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# Kalman Filtering - Science topic

Explore the latest questions and answers in Kalman Filtering, and find Kalman Filtering experts.

Questions related to Kalman Filtering

What is meant by the convergence of the Kalman Filter and to what does it converge? What is the mathematical formulation for convergence in terms of solving a Riccati equation?

Hello, has anyone worked with the CKF filter? How does it perform compared to other non-linear Kalman filters?

Hello who interested with my question,

Firstly, I want to thanks you for spending your time to read this topic!

So I have 3 questions that need some advice in

**Unscented Kalman Filter**about the**3 DoFs Mass-Damping-Stiffness System**. Right now, i'm modifying my UKF code in MATLAB for a new project but some problems seem to occur again. Below there are 2 Code files - one was the UKF test and one was an UKF function that I've writen in my graduated thesis and here are the problems I incurred:1/

**The Cholesky Decomposition**: I used the chol() function from library of MATLAB. However in my test, from the loop k=3, the covariance matrix was starting to fail in excuting chol() because it was not completely positive definited!**My solution**: First, I used a function name "nearestSPD" of Mr. John D'Errico and this function have helped my covariance matrix pass the chol() but the output (state vector) I received was full of 0 from the loop k=3. Second approach was plusing (1e-6)*eye() into the covariance matrix but MATLAB code stopped from the loop 3 and said that matrix wasn't positive definited!

2/

**Kalman Gain**: since the equation of Kalman Gain has the inverse matrix, some value of Kalman Gain of my code in some loop can't be calculate because the covariance matrix is singularity and it doesn't have the inverse version!**My solution**: in MATLAB, I've used pinv() (Moore-Penrose Inverse matrix) instead of the regular inverse inv()

3/

**Choosing the workable Initial Covariance Matrix (P)**: How can we choose the suitable Initial Covariance Matrix for UKF?**My solution**: Usually, I always choose the values of P corresponding to the error between the initial state vector and true parameter. For example, true k1 = 10000 N/m and in my initial state, I choose k1 = 8000 N/m -> value error of k1 in P will be chosen equal to 1e6.

If you have any suggestions, please feel free to repsonse! I would love to hear your idea!

My code is free and as long as you seem interested, you can use it freely! However, my code seems to fail due to 3 reasons above!

Thanks you!

I want to use Kalman filter to estimate battery parameter and observer for state estimation together (SOC)

I use the Kalman filter to estimate the stator and rotor currents for a 2MW doubly fed induction generator, I used the state model in the alpha beta reference, How to calculate the initial matrix P_0, Q_0, R_0 for a extended Kalman filter?

Hello researchers,

Could you give your recommendation for a good book that explains the Kalman filter in a practical way?

Thanks in advance

MAnsour

We combine data from different sensors like the Inertial Measurement Unit (IMU) and Global Positioning System (GPS) to estimate the state of a robot e.g. position using Kalman Filter. My question is why do we need to estimate the position if we are getting it from GPS and IMU?

In kalman filter for state variable estimation we take initial zeros but in ensemble especially for harmonic analysis, which values to take ?

How could we detrmine Fixed-Gain values of the Extended Kalman Filter gain matrix without solving Riccati equation? Is there a simple way?

Look into the book

Y. S. Shmaliy and S. Zhao, Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches, Wiley & Sons, 2022.

This is the first systematic investigation and description of convolution-based (FIR and IIR) state estimation (filtering, smoothing, and prediction) with practical algorithms. In this framework, the Bayesian Kalman filter serves as a recursive computational algorithm for batch optimal FIR and IIF filters. The unbiased FIR filter is shown to be the most robust among other linear estimators. Various robust approaches for disturbed and uncertain systems are also discussed.

I am trying to implement the sliding window Extended Kalman Filter as in the paper "Automated Controller Calibration by Kalman Filtering" ( https://doi.org/10.48550/arXiv.2111.10832 ) but there are several things that are unclear to me and thus I would like to get some clarification.

The first is that I do not understand the idea of a sliding window for a Kalman Filter. Does a Kalman Filter not operate on a sequential manner? How does one operate a KF using a sliding window?

