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Extracting cardiorespiratory signals from non-invasive and non-contacting sensor arrangements, i.e. magnetic induction sensors, is a challenging task. The respiratory and cardiac signals are mixed on top of a large and time-varying offset and are likely to be disturbed by measurement noise. Basic filtering techniques fail to extract relevant information for monitoring purposes.
We present a real-time filtering system based on an adaptive Kalman filter approach that separates signal offsets, respiratory and heart signals from three different sensor channels. It continuously estimates respiration and heart rates, which are fed back into the system model to enhance performance. Sensor and system noise covariance matrices are automatically adapted to the aimed application, thus improving the signal separation capabilities. We apply the filtering to two different subjects with different heart rates and sensor properties and compare the results to the non-adaptive version of the same Kalman filter. Also, the performance, depending on the initialization of the filters, is analyzed using three different configurations ranging from best to worst case.
Extracted data are compared with reference heart rates derived from a standard pulse-photoplethysmographic sensor and respiration rates from a flowmeter. In the worst case for one of the subjects the adaptive filter obtains mean errors (standard deviations) of -0.2 min −1 (0.3 min −1 ) and -0.7 bpm (1.7 bpm) (compared to -0.2 min −1 (0.4 min −1 ) and 42.0 bpm (6.1 bpm) for the non-adaptive filter) for respiration and heart rate, respectively. In bad conditions the heart rate is only correctly measurable when the Kalman matrices are adapted to the target sensor signals. Also, the reduced mean error between the extracted offset and the raw sensor signal shows that adapting the Kalman filter continuously improves the ability to separate the desired signals from the raw sensor data. The average total computational time needed for the Kalman filters is under 25% of the total signal length rendering it possible to perform the filtering in real-time.
It is possible to measure in real-time heart and breathing rates using an adaptive Kalman filter approach. Adapting the Kalman filter matrices improves the estimation results and makes the filter universally deployable when measuring cardiorespiratory signals.
Keywords: Adaptive Kalman filter, Sensor fusion, Heart rate, Breathing rate, Signal processingThe increase in both life quality expectancy and quality of life, together with improvements in medical support, has led to an increase in the mean age of the population in developed lands. The American Administration on Aging (AoA) predicts that, compared with the year 2000, the absolute number of people aged >65 years will double by 2030 and represent 19% of the total U.S. population [1]. The increase in the elderly population will lead to additional strains on the health-care system. Therefore, there is an explicit need to transfer clinical measurement devices and technology to the patient’s home. The goal of personal health care is to relieve clinicians and the clinical infrastructure by means of technical improvements, but without reduction in diagnostic and rehabilitation performance, e.g. with telemonitoring at home [2]. This implies that new technology needs to be integrated into daily activity which, compared with a well-defined clinical environment, poses considerable challenges in terms of signal acquisition and processing. More complex processing algorithms are needed to overcome noise, artifacts and multi-sensor problems. One algorithmic approach is the use of the Kalman filtering technique.
Since its introduction in the 1960s, the Kalman filter has become a well accepted and state-of-the-art approach for many applications, especially in the technical domain. Initially, computational capacity was limited and costly, making it difficult to use Kalman filters in real-time applications. However, over the years computational power has increased, also outside the personal computer domain. Today, high performance devices are available, including microcontrollers, digital signal processors or specialized computational units such as Field Programmable Gate Arrays (FPGA). Therefore, it is now possible to move complex mathematical computations into such devices working in a self-sufficient way. Many examples of technical applications using Kalman filters in real-time have been described [3,4]. In bio-medical engineering, Kalman filters are often applied to smooth or extract physiological signals, such as respiration and cardiac activity [5,6]. Also in the domain of Electrical Impedance Tomography (EIT), the Kalman filter is able to track fast changes in impedance [7]. The Kalman filter is adequate for the present work, as it is possible to integrate prior knowledge (e.g. about sensor or system noise or state transitions). In addition, the Kalman filter is capable to denoise, separate signals or fuse sensor data, all in one architecture. Compared to other filtering or signal separation methods the Kalman filter is able to perform in real-time with very little systemic delays.
To record evaluation data a non-contact measurement technique, called magnetic induction monitoring, was chosen. This technique is a relevant method since it comprises a variety of problems typical for non-contact monitoring of vital signs. The complete employed measurement setup is described in Section ‘Sensors and measurement setup’. Afterwards, the detailed working principle and the implementation of the Kalman filter is explained (Section ‘Kalman filter’). Then, heart and respiration rate extraction results of two different subjects are shown and discussed in Section ‘Results and discussion’. We oppose the non-adaptive, described in earlier work, to the developed adaptive Kalman filter and show the performance increase, especially when no a priori knowledge about the sensor system is present. Finally, the conclusions summarize the results and gives an outlook to future work (see Section ‘Conclusions’).
