Adaptive Stochastic Filtration Based on the Estimation of the Covariance Matrix of Measurement Noises Using Irregular Accurate Observations
Sergey Sinyutin
Vadim Pogorelov
Round 1
Reviewer 1 Report
The solution to an interesting theoretical and relevant practical perspectives to increase the accuracy of Kalman filtering due to the adaptive estimation of the covariance matrix of the noise meter status parameters of the observed system. When solving the problem, a rather original approach was used - based on accurate measurements that are not regularly received in the object measurement system. This situation is very typical for many information management systems and, in particular, for integrated inertial-satellite navigation systems, which have recently become increasingly common. The undoubted advantage of the work is the analytical solution found for the problem, both for uncorrelated and correlated measurement interferences. The numerical example given for the above-mentioned case of an inertial-satellite navigation system, which is very relevant today, convincingly illustrates the possibility of effective practical use of the proposed method. I consider it possible to publish this article in the Inventions journal.
Author Response
The authors thank the referee for reviewing the manuscript and hope that it will arouse readers' interest.
Reviewer 2 Report
Currently, one of the central problems in the practice of using the Kalman filter is to ensure the convergence and accuracy of the filtration process with inaccurately set filter parameters. In this case, one of the most critical parameters is the covariance interference matrix of the observer of the object's phase coordinates. Despite numerous attempts to identify it in the process of assessing the state of the object, an effective solution for a wide class of objects has not yet been found. In this paper, an interesting solution to this problem is proposed for the case when it is possible to use accurate measurements of the phase coordinates of an object that enter the observation system by chance. This situation is typical in practice for many technical systems, which makes the proposed approach relevant. The advantage of this approach is the analytical solution of the problem of adaptive estimation of the observer's covariance matrix for correlated and uncorrelated interference, which is a rather rare case in the theory and practice of adaptive filtration. The results of numerical modeling performed for one of the types of navigation systems that are widely used at the moment confirm the effectiveness of the proposed method. The submitted paper can be published in the Inventions journal without additional revision.
Author Response
The authors thank the referee for reviewing the manuscript and hope that it will arouse readers' interest.
Reviewer 3 Report
An interesting article that author presents a simple algorithms that is able to improve the overall estimation accuracy. In overall, author provides all necessary equations. However, the presentation still need improve to let reader easily understand the flow of the algorithm.
- For all the equations, the matrices have to be properly formatted.
- For Eq (1), since \Phi_k*X_k = X_{k+1}. And as shown in line 108 Page 3, Z_k = H_k*X_k. The term in right hand side, Z_k – H_k*\Phi_k*X_k is not correct. This also applies for Eq (5) and so on. In fact, Eq (1) should be expressed as:
X_{k+1} = \Phi_k*X_k + K_{k+1}*(Z_{k+1} - H_{k+1}*\Phi_k*X_k)
for the condition that X_k, H_k are time variant
- Please ensure that the equation labeling is consistent. For example, the equations between (10) and (11) shall be labeled too.
- For line 184 and 186, what if the matrix is not full rank and it is not invertible?
- A Rk was given in line 215, and another Rk was given in line 236, which Rk should we consider?
- For simulation, what if author consider different type of GPS receiver (or navigation system) that are commercially available, with different performance specification? Does the proposed algorithm provides a similar improvement in terms of ratio?
Author Response
An interesting article that author presents a simple algorithm that is able to improve the overall estimation accuracy. In overall, author provides all necessary equations. However, the presentation still needs improve to let reader easily understand the flow of the algorithm.
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The authors sincerely thank the reviewer for his highly professional comments, which significantly contributed to the improvement of the manuscript.
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