Can someone provide a Matlab script or preferably a Simulink model of such a system?

The Unscented Kalman Filter (UKF) algorithm requires a Cholesky factorization of the prediction error covariance matrix. The problem is that during the iterations, this matrix is not always positive definite and so, the MATLAB code risks tobe stopped.

Could someone tell me how to make this covariance matrix positive definite in order to ensure the running of the code until the end of the iterations?

Thank you

Dear all,

I have been doing research on the leak detection of pipelines for some time. I did the simulations with simcenter software. But unfortunately, I tried to detect the location of the leak using Kalman filter in different ways, but it is not possible. Is it possible to guide me? Is it possible to send me the MATLAB code so that I can try on my own water pipelines and simulations?

We are trying to optimize the values of DEM of a particular catchment with a view of identifying outliers and predict future values. Thanks

Hello researchers!

I want to fit Gaussian Mixture Model to a data set where the number of mixture components is known. The weights of the mixture, the means and variances of the gaussian distributions have known priors attached to them. Can someone please enlighten me on how to use Kalman filter for this problem? Goal is to estimate the weights of the GMM and also the parameters of the gaussian distributions.

I need to estimate a set of 15 constant parameters, which are not directly measured. My state vector is therefore fixed and is made up of these constants so the Kalman filter equations rearrange to those of the Recursive Least Squares. Only 3 quantities, different from the state, can be measured and from these I have to estimate the state vector. Results indicates that the state vector is estimated well but the rank of the observation matrix used in the calculations is much less than 15 because the equations(measures) are less than the constants to be estimated. Is it normal? Must the rank be equal to the number of parameters? Thank you

I'm simulating the process of measuring the positions of the end-effector of a robotic arm but I haven't yet specifications about the measuring device that will be used in actual experiments. Let's suppose the device will be a laser tracking system whose data sheet reports a measurement uncertainty of 15 micrometers = 0.015 mm. The measurement uncertainty is defined as the deviation between a measured coordinate and the nominal coordinate of a point. Can I assume it as the accuracy of the instrument? Can I use it as the standard deviation and then square it to initialize R?

I know I should be using the concept of Dead Reckoning. But how do I use prediction algorithms to determine/estimate the 2D coordinates and yaw angle, if I can get the gyroscope data, wheel encoder data, and global system time or timestamp of each input?

I was wondering how could I implement Kalman filter in Mircoprocessors to caculate position in MPU6050 sensor. Is there anyone here that already had done this project?

My question refers to the following papers:

- S. J. Julier and J. J. LaViola, "On Kalman Filtering With Nonlinear Equality Constraints," in IEEE Transactions on Signal Processing, vol. 55, no. 6, pp. 2774-2784, June 2007, doi: 10.1109/TSP.2007.893949
- A. T. Alouani and W. D. Blair, "Use of a kinematic constraint in tracking constant speed, maneuvering targets," in IEEE Transactions on Automatic Control, vol. 38, no. 7, pp. 1107-1111, July 1993, doi: 10.1109/9.231465.

In particular, my concerns are about the Fig. 1 of [1], the statements at the end of the left column in the page 2 of [1], and the statements in the middle of the left column in the page 2 of [2]. In both papers, it is suggested to apply the constraints only after the update of the state through the measurements. Should be possible to obtain better results projecting the state on the constraining surface both after the prediction and update steps?

Hi,

I face the following problem:

I want to use a measured quaternion (from an AHRS) for the update within an UKF to update the attitude.

My state vector contains a quaternion, therefore I want to know, if I could calculate the Kalman innovation with the quaternion directly or do I need an alternative representation (Euler angles, orientation vector...)?

The problem with Euler angles is, that for the +-180° (South) direction, an UKF would spread its sigma points around a discontinuity. This does not sound harmless from my point of view.

Is there an elegant way to solve my problem?

Best regards

Maximilian

I am using a linear Kalman filter for estimating the position using multiple IMUs. My model is adding the accelerometer readings' double integration onto the previous positions. The state vector is the positions of the IMUs and the input vector is the IMU accelerometer measurements.

Also, I have some constraints in the positions and I am using those constraints in the correction step of the Kalman filter.

