Add Mohit's introduction

journal/journal.org

@@ -96,37 +96,51 @@ Sensor fusion \sep{} Optimal filters \sep{} $\mathcal{H}_\infty$ synthesis \sep{
 ** New introduction                                                  :ignore:
 *** Introduction to Sensor Fusion                                   :ignore:
 
+# Basic explainations of sensor fusion
+
 - cite:bendat57_optim_filter_indep_measur_two roots of sensor fusion
 
 *** Advantages of Sensor Fusion                                     :ignore:
 
+# Sensor Fusion can have many advantages / can be applied for various purposes
+
 - Increase the bandwidth: cite:zimmermann92_high_bandw_orien_measur_contr
 - Increased robustness: cite:collette15_sensor_fusion_method_high_perfor
 - Decrease the noise:
 
 *** Applications                                                    :ignore:
 
+# The applications of sensor fusion are numerous
+
 - UAV: cite:pascoal99_navig_system_desig_using_time, cite:jensen13_basic_uas
 - Gravitational wave observer: cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system
 
 *** Kalman Filtering or Complementary filters                       :ignore:
 
+# There are mainly two ways to perform sensor fusion: using complementary filters or using Kalman filtering
+
 - cite:brown72_integ_navig_system_kalman_filter alternate form of complementary filters => Kalman filtering
 - cite:higgins75_compar_compl_kalman_filter Compare Kalman Filtering with sensor fusion using complementary filters
 - cite:robert12_introd_random_signal_applied_kalman advantage of complementary filters over Kalman filtering
 
 *** Design Methods of Complementary filters                         :ignore:
 
-- cite:pascoal99_navig_system_desig_using_time use LMI to generate complementary filters
+# In some cases, complementary filters are implemented in an analog way such as in [...], but most of the time it is implemented numerically which allows much more complex
-- cite:plummer06_optim_compl_filter_their_applic_motion_measur use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
+
-- cite:jensen13_basic_uas design of complementary filters with classical control theory
+- Analog complementary filters: cite:yong16_high_speed_vertic_posit_stage, cite:moore19_capac_instr_sensor_fusion_high_bandw_nanop
-- cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system: FIR + convex optimization
+
-- 3 complementary filters: cite:becker15_compl_filter_desig_three_frequen_bands
+# Multiple design methods have been used for complementary filters
+
 - Analytical methods:
   - first order: cite:corke04_inert_visual_sensin_system_small_auton_helic
   - second order: cite:baerveldt97_low_cost_low_weigh_attit, cite:stoten01_fusion_kinet_data_using_compos_filter, cite:jensen13_basic_uas
   - higher order: cite:shaw90_bandw_enhan_posit_measur_using_measur_accel, cite:zimmermann92_high_bandw_orien_measur_contr, cite:collette15_sensor_fusion_method_high_perfor, cite:matichard15_seism_isolat_advan_ligo
-- Analog complementary filters: cite:yong16_high_speed_vertic_posit_stage, cite:moore19_capac_instr_sensor_fusion_high_bandw_nanop
+- cite:pascoal99_navig_system_desig_using_time use LMI to generate complementary filters
+- cite:hua05_low_ligo,hua04_polyp_fir_compl_filter_contr_system: FIR + convex optimization
+- cite:plummer06_optim_compl_filter_their_applic_motion_measur use H-Infinity to optimize complementary filters (flatten the super sensor noise spectral density)
+- cite:jensen13_basic_uas design of complementary filters with classical control theory
+
+- 3 complementary filters: cite:becker15_compl_filter_desig_three_frequen_bands
 
 *** Problematics / gap in the research                                                 :ignore:
 
@@ -136,13 +150,17 @@ Sensor fusion \sep{} Optimal filters \sep{} $\mathcal{H}_\infty$ synthesis \sep{
 
 *** Describe the paper itself / the problem which is addressed      :ignore:
 
+Most of the requirements => shape of the complementary filters
+=> propose a way to shape complementary filters.
+
 *** Introduce Each part of the paper                                :ignore:
 
