ABCD lemma is used in recursive least squares to
Reduce computations
Real time processing
Reuse past values
All of these
The ABCD lemma is actually not directly used in recursive least squares (RLS) algorithms. However, RLS algorithms can benefit from reducing computations, enabling real-time processing, and reusing past values. Let me explain how:
1. Reduce computations: RLS algorithms aim to update the estimate of a system's parameters iteratively as new measurements are received. This update process involves matrix inversions and multiplications, which can be computationally expensive for large-scale systems. To reduce computations, various optimization techniques are used in RLS, such as fast matrix factorization methods like the Cholesky decomposition or QR decomposition, or exploiting the properties of the system to simplify the calculations.
2. Real-time processing: RLS algorithms provide real-time estimates by continuously updating the parameter estimates as new data arrives. This makes them particularly useful in applications where online estimation is needed, such as adaptive filtering or control systems. By using the most recent measurements and previous estimates, RLS algorithms can provide timely and up-to-date estimates, ensuring real-time processing capabilities.
3. Reuse past values: RLS algorithms leverage the past values of measurements and estimates to update the current estimate. This reuse of past values allows the algorithm to retain information about the system's dynamics and, as a result, can provide more accurate estimates compared to using only the current measurements. By incorporating past values using suitable weightings, RLS algorithms can enhance the estimation performance and provide better long-term tracking capabilities.
So, while the ABCD lemma itself is not directly used in RLS algorithms, the benefits you mentioned (reducing computations, real-time processing, and reusing past values) play crucial roles in making RLS algorithms more efficient and effective in various applications.