So in the tuning step, I set the R matrix zero so that the Kalman filter relies on the measurement only (so not use the aprior estimate at all). It works fine unless there is no input. However, if I introduce some acceleration to the system, even if I set the R=0 and Q very high, the Kalman filter still takes the contribution from the aprior estimate. The question comes at that point: what is the functionality to set R=0 if it does not disregard the model error?

Another approach to satisfy this behaviour comes from the Kalman gain calculation. As R goes to zero, the Kalman gain should approach to the inverse of the observation matrix (H or C) and so that the a posterior estimate approaches to the measurement. Since the H matrix is not a square and full rank matrix in my case, I cannot intuitively check where exactly the contribution of the aprior estimates take place even though I set the R=0. If anyone has any comments, I would really appreciate.

In a seminal paper titled "Posterior Cramer Rao bounds for discrete-time non-linear filtering" (Link: https://ieeexplore.ieee.org/abstract/document/668800/?casa_token=Ecgr8cQF6RUAAAAA:JtZ8OuUkQLyphtnQnot1ZPGlifREbS393Pg0TJ58J98IilZuIw6xSjS1Af1XDlLchlKMi8LoRfxfmAg), Tichavsky et al. have developed a recursive way to calculate the Cramer Rao bounds for non-linear filtering problems. However, in the paper, the state x

_{k}at time 'k' is a non-linear function of the previous state x_{k-1}only and not on other previous states. Are there any similar works on CR bounds for filtering problems where the current state depends on all the previous states up to the given time instants i.e. x_{k }is a function of x_{1}, x_{2}, and so on up to x_{k-1}?I have seen an example of tracking position in one dimension using an alpha beta filter, and I have a similar problem in a different field. In the example the position is first updated via dead reckoning: New position = old position+ velocity times delta t. Then the new measurement is used to update both the position estimate and the velocity estimate using the alpha and beta weights. I would like to see this problem formulated using a Kalman filter. I think I can come up with the variance estimates required and prefer this to somewhat arbitrarily selecting alpha and beta weights. The change in velocity is a drift, i.e. not driven by any known input.

I am familiar with the equations of basic kalman filter. I was reading a paper where the author's proposed a variant of kalman filter and in the prediction step they had more terms than standard kalman filter. I am referring to equation 10 of the paper "Vehicular Node Localization Using
Received-Signal-Strength Indicator" where author has added a term gamma multiplied with dt^2

https://www.comm.utoronto.ca/~valaee/Publications/07-Parker-TVT.pdf. I understand the idea behind term. I do not how to justify the factor one can add new terms affecting the uncertainty of prediction step of kalman filter.

My specific question how can I justify or prove that the new terms in error covariance equation equation 10 (inside attachment as well is correct)

I was reading a IEEE transaction paper on how to calculate Measurement and Process noise matrix of the Kalman filter when they are unknown. The title of the paper was "On the identification of variances and adaptive Kalman filtering" by Mehra.

As shown in the attached image, In equation 4 of the paper, the term M0 exist on the both sides L.H.S and R.H.S sides of the equations. I do not understand why it is written in such a manner. Do I need to simiplify it to find the value of M0 or my understanding of the equation is incorrect. phi in the equation is a non singular transition matrix,

I am researching UKF, and I would like to know where can I find performance measures of this. The system is a Chemical Process Plant.

For the discrete-time Extended Kalman filter (EKF), a stochastic stability analysis is discussed by Reif et al. in their paper "Stochastic stability of the discrete-time extended Kalman filter" (https://ieeexplore.ieee.org/abstract/document/754809). Recently, there have been works on EKF with unknown inputs, in particular, for arbitrary unknown inputs. Are there any works providing such stability analysis similar to Reif's work available for these EKF with unknown input filters?

Online model updating can improve the prediction ability of the model. Unscented Kalman filter is used to update model parameters. I know it can be used when parameters are constant. Can I also use it to solve time-varying parameters? What's the alternative and what's the difference between online recursive least squares estimation.

I want to use a EKF for parameter (p) and state (x) estimation.

