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Adaptive Estimation Using State-Space Methods

Thesis Info

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Author

Salman, Muhammad

Program

PhD

Institute

National University of Sciences & Technology

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Applied Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1621

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725433967

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This thesis focuses on the development of new variants of adaptive filters. Built around state-space framework, the proposed filters are especially suitable for applications like tracking, output feedback control and recursive spectrum estimation. They operate without prior knowledge of process and observation noise statistics and exhibit good stability properties. The development in this thesis can broadly be classified into state- space least mean square (SSLMS) and finite memory least-squares filters. SSLMS is a generalization of the well-known least mean square (LMS) filter. Incorporating linear time-varying state-space model of the underlying environment, SSLMS exhibits marked improvement in its tracking performance over the standard LMS. An extension of SSLMS is SSLMS with adaptive memory (SSLMSWAM). SSLMSWAM iteratively tunes the step-size parameter by stochastic gradient method in an attempt to yield its most appropriate value. This filter is useful for situations where a suitable value of step-size parameter is difficult to obtain beforehand. Recursive nature of an adaptive filter brings with it stability issues. The concept of finite memory (or receding horizon) for an adaptive filter is appealing because it ensures stability. This motivates the development of finite memory filters, both for iiiunforced and forced systems. Finite impulse response (FIR) adaptive filter, built around structure of an unforced system, uses weighted observations on a finite interval. Uniform weighting of the observations results in rectangular RLS (RRLS). Additional flexibility is achieved by developing an adaptive memory variant of FIR adaptive filter. Similar to SSLMSWAM, the data window size is iteratively tuned so as to minimize the prediction error. For the forced system case, a useful solution in the form of receding horizon state observer is obtained. It finds utility in output feedback control of linear time-varying systems. An insight into convergence properties of finite memory based filters is provided by the convergence analyses. Spectrum update with the arrival of new data is a desirable feature in real-time spectrum estimation applications. The mathematical equivalence of RRLS resonator bank and recursive discrete Fourier transform (DFT) gives the rationale for using the newly developed filters for recursive spectrum estimation. A symmetric windowed variant of RRLS called ‘truncated exponential RLS (TERLS)’ is useful for reducing spectral leakage. Same is true for an SSLMS resonator, which has an attractive feature that spectral side levels and main lobe width may be reduced simultaneously by reducing the step-size parameter. The higher order resonator (HOR), constructed from several SSLMS resonators, exhibits close resemblance to an ideal (rectangular) frequency bin, thus minimizing spectral leakage and increasing resolution.
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سلطان جہان بیگم

والیۂ بھوپال سلطان جہاں بیگم
خادمہ ملت و مخدومہ امت کا ماتم
علیا حضرت سلطان جہان بیگم سابق فرمانرواے کشور بھوپال جن کے نامِ نامی کے ساتھ ہمیشہ قلم کو یہ لکھنے کی عادت تھی کہ خلداﷲ ملکھا، خدا ان کی حکومت ہمیشہ قائم رکھے، اب وہاں کوسدھاریں جہاں کی حکومت واقعاً ہمیشہ ہے، اﷲ تعالیٰ ان کو اپنی مغفرت کی لازوال دولت، اور اپنی رضا و خوشنودی کی غیر فانی سلطنت عطا فرمائے۔
علیا حضرت کی وفات ایک ایسا سانحہ ہے جس کا ماتم نہ صرف بھوپال، نہ صرف ہندوستان نہ صرف مسلمان بلکہ تمام دنیا کررہی ہے، اور کرے گی وہ نہ صرف اسلام کی بلکہ مشرق کی وہ آخری تاجدار خاتون تھیں جن کے کارناموں پرمرد سلاطین اور امراء بھی رشک کرسکتے ہیں، ان کا دور حکومت جو تیس ۳۰ سال سے کم نہیں رہا بھوپال کی تاریخ کا زرین عہد ہے۔
سلطانہ مرحومہ مشرقی و مغربی تعلیم و تمدن کا ایسا مجمع البحرین تھیں، جو آج مصلحین امت کا آئیڈیل ہے، اُن کی مشرقی تعلیم پوری اور مغربی واقفیت بقدر ضرورت تھی، وہ نہ صرف فرمانرواتھیں، بلکہ ہندوستانی خواتین کی رہنما مسلمانوں کی واحد یونیورسٹی کی رئیسۂ علیا، مذہبی تعلیم کی سب سے بڑی حامی، مذہبی علوم و فنون کی سب سے بڑی سرپرست ہندوستان کی معتدل نسوانی اصلاحات کی سب سے بڑی مبلغ، مسلمان عورتوں میں سب سے بڑی کثیرالتصانیف اور سب سے بہتر مقررہ، لیکن ان ہر قسم کے انتظامی، اصلاحی، ملکی، علمی اور تعلیمی کارناموں سے بڑھ کر اُن کا حقیقی شرف، اُن کی مذہبی گرویدگی، دینی عقیدت اور ایمانی جوش و ولولہ تھا۔
وہ ہر قومی و مذہبی و علمی تحریک پر سب سے پہلے لبیک کہتی تھیں، اور اُس کے لئے عملی قدم اٹھاتی تھیں، مسلم یونیورسٹی، مدرسۂ دیوبند، دارالعلوم ندوہ، اور ووکنگ مشن چھوٹے بڑے بیسیوں تعلیمی...

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