Estimation of Stability Bounds of the Second-Order Filter with Effective Finite Memory and Incomplete Range-Doppler Error Compensation
DOI:
https://doi.org/10.52575/2687-0932-2026-53-2-400-407Keywords:
compensation, speed error, filter with constant weight coefficients, filtering, steady stateAbstract
This paper describes a second-order filter with constant weight coefficients and incomplete range-Doppler error compensation that approximates a finite-memory filter. The method of incomplete range-Doppler error compensation consists in correcting the range measurements for the range-Doppler error. The range-Doppler error arises from the use of linear frequency-modulated signals. Using a suboptimal method of range-Doppler error compensation in the filter equations leads to a stability filter problem. The study estimates the stability bounds of the second-order filter with constant weight coefficients and incomplete range-Doppler error compensation, which approximates the finite-memory filter. We have identified the condition of divergence of the filter with incomplete compensation of the speed error and obtained expressions for determining the stability boundaries of a second-order filter with effective finite memory and incomplete compensation of the speed error, in the case of describing the motion model. An expression has been found that describes the law of change in the range of a radar object moving with constant acceleration.
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Blair W. D. 2019. NCV Filter Design for Radar Tracking of Maneuvering Targets with LFM Waveforms. 2019 IEEE Radar Conference (RadarConf): 1-5.
Blair W. D. 2020. Design of NCA Filters for Tracking Maneuvering Targets. 2020 IEEE Radar Conference (RadarConf20): 1–6.
Brookner Eli. 1998. Tracking and Kalman Filtering Made Easy. John Wiley & Sons, Inc.
Fitzgerald, R.J. 1974. Effect of Range-Doppler Coupling on Chirp Radar Tracking Accuracy. IEEE Transactions on Aerospace and Electronic Systems, V. AES-10, 4: 528−532.
Jain V., Blair W.D. 2009. Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms. IEEE Transactions on Aerospace and Electronic Systems, 45(2): 765−773.
Murzova M.A., Farber V.E. 2024. Three-State Kalman Filter for Objects Tracking with LFM Waveforms: αßϒ-Filter and Growing-Memory Filter. 2024 IEEE 9th All-Russian Microwave Conference (RMC): 71–76.
Newton, George C. et al. 1957. Analytical design of linear feedback controls.
Poularikas, A.D. 2000. The Z-Transform. The Transforms and Applications Handbook. Second Edition, Boca Raton: CRC Press LLC.
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