I am currently not understanding the difference between (1) the formulation of the parameters as states:

x_new=[x,p] and using a normal EKF for estimating x_new

and (2) the formulation with a dual extended Kalman filter, where x and p are estimated individually.

Which of them provides more benefits?

I am very thankful for your tips.

Hi, I am currently doing a project which requires me to use Kalman filter to remove the noise in the speech. Now I am using 1D Kalman filter. Can I use Extended Kalman Filter or Unscented Kalman Filter for my application? Thanks.

I am implementing an unscented kalman filter for parameter estimation and I found its performances strongly related to the initialization of the parameter to estimate.

In particular, I don't understand why if I initialize the parameter below the reference value (the actual value to estimate) I get good performances, but if the parameter initialization is above the reference value, performances are very low and the estimation does not converge but continues increasing.

In other words, it seems that the estimation can only make the parameter increase. Is there any mathematical reason behind this?

The Nyquist-Shannon theorem provides an upper bound for the sampling period when designing a Kalman filter. Leaving apart the computational cost, are there any other reasons, e.g., noise-related issues, to set a lower bound for the sampling period? And, if so, is there an optimal value between these bounds?

I am looking for a complete solution for 10-DOF IMU Kalman Filtering (acceleration x-y-z, gyro x-y-z,magnetometer x-y-z,altitude).

I am interested in all example ,codes

Thanks for helping

Consider a digital control loop which consists of a controller C and Kalman filter K, which is used to fuse and/or filter multiple sensor inputs from the plant and feed the filtered output to the controller. The prediction (or also called time-update) step of the KF, and the analysis and tuning of the control loop utilize a discretized state-space model of the plant, defined as

x_{k+1} = F * x_k + G * u_k,

y_k = H * x_k

where F is a transition matrix, G is the input gain matrix and H the measurement output matrix. For now I will ignore the process and measurement noise variables.

According to many text books about digital control and state estimation (for example "Digital Control of Dynamic Systems" by Franklin et al.), u_k = u(t_k), x_k = x(t_k) and y_k = y(t_k) are the control input, state and measurement output of the plant, which seem to available at the same point in time, t_k. This would mean that the output from the DAC of u_k, and sampling of y_k happen at the same moment in time, t_k. However this does not seem to hold for some classical implementations. Consider a typical pseudocode of a control loop below:

for iteration k = 1:inf

sample y_k from ADC

measurement update of KF x_k

compute u_k

output u_k through DAC

time update of KF x_{k+1}

wait for next sampling moment t_{k+1}

end for

Ignoring the time durations of the DAC and ADC processes, the description above will introduce error in the prediction step of the KF, because it is assumed that the value u_k is actuated at the same moment of time that y_k is sampled - t_k. However due to the time delay introduced from computations of the update step of the KF, and the controller this is not the case. If we define s_k to be the time when the value u_k is actuated, then clearly t_{k+1} - s_k < T, where T is the sampling period. It is clear that the prediction step no longer computes the predicted state correctly because it either a) uses the old actuation value u_{k-1} or b) uses the newly actuated u_k, and in both cases the time between actuation and sampling is equal to the sampling period, assumed in the model.

This leads me to believe that the control value u_k should be actuated at time t_{k+1}, to keep consistency white the sampling period and the prediction model.

Also consider the case when the KF's prediction and update steps are executed before the controller during iteration k. Then the prediction step clearly makes use of u_{k-1} to compute a time update x_{k+1} of the state. This also seems to contradict the original definitions.

So with all these assumptions laid forward, I would like to know what are the correct sampling and actuation times, and why such ambiguity exists in modern literature about such hybrid systems.

NOTE: Some of you may say that the definition holds for small sampling periods and when the computations are fast. However I consider the general case where sampling periods may be very large due to the computations involved in the control loop.

Hi,

I am doing a project related to estimate a state variable from different sensing channels, and these two channels contain different measurement sampling rates and delays. I would like to use a modified Kalman filter like sequential processing first proposed by Alexander, but I did not how to do the Lyapunov-method-based convergence analysis. Could anyone give me some suggestions for this proof?

Also, I try to combine this observer with an adaptive impedance controller and analyze the hybrid stability, but I am not sure how to do the proof.

Thanks a lot for any suggestions.

