therefore, the experimental results demonstrate the effectiveness and usefulness of the proposed methods in the sensorless control of SPMSM with non-sinusoidal back-EMF, as well as advantages over other existing and consolidated techniques in the literature.

This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 s. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

Object-Oriented Environment for Assessing Tracking Algorithms

In this paper, a joint channel estimation and turbo equalization scheme is proposed with low complexity and high accuracy for doubly selective fading channels. Based on the traditional data frame, by adding several pre-training sequences, the spectral efficiency is improved in the proposed two stage scheme. In the first stage, with the adaptive subblock-wise inverse QR recursive least square (IQR-RLS) filter, more trustworthy estimated values of the channel coefficients are generated with a non-priori model compared with the first order autoregressive (AR) modeling extended Kalman filter (EKF), based on complex exponential basis expansion models (CE-BEMs). Particularly, the calculation of operations is significantly reduced. In the second stage, a turbo equalizer is provided by utilizing a non-linear Kalman filter, which has a remarkable improvement in BER performance over EKF. Furthermore, complexity analysis is presented and illustrates the advantage of the proposed scheme. Finally, simulation results demonstrate the validity of the proposed scheme.

The development of a Kalman filter for state and parameter estimation of a biotechnical process is discussed. Because of the large complexity of biotechnical processes, mathematical models for online estimation are based on extensive simplifications. Therefore model errors in the structure and parameters cannot be avoided. In such situations, simulations of the process in combination with the estimator are very helpful during the design phase: these permit fast examinations of the different behaviour of linear filters compared to nonlinear algorithms and also investigations of the influence of sampling interval and initial values of state and filter variables on the estimation. By the use of such simulations, the suitability of process models with various degrees of simplifications can also be easily tested. Based on the simulations, an extended Kalman filter with iteration of the output equations was chosen. Besides the states, two parameters of a third order process model are estimated online. The filter algorithm was tested during batch processes and worked well after a slight modification. The filter behaviour observed in the experiments was very similar to the simulations.

In this study, an extended Kalman filter (EKF) for estimation of spacecraft's position and velocity by single station antenna tracking data in the presence of singularities is proposed. The designed EKF estimates the position and velocity of the spacecraft on direct nonlinear range-azimuth-elevation measurements. The proposed EKF is examined through the geostationary satellite orbital motion simulations. The corruption in the results by EKF emerges from singularities caused by the highly complex elements of the Jacobian measurement matrix. The recommendations to prevent the mentioned problem are given.

Joint data and channel estimation for mobile communication receivers can be realized by employing a Viterbi detector along with channel estimators which estimate the channel impulse response. The behavior of the channel estimator has a strong impact on the overall error rate performance of the receiver. Kalman filtering is an optimum channel estimation technique which can lead to significant improvement in the receiver bit error rate (BER) performance. However, a Kalman filter is a complex algorithm and is sensitive to roundoff errors. Square-root implementation methods are required for robustness against numerical errors. Real-time computation of the Kalman estimator in a mobile communication receiver calls for parallel and pipelined structures to take advantage of the inherent parallelism in the algorithm. In this paper different implementation methods are considered for measurement update and time update equations of the Kalman filter. The unit-lower-triangular-diagonal (LD) correction algorithm is used for the time update equations, and systolic array structures are proposed for its implementation. For the overall implementation of joint data and channel estimation, parallel structures are proposed to perform both the Viterbi algorithm and channel estimation. Simulation results show the numerical stability of different implementation techniques and the number of bits required in the digital computations with different estimators.

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

This paper presents a novel approach for an adaptive Extended Kalman Filter (EKF), which is able to handle bad signal quality caused by shading or loss of Doppler Effect for low cost Global Navigation Satellite System (GNSS) receiver and Inertial Measurement Unit (IMU) sensors fused in a loosely coupled way. It uses the estimated position error as well as the speed to calculate the standard deviation for the measurement uncertainty matrix of the Kalman Filter. The filter is very easy to implement, because some conversions of the measurement, as well as the state variables, are made to reduce the complexity of the Jacobians, which are used in the EKF filter algorithm. The filter implementation is tested within a simulation and with real data and shows significantly better performance, compared to a standard EKF. The developed filter is running in realtime on an embedded device and is able to perform position and attitude estimation of a vehicle with low cost sensors.

Firstly, the problems and common methods of power system dynamic state estimation are briefly introduced, and then the basic principles of Kalman filtering are introduced. Based on this principle, the common methods of power system dynamic state estimation problems are derived: extended Kalman filter, unscented Kalman filter and cubature Kalman filter, which are introduced respectively. The advantages and disadvantages of these methods and their applications in power system dynamic state estimation are compared and analyzed. Finally, the development trend of Kalman filter in dynamic state estimation is prospected.

The application of maximum a posteriori (MAP) detection to DS-CDMA systems in time-selective fading channels is investigated. By sampling the outputs of a matched filter and combining antenna array elements, strong multiple-access interference (MAI) is estimated and suppressed. By incorporating channel approximations, Kalman filtering, and the probability density of the prediction error, a joint channel estimation and MAP detection algorithm is developed. Unknown channel parameters are identified by using an algorithm similar to the extended Kalman filter (EKF). Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, a near-optimum bit-error-rate (BER) performance is found.

The paper presents a method for joint channel and data estimation for transmission over frequency-selective and time-variant channels. Hereby, fast time-variant channels can be tracked, which is important for mobile communications at very high velocities. We approach the problem by estimating the scattering function, which is assumed to be limited in delay and Doppler frequency. At the transmitter, a short training sequence is inserted at the beginning of the data block. This sequence is used for initializing a Kalman filter, which carries out the joint channel and data estimation adaptively. After the training sequence, hypothetical data symbols are considered to extend the persecuted paths in the data tree.

A code-tracking algorithm based on the extended Kalman filter (EKF), that provides both code synchronization and joint estimates of interferer and channel parameters is described. It is assumed that the interference in direct sequence spread spectrum communications can be modeled by an N-th order autoregressive (AR) process and the channel by a finite impulse response (FIR) filter. A composite channel, equivalent to the convolution of the AR coefficients alpha /sub n/ and channel coefficients f/sub n/ is constructed, yielding a set of parameters beta /sub m/. The received waveform is shown to be a linear function of the alpha and beta coefficients, which can be directly estimated by a Kalman filter. The code delay tau is viewed as a nonlinear parameter, which can likewise be estimated after an appropriate linearization, using the EKF. The performance of the algorithm is evaluated by computing the average bit-error rate (BER) of a digital RAKE receiver that uses the joint delay, channel, and interferer estimates derived from the EKF. >

This work presents a comparative study between a new approach for robust speed estimation in induction motor sensorless control, using a reduced order extended Kalman filter (EKF), and the one performed by the full order EKF. The new EKF algorithm uses a reduced order state-space model that is discretized in a particular and innovative way. In this case only the rotor flux components are estimated, besides the rotor speed, while the full order EKF also estimates stator current components. This new approach strongly reduces the execution time and simplifies the tuning of covariance matrices. The performance of speed estimation using both EKF techniques is compared with respect to computation effort, tuning of the algorithms, speed range including low speeds, load torque conditions and robustness relatively to motor parameter sensitivity.