 ** Old Introduction                                         :ignore:noexport:
 *** Establish the importance of the research topic                 :ignore:
 # What are Complementary Filters
 A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
-These filters are used when two or more sensors are measuring the same physical quantity with different noise characteristics. Unreliable frequencies of each sensor are filtered out by the complementary filters and then combined to form a super sensor giving a better estimate of the physical quantity over a wider bandwidth.
+These filters are used when two or more sensors are measuring the same physical quantity with different noise characteristics.
+Unreliable frequencies of each sensor are filtered out by the complementary filters and then combined to form a super sensor giving a better estimate of the physical quantity over a wider bandwidth.
 This technique is called sensor fusion and is used in many applications.\par
 
 *** Applications of complementary filtering                        :ignore:
@@ -184,6 +202,68 @@ In section ref:sec:hinf_method, a new design method for the shaping of complemen
 In section ref:sec:application_ligo, the method is used to design complex complementary filters that are used for sensor fusion at the LIGO.
 Our conclusions are drawn in the final section.
 
+** Mohit's Introduction                                            :noexport:
+The sensors used for measuring physical quantity often works well within a limited frequency range called as the bandwidth of the sensor.
+The signals recorded by the sensor beyond its bandwidth are often corrupt with noise and are not reliable.
+Many dynamical systems require measurements over a wide frequency range.
+Very often a variety of sensors are utilized to sense the same quantity.
+These sensors have different operational bandwidth and are reliable only in a particular frequency range.
+The signals from the different sensors are fused together in order to get the reliable measurement of the physical quantity over wider frequency band.
+The combining of signals from various sensor is called sensor fusion cite:hua04_polyp_fir_compl_filter_contr_system.
+The resulting sensor is referred as "super sensor" since it can have better noise characteristics and can operate over a wider frequency band as compared to the individual sensor used for merging cite:shaw90_bandw_enhan_posit_measur_using_measur_accel.
+
+Sensor fusion is most commonly employed in the navigation systems to accurately measure the position of a vehicle.
+The GPS sensors, which are accurate in low frequency band, are merged with the high-frequency accelerometers.
+Zimmermann and Sulzer cite:zimmermann92_high_bandw_orien_measur_contr used sensor fusion to measure the orientation of a robot.
+They merged inclinometer and accelerometers for accurate angular measurements over large frequency band.
+Corke cite:corke04_inert_visual_sensin_system_small_auton_helic merged inertial measurement unit with the stereo vision system for measurement of attitude, height and velocity of an unmanned helicopter.
+Baerveldt and Klang cite:baerveldt97 used an inclinometer and a gyroscope to measure the orientation of the autonomous helicopter.
+The measurement of the 3D orientation using a gyroscope and an accelerometer was demonstrated by Roberts et al. cite:roberts03_low.
+Cao et al. cite:cao20_adapt_compl_filter_based_post used sensor fusion to obtain the lateral and longitudinal velocities of the autonomous vehicle.
+
+Sensor fusion is also used for enhancing the working range of the active isolation system.
+For example, the active vibration isolation system at the Laser Interferometer Gravitational-Wave Observatory (LIGO) cite:matichard15_seism_isolat_advan_ligo utilizes sensor fusion.
+The position sensors, seismometer and geophones are used for measuring the motion of the LIGO platform in different frequency bands cite:hua05_low_ligo.
+Tjepkema et al. cite:tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip used sensor fusion to isolate precision equipment from the ground motion.
+The feedback from the accelerometer was used for active isolation at low frequency while force sensor was used at high frequency.
+Various configurations of sensor fusion for active vibration isolation systems are discussed by Collette and Matichard cite:collette15_sensor_fusion_method_high_perfor.
+Ma and Ghasemi-Nejhad cite:ma04_frequen_weigh_adapt_contr_simul used laser sensor and piezoelectric patches for simultaneous tracking and vibration control in smart structures.
+Recently, Verma et al. cite:verma21_virtual_sensor_fusion_high_precis_contr presented virtual sensor fusion for high precision control where the signals from a physical sensor are fused with a sensor simulated virtually.