Best regards,

Qiang

Hello,

using Cholesky decomposition in the UKF induces the possibility, that the UKF fails, if the covariance matrix P is not positiv definite.

Is this a irrevocable fact? Or is there any method to

**completely**bypass that problem?I know there are some computationally more stable algorithms, like the Square Root UKF, but they can even fail.

Can I say, that problem of failing the Cholesky decomposition occurs only for bad estimates during my filtering, when even an EKF would fail/diverge?

I want to understand if the UKF is not only advantagous to the EKF in terms of accuarcy, but also in terms of stability/robustness.

Best regards,

Max

Hello,

I'm currently working with a system consisting of an accelerometer, that samples in bursts of 10 seconds with a sample frequency of 3.9 Hz, before going into deep sleep for an extended (and yet undetermined) time period, then waking up again and sampling for 10 seconds and so on.

I've recently taken over this project from someone else and I can see that this person has implemented a Kalman filter to smooth the noise from the accelerometer. I don't know much about Kalman filters, but to me it seems that the long deep sleep period would make the previous states too outdated to be useful in predicting the new ones.

So my question is: can the previous states become outdated?

Hello everybody , I'm looking for a method able to create a transition matrix for my linear kalman filter. I need to work on the heading of a Pedestrian Dead Reckoning experiment. in my state vector I thought to insert the angular displacement referred only to the last sample . In my mesurement vector instead I thought to insert the gyro data. Somone can help me?

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But no body in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of Linear Time Variant (LTV) systems, So my question is why don't people use Kalman Filter for Hybrid systems with linear modes and resort to robust estimation approaches?

I would like to implement a Kalman filter for tracking applications for IoT nodes. I cannot do floating point on our nodes but only fixed point.

Could you recommend some good references?

Hi community,

I am new in the domain of Data Assimilation. I am trying to understand the process of Joint state and parameter estimation using Kalman Filtering approach; especially how the parameter(s) is estimated.

I understand that state variables are updated ta each time step using an updated Covar. matrix and Kalman Gain and then doing some matrix operation. However, what about the parameters. Is it affected by Kalman gain and/or Covar. matrix? I know that parameter at a new time step is calculated = previous time step parameter+ some noise. So, how does this noise evolves/changes/affacted by Kalman gain as scuh. I have tried to read different other papers, but couldn't find a definite answer.

To summarize my question, I guess I am looking for the detailed steps to estimate parameter.

Thanks in advance for your cooperation.

I currently have the assignment to make a small demo for a specific algorithm, here we want to explain the Kalman Filter in its basic form. Sadly we havent really found any " noob friendly " examples and are trying to just jump ahead in other peoples code and trying to reverse engineer it.

Here in the dlm package on R, we've found the variables GG, FF, c0, CO etc. being used in the dlm function. Altought reading page 7 ( https://cran.r-project.org/web/packages/dlm/dlm.pdf ) these variables arent really explained and i would like to know what these mean. Or are these random variable names to use the algoritm with. This is the first day of the assignment, if anyone has any tips how to approach this or a easy "noob " friendly R language based example please do reffer this to me.

Many thanks!

Or can the Kalman filter be used for medical image processing ?

I am trying to implement Kalman filter to get rid of multipath error points on GPS data while my data contains Latitude, Longitude, accuracy, altitude, speed and time. I am using python but unable to figure out how can I choose parameters for solving this issue.

Guidence will be very much apreciated.

Thanks in advance

Is it theoretically possible, that after discretization by using Talyor Series Expansion, a non-observable nonlinear system will became an observable?

It was proved, that used continuous model of PMSM is non-observable (see attached). I want to know, if resulting discrete system is observable or not. Any comment appreciated. Thanks.

LMMSE estimator and kalman filter

which of this estimator achieve more performance in FBMC?

I want to understand the overview of Kalman filters and what purpose do they serve. I am trying to leverage this platform as I am not sure about other authentic sources on the internet to get this information. Please suggest one if you know. On another note, if I have a signal that is a mixture of various frequencies; can Kalman filter be used to extract the DC or average value of this signal? Please let me know how does it work. Thanks in advance.

