Covariance profiling for an adaptive Kalman filter to suppress sensor quantization effects (original) (raw)

Abstract

This paper presents a generic approach to model the noise covariance associated with discrete sensors such as incremental encoders and low resolution analog to digital converters. The covariance is then used in an adaptive Kalman Filter that selectively and appropriately carries out measurement updates. The temporal as well as system state measurements are used to predict the quantization error of the measurement signal. The effectiveness of the method is demonstrated by applying the technique to incremental encoders of varying resolutions. Simulation of an example system with varying encoder resolutions is presented to show the performance of the new filter. Results show that the new adaptive filter produces more accurate results while requiring a lower resolution encoder than a similarly designed conventional Kalman filter, especially at low velocities.

Key takeaways

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  1. The new adaptive Kalman filter reduces quantization noise effectively, enabling lower resolution encoder use.
  2. Covariance profiling adapts to system state and quantization levels, enhancing measurement updates' accuracy.
  3. Simulation results show 4 times less encoder resolution achieves comparable performance to traditional filters.
  4. The filter distinguishes between trusted and untrusted measurements based on edge detection of quantized signals.
  5. At low velocities, the adaptive filter significantly outperforms the traditional Kalman filter in state estimation.

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References (10)

  1. Kavanagh, R.C. and Murphy, J.M.D., "The Effects of Quantization Noise and Sensor Nonideality on Digital Differentiator-based Rate Measurement", IEEE Transactions on Instrumentation and Measure- ment, vol. 47, no. 6, 1998, pp 1497-1463.
  2. S. Venema and B. Hannaford, "Kalman Filter Based Calibration of Precision Motion Control", Proceedings of the IEEE International Conference on Intelligent Robots and Systems, vol. 2, no. 5-9, 1995, pp 224-229.
  3. Efe, M., Bather, J.A. and Atherton, D.P., "An Adaptive Kalman Filter With Sequential Rescaling of Process Noise", Proceedings of the American Control Conference, 1999, pp 3913-3917.
  4. Gene F. Franklin, G. F., Michael L. Workman and Dave Powell, Digital Control of Dynamic Systems, Addison-Wesley Longman Publishing Co., 1997, pp 434.
  5. Rull, J., Sudria, A., Bergas, J. and Galceran, S., "Programmable logic design for an encoder-based velocity sensor in a DSP-controlled motion system", Proceedings of the IEEE International Conference on Emerging Technologies and Factory Automation, vol. 2, 1999, pp 1243-1247.
  6. Briz, F., Cancelas, J.A. and Diez, A., "Speed measurement using rotary encoders for high performance AC drives", Proceedings of the IEEE International Conference on Industrial Electronics, Control and Instrumentation, vol. 1, no. 5-9, 1994, pp 538-542.
  7. Belanger, P.R., "Estimation of angular velocity and acceleration from shaft encoder measurements", Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, 1992, pp 585-592.
  8. Jeffrey B. Burl, Linear Optimal Control, Addison Wesley Longman, Inc., 1998, pp 56-57.
  9. Mohinder S. Grewal and Angus P. Andrews, Kalman Filtering: Theory and Practice, John Wiley & Sons, Inc., 2001, pp 121.
  10. Luong-Van D. and Katupitiya J., "An Adaptive Kalman Filter With Quadrature Encoder Quantisation Compensation", Proceedings of the IFAC 3rd IFAC Symposium on Mechatronic Systems, vol. 1, 2004, pp 110-114.

FAQs

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What advancements does the new adaptive Kalman filter offer over traditional methods?add

The paper demonstrates that the new adaptive Kalman filter requires four times less resolution to achieve comparable results to standard filtering techniques with enhanced accuracy in state estimation.

How does the proposed method handle quantization effects in sensor measurements?add

It profiles measurement covariance based on current estimated states and quantization edge detection, allowing for effective noise reduction and improved trustworthiness in measurements.

What methodology is used to distinguish between trusted and untrusted measurements?add

The algorithm identifies trusted measurements based on detected changes in quantized signals, which minimizes the influence of measurement noise during the estimation process.

What findings were observed in the comparison between adaptive and standard filters?add

Simulations showed the adaptive filter significantly reduces estimation error, particularly at low to medium velocities, compared to the standard Kalman filter.

How does sampling frequency influence quantization error in the proposed method?add

The maximum quantization error is bounded as a function of the encoder velocity and sampling rate, optimizing error correction in the adaptive filtering process.