Least Squares and Adaptive Multirate Filtering
This thesis addresses the problem of estimating a random process from two observed signals sampled at different rates. The case where the low–rate observation has a higher signal–to– noise ratio than the high–rate observation is addressed. Both adaptive and non–adaptive filtering techniques are explored. For the non–adaptive case, a multirate version of the Wiener–Hopf optimal filter is used for estimation. Three forms of the filter are described. It is shown that using both observations with this filter achieves a lower mean–squared error than using either sequence alone. Furthermore, the amount of training data to solve for the filter weights is comparable to that needed when using either sequence alone. For the adaptive case, a multirate version of the LMS adaptive algorithm is developed. Both narrowband and broadband interference are removed using the algorithm in an adaptive noise cancellation scheme. The ability to remove interference at the high rate using observations taken at the low rate without the high–rate observations is demonstrated.
Summary
This master's thesis presents methods for estimating a random process from two observations sampled at different rates, focusing on the case where the lower-rate signal has higher SNR. It explains multirate versions of the Wiener–Hopf optimal filter and an adaptive multirate LMS, comparing mean-squared-error performance and training-data needs when combining both sequences versus using each alone.
Key Takeaways
- Apply a multirate Wiener–Hopf filter formulation to optimally combine low-rate, high-SNR and high-rate, low-SNR observations for MMSE estimation.
- Design and implement a multirate LMS adaptive filter that operates on mixed-rate input sequences for online estimation and tracking.
- Quantify MSE improvements achieved by fusing both observation streams compared with single-stream estimation.
- Estimate training-data requirements for solving multirate filter weights and compare them to equivalent single-rate solutions.
Who Should Read This
DSP engineers or researchers with an intermediate-to-advanced background working on sensor fusion, communications, radar, or audio who need practical multirate estimation and adaptive-filtering techniques.
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