In case of blind equalization, information about reference input is not available. Thus channel modeling using NLMS, RLS or even Kalman filter is really difficult. Because weight update needs the information about desired or reference input.

the error convergence matrix in Kalman Filter provides the convergence of the filter. In similar war, how the convergence of the Complementary Filter can be obtained?

Thanks in advance.

Dual control in Stochastic optimal control suggests that control input has probing action that would generate with non zero probability the uncertainty in measurement of state.

It means we have a Covariance error matrix at each state.

The same matrix is also deployed by Kalman filter so how it is different from Dual Control

In the paper "Magnetometer-Only Attitude Determination Using

Novel Two-Step Kalman Filter Approach" in equation 19 do I need to complete quaternion multiplication first and then do simple mathematical finite differencing or it is in other way?

Hi.

I'm modelling OFDM rayleigh fading channel, and I want to trace channel state information with Unscented Kalman Filter through MATLAB. I'm using autoregressive model to construct the filter.

I have no problem with creating state transition function for first order autoregressive model (AR(1)). But when it comes to second order AR(2) , I don't know how the create state transition function.

I can create state transition matrix A as shown in the picture. Kalman filter needs to reach 2 previous state at once. So how do I construct the filter?

By the way, I edited the example in the link below:

I am looking for a MATLAB code to implement channel prediction or channel state information (CSI) using a Kalman filter-based approach. Specifically, for a MIMO environment.

suggest me literature regarding this topic and the gaudiness to start my thesis

please.....!

hope for good response...

Hi everyone,

I have implemented an EKF in a power systems application. When I run a simulation in Matlab, in some iterations of the filter I get a Kalman gain matrix (

**K**) with negative values and/or absolute values greater than 1. In some books I have read that the Kalman gain is a real value between 0 an1.Is this correct ? Or is it an indication that something wrong with the Kalman filter?

I started to learn the Kalman filter. However, I couldn't understand its' difference with the feedback/feedforward control system. Ultimately both systems are used to minimize the errors between the measurement and estimated state.

Hi,

I have an implementation of Kalman filter for a tracking problem, with constant acceleration model. In this model:

My State Matrix is:

x = [x, y , Vx, Vy, ax, ay] ;

My measurement Matrix is:

Y = [x' , y', Vx', Vy'];

I am putting the following as my Measurement Covariance matrix:

R = [r11, r12, 0, 0

r21, r22, 0, 0

0, 0 , r33, r34

0, 0, r43, r44];

Sometimes I have my measurement Position (x',y') that is not sometimes not so perfect. One solution is that:

- if I put a high Measurement Covariance on Position [r11, r12, r21, r22] then I can avoid a big effect on my filtered output, but it will effect both Position and Velocity.

What my problem is, that: I want to separate the Position and Velocity under certain conditions, which essentially means that I want my Position measurement (x',y') to not effect my Filter velocity. The filter should be updating the Position and Velocity Separately.

Is there a good way to do that?

I am trying to put the measurement covariance matrix on "Top Right" and "Bottom Left" but that ultimately makes my filter more unstable. Any ideas here?

I am using Kalman filter to filter out noise from PMU data for load parameter estimation. I am successfully able to filter out noise by hit and trial (Tuning values of R and Q). I am interested in knowing if there is anyway I can automatically tune the parameters of Kalman filter once I get a window of PMU measurements.

Dear friend,

These days, I'm trying to finish my Ph.D. in electrical engineering (control engineering). I'm specialized in Extended-Kalman fitter application, fault detection, neural network, digital transportation, digital twins and machine learning respectively. It is necessary to say that, my thesis about

**industry 4.0 at pipeline performance management (software)**. I'm enthusiastic to join a team for my postdoc. And I struggle to study at the edge of science topics for my postdoc.Would you help me please to join in the on the team for my postdoc, study abroad or a way to join in this kind of program?

I have a human skeletal data for 25 different joints from a depth sensor camera (Kinect) while performing a lifting work. But the data has some noise and inferred data due to occlusion. I am trying to use Tobit-Kalman Filter for data processing but could not figure out how to get the co-variance of process and observation noise for my data? I read multiple papers regarding the use of Tobit-Kalman Filter for processing Kinect data but could not find an in-depth explanation of the process involved. Can anyone help me out with my problem?