+
+Fusing signals from different sensors can typically be done using Kalman filtering cite:odry18_kalman_filter_mobil_robot_attit_estim, ren19_integ_gnss_hub_motion_estim, faria19_sensor_fusion_rotat_motion_recon, liu18_innov_infor_fusion_method_with, abdel15_const_low_cost_gps_filter, biondi17_attit_recov_from_featur_track or complementary filters cite:brown72_integ_navig_system_kalman_filter.
+A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies.
+When two filters are complementary, usually one is a low pass filter while the other is an high pass filter.
+The complementary filters are designed in such a way that their magnitude is close to one in the bandwidth of the sensor they are combined with.
+This enables to measure the physical quantity over larger bandwidth.
+There are two different categories of complementary filters --- frequency domain complementary filters and state space complementary filters.
+Earliest application of the the frequency domain complementary filters was seen in Anderson and Fritze cite:anderson53_instr_approac_system_steer_comput.
+A simple RC circuit was used to physically realize the complementary filters.
+Frequency domain complementary filters were also used in cite:shaw90_bandw_enhan_posit_measur_using_measur_accel, zimmermann92_high_bandw_orien_measur_contr, baerveldt97, roberts03_low.
+State space complementary filter finds application in tracking orientation of the flexible links in a robot cite:bachmann03_desig_marg_dof, salcudean91_global_conver_angul_veloc_obser, mahony08_nonlin_compl_filter_special_orthog_group and are particularly useful for multi-input multi-output systems.
+Pascoal et al. cite:pascoal00_navig_system_desig_using_time presented complementary filters which can adapt with time for navigation system capable of estimating position and velocity using GPS and SONAR sensors.
+
+The noise characteristics of the super sensor are governed by the norms of the complementary filters.
+Therefore, the proper design of the complementary filters for sensor fusion is of immense importance.
+The design of complementary filters is a complex task as they need to tuned as per the specification of the sensor.
+In many applications, analytical formulas of first and second order complementary filters are used cite:corke04_inert_visual_sensin_system_small_auton_helic,jensen13_basic_uas.
+However, these low order complementary filters are not optimal, and high order complementary filters can lead to better fusion cite:jensen13_basic_uas,shaw90_bandw_enhan_posit_measur_using_measur_accel.
+
+Several design techniques have been proposed to design higher order complementary filters.
+Pascoal cite:pascoal00_navig_system_desig_using_time used linear matrix inequalities (LMIs) cite:boyd94_linear for the design of time varying complementary filters.
+LMIs were also used by Hua et al. cite:hua04_polyp_fir_compl_filter_contr_system to design finite impulse response (FIR) filters for the active vibration isolation system at LIGO.
+Plummer cite:plummer06_optim_compl_filter_their_applic_motion_measur proposed an optimal design method using the $\mathcal{H}_{\infty}$ synthesis and weighting functions representing the measurement noise of the sensors.
+
+Although various methods have been presented in the literature for the design of complementary filters, there is a lack of general and simple framework that allows to shape the norm of complementary filters.
+Such a method would prove to be very useful as the noise of the "supper sensor" and its dynamical characteristics depend on the norm of the filters.
+This paper presents such a framework based on the $\mathcal{H}_\infty$ norm minimization.
+The proposed method is quite general and can be easily extended to a case where more than two complementary filters needs to be designed.
+The organization of this paper is as follows.
+Section [[*Complementary filters requirements][2]] presents the design requirements of ideal complementary filters.
+It also demonstrates how the noise and robustness characteristics of the "super sensor" can be transformed into upper bounds on the norm of the complementary filters.
+The framework for the design of complementary filters is detailed in Section [[*Design formulation using $\mathcal{H}_\infty$ synthesis][3]].
+This is followed by the application of the design method to complementary filter design for the active vibration isolation at LIGO in Section [[*Application: Complementary Filter Design for Active Vibration Isolation of LIGO][4]].
+Finally, concluding remarks are presented in Section [[*Concluding remarks][5]].
+
 * Complementary Filters Requirements
 <<sec:requirements>>
 ** Sensor Fusion Architecture