The signal were acquired in voluntary self-experiments of the first two authors (JF and DT). Both signed an informed consent to participate in this study. The local ethics committee decided that this type of study with this device was not in the scope of their responsibility (internal reference number EK 013/14). In addition it was stated that the self-measured data can be used for publication. Both signed an informed consent to participate in this study. Consider, that this work is not conceived to be an extensive study but rather a proof of concept. Magnetic induction monitoring is a non-contact technique for recording thoracic activity. The technique is based on magnetic coupling between the thorax and a nearby sensor-coil, as developed by Teichmann et al.[8,9]. As the coil has no conductive contact with the skin it is called a non-contact technique. The sensor-coil is driven by an alternating current and sends out an alternating magnetic field. This field induces eddy currents within conductive objects in the vicinity of the coil. In turn, these eddy currents reinduce a secondary alternating magnetic field, which affects the primary one and thereby changes the reflective impedance of the coil. If the coil is placed near the thorax, cardiorespiratory activity modulates the impedance of the coil due to motions of inner organs and the thoracic wall and/or because of changes in conductivity, e.g. caused by more or less air in the lungs or blood shifts in the heart. In this way, respiration and pulse can be easily obtained by measuring the impedance changes of the sensor-coil.
In this work, processed data were collected by three magnetic induction sensors attached to the thorax, as described in [10,11]. The sensors were located on left breast, right breast and stomach level (Figure (Figure1). 1 ). With this setting it is possible to detect motion patterns. In addition to those three sensor signals, two reference channels acquire data in parallel: one for a pulse photoplethysmographic (PPG) finger clip sensor (ChipOx, Corscience GmbH & Co. KG) the other for a thermal mass flowmeter (Model 4040, TSI). ECG and respiratory induction plethysmography (RIP) as references have been discarded as they might influence the magnetic measurement system. All measurements have been performed in resting state, so that no artifacts due to running or other movements are induced since we want to show the performance of being able to extract heart and respiration rates. The task of detecting artifacts is not part of this work, since motion patterns have been analyzed in previous work [11]. Magnetic induction monitoring is completely contact free, i.e. no mechanical, conductive or optical contact is necessary. Although this offers a considerable advantage over other monitoring methods, there are problems related to this and other non-contact monitoring techniques. A major drawback of magnetic induction monitoring is its sensitivity to other thoracic motion not related to respiration or pulse; therefore, motion artifacts are a common problem. Also, the signal content related to respiration is much higher than the cardiac-related signal content, since the thoracic conductivity distribution is more strongly affected by respiratory motion. Often, the higher harmonics of the respiratory signal may overlap the much smaller cardiac signal; in this case signal separation by common frequency filtering is not possible. To overcome these issues (at least to some extent), an adaptive Kalman filter was developed, based on previous work [5,12]. The Kalman filter system consists of three individual sensor signals (S1 to S3), that are direct inputs of the Kalman filter (Figure (Figure1). 1 ). In addition to the filter system described earlier [12], the respiratory rate and heart rate are estimated continuously and fed back to the Kalman filter where internal states and matrices are updated. Also some of the state matrices containing information about the measurement system are updated recursively and thus, automatically adapting itself to any new configuration. This procedure is described in detail in the following sections.
Kalman filter sensor fusion. Kalman filter sensor fusion (sensors: S1 to S3 with flow and PPG references) and vital signs extraction with frequency adaptation.
The raw sensor data were acquired at a sampling rate of 95 Hz, which is also the processing rate of the Kalman filter. No pre-processing of the data is performed. Figure Figure2 2 presents a 30-s representative example of the employed sensor signal with the PPG and flow reference acquired in parallel.
Raw signal example with parallel Flow and PPG reference recordings. Raw signal of sensor 1-3 example (top with arbitrary units [a.u.]) with parallel flow and PPG reference recordings (bottom with arbitrary units [a.u.]) (30 s window).
In summary, the Kalman filter has to deal with the following signal properties:
● A very high offset compared to the signal amplitude
● Respiration is visible in the time domain
● Heart activity is only slightly visible in the time domain (very low ratio of heart to respiration signal level)
● Good signal-to-noise ratio (SNR) for the respiratory signal, since noise is not noticeable in the time domain for this sensor
● Higher harmonics of the respiratory signal may overlap the pulse signal in the frequency domain
In 1960, R.E. Kalman reported a new method for linear filtering and solving problems related to prediction [13]. Generally, the so-called “Kalman filter” consists of mathematical equations that represent an efficient way to predict a future and/or unknown state of a system, based only on the use of the preceding step. The calculations are very efficient so that they can be performed and implemented in today’s standard default personal computers, in digital signal processors (DSP) and in microcontrollers, to work in real-time applications. When process and sensor noise have time-dependent characteristics, the filter is also called a “time-varying Kalman filter”. The filter finds a prediction value x ^ with minimum variance for a disturbed state vector x[14]. The transitions from one state to another are represented in the state transition matrix A when no disturbance is present.
System and measurement noise, which are assumed to be white (zero mean) and statistically independent from each other, are represented by w and v, with their co-variance matrices Q and R (both hermitian symmetric and positive semidefinite), respectively. External disturbances (e.g. systematic errors) are fed into the system with the control vector u and the matrix B, that describe the dynamics of the disturbance. Finally, the measurement matrix H describes the integration of a real measurement into the filter procedure.
The matrices A, Q, R, B and H are generally time invariant, but may be adaptable over time. Especially when the acquired quality of the sensor data changes over time, the values of Q, R and H should take this into consideration. When the assumed system model is exposed to changes, A and B also need to be updated. All time variant matrices and vectors are denoted with a small index k.