Thank you.

Hi. I have read in several articles that it is possible to improve the performance of the Kalman Filter using neural networks to dynamically change the filter model, thus adapting it to the non-modeled variations of the system with greater efficiency.

I have the Kalman filter working correctly, but I don't know how to incorporate the information provided by the neural networks, nor with what parameters to train them.

I am a beginner in the subject and would appreciate some advice on how to implement this at a simulation level in matlab.

How to design the Kalman filter for closed-loop boost converter?

Dear friend,

These days, I'm trying to finish my Ph.D. in electrical engineering (control engineering). I'm specialized in Extended-Kalman fitter application, fault detection, neural network, digital transportation, digital twins and machine learning respectively. It is necessary to say that, my thesis about

**Industry 4.0 at pipeline performance management (software).**I'm enthusiastic to join a team for my postdoc. And I struggle to study at the edge of science topics for my postdoc.Would you help me please to join in the on the team for my postdoc, study abroad or a way to join in this kind of program?

Dear Community, I am wondering if there are articles/books/references proposing implementations of Kalman Filters for positioning based on a single accelerometer ? (no GPS, no camera, no gyro, no odometery...)

For example, I need to estimate the state (position, speed, acceleration) of a vehicle, but I can only observe the its position inaccurately. The problem is, without knowing the speed, I cannot update the state for the next time point. If I calculate the speed using the position difference between 2 time points i.e. v_t=(p_t-p_(t-1))/(delta t), the estimation becomes very unstable: if one estimation has a large deviation, the speed would also deviate from the real one, so the forecast of the next time point is even more inaccurate.

Does any one have any good ideas? Thanks in advance!

Hello all,

I have a question regarding the implementation presented in paper titled "Real-Time Metric State Estimation for Modular Vision-Inertial Systems" by Stephan Weiss.

at

**Epoch 1**: The monocular visual odometry starts at origin like IMU (both are aligned with world coordinate system).**Epoch 2**is shown below, where visual odometry moves along Z-axis (in world frame), IMU moves along X-axis (in world frame) and the position of Camera (in world)

The update & correction will be visual frame (which moves along Z-axis).
For fusion to be successful, If we transform the visual odometry

**to**IMU frame then they will be pointing in the same direction.Then our measurement vector Zp would also change

**or**we use the same formula as in the paper?Thank you very much for your suggestions and answers in advance.

I have a basic doubt in statistics.(I am working with kalman filter)

Lets say i get a state variable 'Xt' for each time instance t as the kalman filter output.And for each time step, i also have a ground truth 'Yt' from an expensive sensor.

So,

Yt=Xt+ Nt , where Nt is the noise with covariance P.

I have the complete csv data of Yt and Xt measured for every time stamp. How can i evaluate the covariance P from the data?

Square root cubature Kalman filter gain

**K_k**directly without the need for a matrix inversion:Efficient least-squares: The least-squares method is used to compute the Kalman filter gain. If we substitute the innovation covariance matrix by its square-root representation we get the following expression:

**K**

_{k }(

**S**

_{yy,k|k-1}

**S**

_{yy,k|k-1}

^{T}) =

**P**

_{xy,k|k-1 }

The square root cubature Kalman filter use the symbol / (as it is a common notation in Matlab), to represent the matrix right divide operator. When we perform the operation

**A/B**, it applies the back substitution algorithm for an upper triangular matrix**B**and the forward sub- stitution algorithm for a lower triangular matrix**B**:**K**

_{k}= (

**P**

_{xy,k|k-1}/

**S**

_{yy,k|k-1}

^{T})/

**S**

_{yy,k|k-1}

Now the it seems that the problem of matrix inversion is overcome, but I still get in this message in the Matlab command for some state estimation problems:

**Warning: Matrix is singular to working precision**

**Warning: Matrix is close to singular or badly scaled. Results may be inaccurate**

Is this expression of the Kalman gain can hold even when

**S**_{yy,k|k-1}or**S**_{yy,k|k-1}^{T }are singular or nearly singular?